ACTAUNIVERSITATISUPSALIENSISUPPSALA2007

Digital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology 297

Soft X-ray Scattering DynamicsClose to Core IonizationThresholds in Atoms andMolecules

JOHAN SÖDERSTRÖM

ISSN 1651-6214ISBN 978-91-554-6874-3urn:nbn:se:uu:diva-7832

till min familj - tack för allt!

List of Papers

This thesis is based on the following papers, which are referred to in the textby their Roman numerals. Reprints were made with the permission from thepublishers. The original articles can be found on each publishers webpage.

I X-ray-emission-threshold-electron coincidence spectroscopyJ. Söderström, M. Alagia, R. Richter, S. Stranges, M. Agåker, M.Ström, S. Sorensen, and J.-E. RubenssonJournal of Electron Spectroscopy and Related Phenomena, 141,161-170 (2004)

II Core level ionization dynamics in small molecules studied byx-ray-emission threshold-electron coincidence spectroscopyM Alagia, R. Richter, S. Stranges, M. Agåker, M. Ström, J. Söder-ström, C. Såthe, R. Feifel, S. Sorensen, A. De Fanis, K. Ueda, R.Fink, and J.-E. RubenssonPhysical Review A, 71, 012506 (2005)

III The Oxygen K Edge X-ray-Emission-Threshold-Electron Co-incidence Spectrum of CO2

J. Söderström, M. Agåker, R. Richter, M. Alagia, S. Stranges, andJ.-E. RubenssonIn manuscript

IV Resonant Inelastic Photon Scattering in HeliumJ. Söderström, M. Agåker, A. Zimina, R. Feifel, S. Eisebitt, R.Follath, G. Reichardt, O. Schwarzkopf, J.-E. Rubensson and W.EberhardtIn manuscript

V Double Excitations of Helium in Weak Static Electric FieldsC. Såthe, M. Ström, M. Agåker, J. Söderström, J.-E. Rubensson,R. Richter, M. Alagia, S. Stranges, T. W. Gorczyca, and F. Ro-bicheauxPhysical Review Letters 96, 043002 (2006)

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VI Magnetic-Field Induced Enhancement in the FluorescenceYield Spectrum of Doubly Excited States in HeliumM. Ström, C. Såthe, M. Agåker, J. Söderström, J.-E. Rubensson,S. Stranges, R. Richter, M. Alagia, T. W. Gorczyca, and F.RobicheauxPhysical Review Letters 97, 253002 (2006)

VII Vibrationally resolved nitrogen K-shell photoelectron spectraof the dinitrogen oxide molecule: Experiment and TheoryM. Ehara, R. Tamaki, H. Nakatsuji, R. R. Lucchese, J. Söder-ström, T. Tanaka, M. Hoshino, M. Kitajima, H. Tanaka, A. DeFanis, and K. UedaChemical Physics Letters, 438, 14-19 (2007)

VIII Vibrationally resolved partial cross sections and asymmetryparameters for nitrogen K-shell photoionization of the N2OmoleculeJ. Söderström, R. R. Lucchese, T. Tanaka, M. Hoshino, M. Kita-jima, H. Tanaka, J.-E. Rubensson, and K. UedaIn manuscript

The following is a list of published papers that I have contributed to, butthat are not included in this thesis.

I High-resolution study of the doubly excited states of Helium– excitation of 1,3S metastable Helium atomsM. Alagia, M. Coreno, H. Farrokhpour, P. Franceschi, K. C.Prince, R. Richter, J. Söderström, and S. StrangesIn preparation

II Soft X-ray Induced Formation of N2 Molecules in AmmoniumCompoundsE. Aziz, J. Gråsjö, J. Forsberg, E. Andersson, J. Söderström, L.Duda, W. Zhang, J. Yang, S. Eisebitt, C. Bergström, Y. Luo, J.Nordgren, W. Eberhardt, and J.-E. RubenssonIn preparation

III Resonant inelastic soft x-ray scattering at double core excita-tions in solid LiClM. Agåker, T. Käämbre, C. Glover, T. Schmitt, M. Mattesini, R.Ahuja, J. Söderström, and J.-E. RubenssonPhysical Review B 73, 245111 (2006)

IV Doubly excited He states in static electric fieldsM. Agåker, J.-E. Rubensson, C. Såthe, J. Söderström, M. Ström,M. Alagia, M. de Simone, A. Kivimäki, M. Coreno, V. Feyer, T.W. Gorzcyca, A. Mihelic, M. Zitnik, K. C. Prince, R. Richter, F.Robicheaux, and S. StrangesElettra Highlights, p. 17-18 (2005-2006)

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V X-ray yield and selectively excited X-ray emission spectra ofatenolol and nadololJ. Söderström, J. Gråsjö, S. Kashtanov, C. Bergström, M. Agåker,T. Schmitt, A. Augustsson, L. Duda, J. Guo, J. Nordgren, Y. Luo,P. Artursson, and J.-E. RubenssonJournal of Electron Spectroscopy and Related Phenomena 144-147, 283-285 (2005)

VI Resonant Inelastic Soft X-ray Scattering at Hollow LithiumStates in Solid LiClM. Agåker, J. Söderström, T. Käämbre, C. Glover, L. Gridneva,T. Schmitt, A. Augustsson, M. Mattesini, R. Ahuja, and J.-E.RubenssonPhysical Review Letters 93, 016404 (2004)

VII Core level ionization dynamics in small molecules studies byX-ray-emission-threshold-electron coincidence spectroscopyJ. Söderström, R. Richter, M. Alagia, S. Stranges, M. Agåker, M.Ström, R. Fink, and J.-E. RubenssonElettra Highlights p. 27-31 (2003-2004)

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Contents

List of Papers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5List of abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Comments on my participation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Populärvetenskaplig sammanfattning . . . . . . . . . . . . . . . . . . . . . . . 15

1.1 En annorlunda atommodell . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.1.1 Molekyler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

1.2 Verktyg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191.3 Min forskning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.1 My research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3 Synchrotrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.1 Synchrotron radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.2 Storage ring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2.1 Insertion devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.3 Beamlines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.3.1 Grazing incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.3.2 Monochromator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.4 End stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 Experimental equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.1 Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.1.1 Multi Channel Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.1.2 Channeltrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.1.3 Photodiodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.1.4 Advantages and disadvantages . . . . . . . . . . . . . . . . . . . . . 35

4.2 Spectrometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.2.1 The XES spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.2.2 The photoelectron spectrometer . . . . . . . . . . . . . . . . . . . . 374.2.3 Advantages and disadvantages . . . . . . . . . . . . . . . . . . . . . 39

5 The physics studied . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.1 The atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.1.1 The orbital picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.2 Couplings and selection rules . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.2.1 Metastable states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455.3 Probing the orbitals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5.3.1 X-ray Absorption Spectroscopy . . . . . . . . . . . . . . . . . . . . 475.3.2 X-ray Emission Spectroscopy . . . . . . . . . . . . . . . . . . . . . 49

5.3.3 X-ray Photoelectron Spectroscopy . . . . . . . . . . . . . . . . . . 505.4 Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.4.1 Molecular vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525.5 Peak shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

6 XETECO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576.1 The physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

6.1.1 Threshold photoelectron spectroscopy . . . . . . . . . . . . . . . 576.1.2 Post Collision Interaction . . . . . . . . . . . . . . . . . . . . . . . . . 58

6.2 Principle of operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596.2.1 Fluorescence detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . 606.2.2 Threshold photoelectron analyzer . . . . . . . . . . . . . . . . . . 606.2.3 Detecting coincidences . . . . . . . . . . . . . . . . . . . . . . . . . . 606.2.4 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

6.3 End Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

7.1 Neon - Ne . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657.2 Nitrogen - N2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 677.3 Oxygen - O2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 697.4 Nitrous oxide - N2O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 717.5 Carbon dioxide - CO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 787.6 Helium - He . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

7.6.1 Field free environment . . . . . . . . . . . . . . . . . . . . . . . . . . . 827.6.2 Helium in weak external fields . . . . . . . . . . . . . . . . . . . . . 89

7.7 End remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 978 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

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List of abbreviations

This is a list of abbreviations, most of them are accepted by the academiccommunity, but I hope this list can make the thesis a bit more easy to read incase you forgot some of the abbreviations.

AE Auger Electron

CVR Core Vacancy Rearrangement

eV Electron Volt

EY Electron Yield

fs femtosecond (10−15 seconds = 0.000000000000001 seconds)

FBR Fluorescence Branching Ratio

FY Fluorescence Yield

g gerade

GS Ground State

nm nanometer (0.000000001 meter = 10 Å)

ID Insertion Device

IY Ion Yield

MCP Multi/Micro Channel Plate

PE Photoelectron

QE Quantum Efficiency

TPE Threshold Photoelectron

u ungerade

XAS X-ray Absorption Spectroscopy

XES X-ray Emission Spectroscopy

XETECO X-ray-Emission-Threshold-Electron Coincidence

XPS X-ray Photoelectron Spectroscopy

Å Ångström (0.0000000001 meter = 0.1 nm)

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Comments on my participation

Research is (almost) always the effort of several people, it would not be fun,nor possible, if that was not the case. In all papers included in this thesis I havebeen one of the experimental investigators. Besides doing the experiments andperforming data treatment/analysis I have also been involved in some of theexperimental design.• I designed the experimental setup used in the XETECO papers (Papers I, II

and III). Together with my supervisor I also designed the gas cell used inPaper IV.

• I took part in the experiments and did parts of the data analysis leading upto Paper I.

• I was one of the experimental investigators, I did the analysis and con-tributed to the writing of Paper III.

• I was one of the people who did the experiments for Paper II, V and VI.• I participated in the experiment leading up to Paper IV and did the data

treatment and comparisons to theory.• For Papers VII and VIII I participated in the experiment, did the experi-

mental data analysis and participated in the writing of the papers.

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1. Populärvetenskaplig sammanfattning

I min avhandling presenterar jag delar av min forskning inom atom- ochmolekylfysiken. Atom- och molekylfysik är, som det låter på namnet, studienav atomer och molekyler. I min forskning har jag riktat in mig på studien avinnerskalselektroner (core electrons) hos lätta atomer så som helium, syre,kväve och kol samt små molekyler uppbyggda av lätta atomer.

Figure 1.1: En översikt av det elektromagnetiska spektrumet. Mjukröntgenfotoner lig-ger i ett område som ligger lite i det ultravioletta området, och lite i röntgen området.Tack till M. Lundwall och B. Wickström för denna figur.

Min forskning är ren grundforskning, dvs. det finns inga direkta applika-tioner för mina resultat. Denna typ av forskning bedrivs för att verifiera ellerförkasta teoretiska modeller, som baseras på kvantmekaniska teorier.

För att studera dessa atomer och molekyler använder jag mig avmjukröntgenstrålning (soft X-rays). Mjukröntgenstrålning består avljuspartiklar (fotoner - precis som vanligt synligt ljus) som är endel av det elektromagnetiska spektrumet. I Fig. 1.1 visar jag en bildöver det elektromagnetiska spektrumet, de fotoner jag använt mig

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av ligger i våglängdsintervallet ∼1.25 - 31 nm. Dessa fotoner kallasmjukröntgenstrålning eller vakuum-ultraviolettstråling (soft X-rays ellervacuum violet radiation) beroende på vem du frågar. De kallas så eftersom deligger lite i det ultraviolettaområdet och lite i Röntgenområdet, se Fig. 1.1.

Beroende på vilket atomslag samt vilken typ av process jag vill studeraväljer jag ut fotoner med olika våglängder. Varje våglängd motsvaras av enenergi enligt den enkla formeln E = hc

λ , där E är fotonens energi, h och c ärnaturkonstnanter och λ är fotonens våglängd; våglängden 1.25 nm motsvararenergin 1000 elektron volt (eV) och våglängden 31 nm motsvarar energin 40eV.

För att förstå varför olika våglängder (energier) måste användas behövs enförståelse för atomens elektronstruktur. Det finns många populärvetenskapligabeskrivningar av en atom, här har jag valt att hitta på min egen liknelse -eftersom detta är min bok.

1.1 En annorlunda atommodell

Figure 1.2: Det går att dra vissa liknelser mellan ett fotbollslag och en atom. I bildenvisas två fotbollslag som representerar två atomer. Atomkärnan motsvarar målburen,spelarna (som representeras av fyllda cirklar) motsvarar elektroner och fotbollen rep-resenteras av en stjärna. De ihåliga cirklarna representerar några av de anfallsposi-tioner som spelarna kan ta om de vill och får. Pilen motsvarar fotbollens hastighet ochriktning.

I Fig. 1.2 visar jag en schematisk bild av en fotbollsplan, två lag med 10spelare vardera, en målvakt och en målbur. Varje planhalva får representeraen atom med målburen som atomkärna, målvakten och backarna som inner-skalselektroner och anfallsspelare som valenselektroner.

Målvakten och backarna (innerskalselektronerna) kommer nästan aldrig attgå långt från målet (atomkärnan). Dock kan det tänkas att de lämnar sinapositioner om de motiveras starkt, t.ex. om de får bollen (fotonen) och inlederen kontring. Anfallsspelarna (valenselektronerna) kommer däremot att kunna

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vara över stora delar av spelplanen. I denna liknelse kommer fotbollen attsymbolisera en foton och fotbollens hastighet symboliserar fotonens energi.

I dessa fotbollslag kan spelarna inte befinna sig var som helst på planen utanmåste stå på, eller väldigt nära, sina förutbestämda positioner - som represen-teras av en fylld cirkel. Detta kan tyckas något lustigt men så förhåller det sigi dessa lag. Stjärnan representerar en fotboll med hastighet i pilens riktning.

De båda lagen är just nu uppställda i något defensiva positioner, i Fig. 1.2finns också ihåliga cirklar, dessa cirklar representerar några av de anfallsposi-tioner som spelarna kan ta om de vill och får.

I fortsättningen fokuserar jag på det svarta laget och dess planhalva.Om en boll (foton) sparkas in mot det svarta laget (atomen) kan bollen (fo-

tonen) komma snabbt (med en hög energi) eller långsamt (med en låg en-ergi). Om bollen (fotonen) kommer långsamt kommer den att fångas upp avnågon av anfallsspelarna (valenselektronerna), medan om den kommer snabbtkommer anfallsspelarna (valenselektronerna) inte att hinna ta bollen (fotonen),men den kommer förhoppningsvis att fångas upp av en back eller målvakten(innerskalselektronerna). En riktigt snabb boll kommer att gå förbi hela laget,och om den inte går i mål kommer den att fortsätta ut i publiken.

Figure 1.3: Om en back får bollen kan han inleda en kontring, backen kommer dåatt springa upp till en av anfallspositionerna, då kommer backens position att bli tomvilket indikeras av en ihålig cirkel i figuren. I det atomära fallet motsvaras detta av enresonant excitation av en innerskalselektron till en valensorbital.

Låtom oss studera det fall när en spelare (elektron) fångar bollen (foto-nen). Den spelare (elektron) som fångar upp bollen (fotonen) kan välja attspela vidare bollen (fotonen), han skjuter då iväg bollen (fotonen) med sammahastighet som den kom, men kanske i en annan riktning (i atomen kallas dettaelastisk spridning). Han kan också välja att kontra, att inleda ett anfall.

Om en back (innerskalselektron) får bollen (fotonen) och han bestämmersig för att kontra så kommer han att springa upp till en anfallsposition (enav de ihåliga cirklarna), så som i Fig. 1.3. Hans backposition blir då vakant,vilket syns i Fig. 1.3. I atomen kallas detta för en resonant excitation.

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Om bollen kommer riktigt riktigt snabbt (med en väldigt hög energi) kan dethända att en spelare blir knockad av bollen, han blir då utburen från planen, ien atom motsvarar detta en jonisation; när en elektron lämnar atomen.

I Fig. 1.3 är en backposition vakant, och i ett duktigt lag kommer någon an-nan spelare att springa ner för att spela försvar, se Fig. 1.4. Det är inte alls svårtatt tänka sig att den här spelaren som helt plötsigt tvingas ner i försvaret kom-mer att vara arg och upprörd över denna plötsliga omstrukturering av laget.På vägen ner till målet kanske han blir så förbannad på en av sina lagkamrateroch knuffar iväg denna spelare från planen, eller så kanske han bara skrikeren massa svordommar åt tränaren.

Figure 1.4: En av anfallsspelarna tar backens, numera lediga, position för att spelaförsvar. I det atomära fallet motsvarar detta ett sönderfall. I sönderfallet kommer enelektron eller en foton att emitteras.

I atomen är det här är en process som beskrivs i kapitel 5.3 som en resonantexcitation och sönderfall (resonant excitation and decay), där den exciterandefotonen (bollen) har precis rätt energi (hastighet) för att flytta en elektron frånen innerskals orbital (backen) till en icke ockuperad orbital (anfallspositio-nen). Detta atomära tillstånd kommer sedan att sönderfalla genom att inner-skalsvakansen (backens numera tomma position) fylls av en annan elektron(spelare), i sönderfallet gör sig atomen av med den överblivna energin i formav en Augerelektron (spelaren som knuffas av planen) eller genom att skickaut en foton (som här symboliseras av skrik).

Det är givetvis uppenbart att endast vissa spelare kommer att springa nerför att agera back, nämligen de spelare som vet hur man spelar försvar, dettamotsvarar de urvalsregler jag beskriver i kapitel 5.2.

1.1.1 MolekylerOm vi betraktar båda lagen på planen (i stället för bara det svarta, somvi gjorde ovan), med varsin målbur (atomkärna) och spelare (elektroner)kommer dessa, när matchen väl är igång, att interagera med varandra. Detär uppenbart att de spelare som spelar anfall kommer att befinna sig pådet andra lagets planhalva och beblanda sig med det andra lagets spelare,

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Figure 1.5: Under en fotbollsmatch kommer de båda lagen att ha spelare som befinnersig över hela planen. De spelare som rör sig mest är anfallsspelarna, medans backaroch målvakt sällan lämnar området kring målburen. Detta är en förenklad bild av hurtvå atomer bygger upp en diatomär molekyl.

medans backarna och målvakten kommer att befinna sig nära målburen ochinte komma i kontakt med det andra lagets spelare, så som i Fig. 1.5. Dettaskulle motsvara en bindning mellan två atomer (som bildar en molekyl) somjag beskriver i kapitel 5.4. Återigen ser vi skillnaden mellan backar ochmålvakt (innerskalselektroner) som håller sig nära målburen (atomkärnan)samt anfallsspelare (valenselektroner) som rör sig mer fritt över hela planen(molekylen).

Detta är en liknelse och det blir svårt att förklara t.ex. vibrationer (se kapitel5.4.1), samt vad som egentligen händer med fotbollen när en back springerupp för att ta en anfallsposition. som i Fig. 1.3. Men just eftersom det är enliknelse går det inte att förklara allt med den.

1.2 VerktygFör att kunna göra dessa excitationer använder jag mig av fotoner av enbestämd energi, för att få dessa fotoner åker jag till olika synkrotroner.Synkrotroner kan producera väldiga mängder mjukröntgenfotonerfotoner, jagbeskriver synkrotroner i kapitel 3.

I korta drag kan en synkrotron beskrivas som en "Röntgen-lampa", och intenog med det, man kan ändra energin hos fotonerna som kommer ut. Om dettavore en vanlig lampa skulle det betyda att man skulle kunna få den att lysa,grönt, gult, blått eller vilken färg som helst. Och denna lampa är otroligt stark,om man använder sig av definitionen spectral brightness (se kapitel 3.1) sålyser en synkrotron starkare än solen.

Vad vi studerar är ofta sönderfall eller joniseringar. För att kunna studeradessa fenomen måste vi kunna detektera elektroner, fotoner eller joner (ellerandra partiklar). För detta har vi olika typer av detektorer och spektrometrar,jag har beskrivit några av dem i kapitel 4.

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1.3 Min forskningJag har studerat hur atomer och molekyler påverkas av en innerskalsexcitation(när en back inleder en kontring) samt jonisationer (när en back knockas ochfår bäras av planen). Självkart sätter en sådan händelse hela laget i gungning;för molekyler rent bokstavligt, de börjar ofta vibrera (se Fig. 5.6). Atomer kaninte vibrera, men de kommer (liksom molekylerna) att att skicka ut fotonereller Augerelektroner i sönderfallet. Utifrån dessa fotoner och elektroner kanvi dra slutsatser om vilka orbitaler (spelarpositioner) som var involverade isönderfallet, och hur dessa interagerar med varandra.

I kapitel 7 kan du läsa om några av de resultat som vi kom fram i artiklarnaI - VIII.

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2. Introduction

All research presented in this thesis falls under a category we call Atomic andmolecular physics, which is the study of atoms and molecules.

The whole world around us is built up by atoms and molecules, the proper-ties of all materials depend on what atoms and molecules the material consistsof. If we can increase our understanding of these "small building blocks of theuniverse" we can perhaps increase our understanding of the universe we livein.

The research presented in this thesis is focused on the electronic structureof light atoms (such as helium, carbon, nitrogen, oxygen and neon) and smallmolecules that consist of light atoms. More specifically I have studied atomsand molecules using by investigating the core electrons properties, core elec-trons are the inner shell electrons of an atom or molecule. In a molecule thecore electrons are mostly localized at one nuclear site while valence electronsare more shared throughout the molecule. Core electrons were for a long timeconsidered to be non-binding electrons, hence it came as a great surprise thatthe removal of a core electron could significantly impact the bond lengths andvibrations in a molecule.

Atomic and molecular physics have been studied for a long time, but westill have great difficulties to understand most atoms and molecules. Today it ispossible to calculate the behavior of the simplest atom, hydrogen, with a highaccuracy. As soon as we try to approach more complex systems our modelsare far from perfect. To this date we still cannot (in general) calculate thebehavior of a three body system - not classically nor quantum mechanically.

The experimental studies of atoms and molecules help us to realize whatapproximations can be made for different systems, thereby giving us a betterunderstanding of the fundamental behavior of the nature around us.

2.1 My researchMy research is basic research, i.e. there are no direct applications of my re-sults. Except from making us understand the fundamental interactions better,basic research can sometimes also give tangible products. There have beenseveral offspring-projects from basic research leading up to everyday objects,perhaps the most famous example of a product sprung from atomic researchis the laser.

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I have studied the effect of removing a core electron from atoms andmolecules. The removal of a core electron from an atom/molecule will leadto a redistribution of the remaining electrons (as described in Chapter 5.3).In this redistribution yet other electrons or photons can be emitted from thesystem, if this happens in a molecule the molecule can also start vibrating (asdescribed in Chapter 5.4).

If we can detect these emitted particles it is possible to draw conclusionsabout the orbitals involved in the redistribution of the remaining electrons (seeChapter 5), and from this information we can draw conclusions about some ofthe atomic/molecular properties.

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3. Synchrotrons

All my research has been done at synchrotrons. The main part of a synchrotronis called a storage ring, in this ring electrons are kept orbiting at speeds close tothe speed of light. These electrons are then used to produce extremely intenseX-rays.

Synchrotrons are a research field in themselves and I will only briefly in-troduce them here, the interested reader is recommended to read Ref. [1] andreferences therein.

Figure 3.1: A schematic drawing of a synchrotron, see the text for more details.

In Fig 3.1 I show a schematic drawing of a synchrotron, in this figure Ishow:

The accelerator that is used to accelerate electrons up to velocities close tothe speed of light.

The booster ring that some synchrotrons have, if the accelerator cannot ac-celerate the electrons enough a small booster ring is used to boost upthe energy of the electrons before they are inserted into the storage ring.

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The storage ring is the main part of the synchrotron, the storage ring is fur-ther discussed in Chapter 3.2.

The cavity is used to keep the electrons at relativistic velocities, at each rev-olution the electrons gets an acceleration from the cavity’s radio fre-quency field.

The insertion devices and bending magnets used to produce X-rays as dis-cussed in Chapter 3.2.1. To each undulator and bending magnet a beam-line is attached, see Chapter 3.3. In Fig. 3.1 additional magnets are alsoshown, these magnets are there to keep the electron beam focused andkeep the shape of the electron bunches.

3.1 Synchrotron radiationSynchrotron radiation has many different applications in research. I used it tostudy the electronic structure of atoms and molecules, but they can be used incrystallography, studies of magnetic materials, studies of correlated materialsetc.

Depending on your field of interest you will focus on different aspects ofthe synchrotron radiation, I will briefly mention some of the aspects importantto my research here. Note that this is not a list of all properties of synchrotronradiation, but it is a list of what I deem important properties for the researchpresented in this thesis.

• Polarization X-rays produced at a synchrotron can have different polariza-tion, typically we talk about linearly polarized and circularly polarized ra-diation. The polarization describes how the E-vector of the radiation rotatesaround the axis of propagation. The polarization of radiation is describedin e.g. Ref. [2].

• Spectral brightness of a synchrotron is orders of magnitude largerthan the sun. The spectral brightness is defined as number ofphotons/s/mm2/mrad2/0.1%BW, where BW is the band width centeredaround a selected frequency (energy).

• Pulsed radiation source The radiation from a synchrotron comes in pulses.These radiation pulses correspond to the electron bunches in the storagering. The time between each photon pulse varies depending on how manyelectron bunches there are in the ring, for most experiments in this thesisthe time between pulses has been 2 ns.

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3.2 Storage ringIn the storage ring electrons are kept circulating at velocities close to the speedof light, they are guided in the storage ring by a set of magnets and eachrevolution they are accelerated to maintain their relativistic velocity.

The electrons are not spread uniformly in the storage ring, but instead theyare kept in bunches. This way it is possible to accelerate electrons, withoutat the same time decelerating other electrons. This also gives rise to the timestructure of the synchrotron. The time structure can differ between differentsynchrotrons and different fill modes.

The synchrotron storage ring is kept under ultra high vacuum to minimizecollisions between the fast electrons and other particles, such collisions willcause the amount of electrons in the storage ring to rapidly decrease.

3.2.1 Insertion devicesSynchrotron radiation is created by bending magnets or insertion devices, typ-ically an undulator or a wiggler. All research in this thesis has been doneusing undulators and therefore I will only present undulators here. A more de-tailed description of undulators, wigglers and bending magnets can be foundin Ref. [1].

Figure 3.2: A schematic drawing of an undulator with the magnetic period λu. Thegray and white blocks are magnets of different polarity yielding an alternating mag-netic field in the undulator. The path of the electron beam is schematically shown asan undulating movement.

In Fig. 3.2 I show a schematic picture of an undulator. When a chargedparticle pass through the undulator, it is subject to a magnetic field from themagnetic poles, hence the Lorentz force will act upon it, see Equ. 3.1.

F = q(E + v×B) (3.1)

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The electron will then deviate from its path in the synchrotron. This devi-ation is an acceleration of the electrons since a = dv

dt and the deviation is achange in the direction of the velocity. If we accept that accelerated chargedparticles will radiate, it is obvious that the electrons passing through the un-dulator will radiate.

Depending on the strength of the magnetic field the acceleration will be dif-ferent (as F = ma), and the energy of the emitted photons will have a differentenergy distribution - for undulators this is known as the undulator peak. Theradiation is then guided through a beamline to the experimental chamber.

How X-rays are produced in an undulator (and wiggler) is well explained inChapter 5 in Ref. [1] and I do not intend to reproduce the same arguments here.What turns out to be critical is that the electrons has a relativistic velocity, thiswill cause a Lorentz contraction of e.g. an undulator. The relativistic velocitywill also give a relativistic Doppler shift that further increases the energy ofthe emitted photons.

The emitted radiation will also be "focused" into a narrow cone instead offollowing the classical distribution sin2 θ as shown in Fig. 3.3. Note that in theclassical radiation pattern no radiation is cast in the direction of acceleration(sin2 (0) = 0). The "forward focusing" of the emitted photon beam from anundulator can be easily understood using Lorentz transformations.

Figure 3.3: The classical sin2 θ distribution of radiation from an accelerated chargedparticle. The direction of acceleration is noted in the figure by a.

Consider an electron that emits a photon according to Fig. 3.4, the anglebetween the axis of propagation and the emitted photon is θ ′, let’s considerthe case shown in Fig. 3.4 where θ ′ = 90. In this example the electron’scoordinate system is denoted by a prime (′).

Now divide the velocity of the photon in the lab frame into two perpendic-ular components (ux,uy). It is the straightforward to express these as:

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Figure 3.4: An electron, symbolized by a black circle, with velocity v along the x-axis emitting a photon, symbolized by an undulating line, perpendicular to the axis ofmotion (along the y-axis) at time t = 0.

ux =u′x + v

1+ vu′xc2

= v (3.2)

uy =1γ

u′y1+ vu′x

c2

=1γ

c (3.3)

where γ ≡ 1√1− v2

c2

and u′x, u′y are the velocities in the electron frame, u′x = 0 in

this specific case as θ ′ = 90, this means that u′y = c.As v≈ c⇒ γ >> 1 the perpendicular component (uy) almost vanishes com-

pared to the component parallel with the electrons velocity (ux). CombiningEqus. 3.2 and 3.3 we can express

tan(θ) =uy

ux≈ 1

γ(3.4)

and for small angles tan(θ) ≈ θ , hence Equ. 3.4 can be approximated as

θ ≈ 1γ

(3.5)

where θ is the angle in the lab system.It is evident that this will benefit all angles θ < 90 "focusing" them in a

narrow cone. For angles θ > 90 the derivation is almost as straightforwardand is left as an exercise for the reader.

This derivation is not strictly true for an undulator, as the velocity of theelectrons is not always parallel to the same axis, and photons emitted at an-gles θ > 90 will be less "focused" than photons emitted at angles θ ≤ 90 etc.The undulator condition implies that all electrons in the electron bunch hasa smaller angular variance than 1

γ√

N[1], where N is the number of magnetic

poles in the undulator. If this is the case the approximation in Equ. 3.5 is valid,then the emitted radiation from an undulator is "focused" into a cone with thetop angle θ ≈ 1

γ . A more detailed investigation shows that a significant amount

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of this radiation is contained in a cone with a top angle of θ = 1γ√

N[1]. Within

this cone the resolution can be expressed as ∆λ = λN .

The undulator equation gives the wavelength (λ ) of the emitted radiation

λ =λu

2γ2

(1+

K2

2+ γ2θ 2

)(3.6)

where θ is the angle the photon is emitted in with respect to the axis of theelectron’s propagation, λu is the undulator period (see Fig. 3.2) and K = eB0λu

2πmec(me is the rest mass of the electron, c the speed of light in vacuum and B0 isthe magnetic flux density) [1].

3.3 BeamlinesI have performed my experiments at several beamlines, hence I will not showthe layout of a specific beamline. Instead I will discuss some of the similaritiesbetween the beamlines I have been at.

As most beamlines have similar purpose they also have similar designs.In the beamline the X-rays produced in the undulator will be focused andmonochromatized, this is done through a set of refocusing mirrors and amonochromator. A monochromator for soft X-rays is a grazing incidencegrating monochromator, and the mirrors used are grazing incidence mirrors,both of these are further discussed below.From a users point of view some differences between beamlines are:• What energies they can reach - a combination or the efficiency of the un-

dulator and monochromator.• Resolution, E

∆E - how well the beam is monochromatized after themonochromator.

• Photon flux - how many photons will hit the sample per time unit.• Polarization of the synchrotron radiation, as discussed in Chapter 3.1.• The size of the photon-beam’s focal point.• Collection software at the beamline.• If you manually need to tweak the beamline to optimize it or if it is stable

and almost optimized without too much interference from the experimen-talists.

Depending on your field of research there might be other features you deemimportant from beamlines, e.g. coherence. For my research the points abovehave been important.

There are several reasons why beamlines are kept under ultra high vacuum,some of them has to do with the total transmission of photons through thebeamline. We are using what we call soft X-rays, that is X-rays with energiesbetween ∼20 →∼1000 electron volt (eV), these X-rays are quickly absorbedin a non-vacuum system. In e.g. 1 cm of atmospheric pressure of air almost allphotons in this energy regime will be absorbed [3]. X-rays might also cause

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gas molecules in the beamline to dissociate. The atoms might then form a thinfilm on, or be implanted in, the reflective surface of mirrors and gratings. Thiswill cause degradation of the reflective surface, this degradation can becomea serious problem over time; it can be seen to some extent at almost all beam-lines. For me the most common problems are around 290 eV (C 1s), 400 eV(N 1s) and 530 eV (O 1s), the carbon edge is usually the most severe.

Figure 3.5: A schematic drawing of a beamline. The drawing shows the undulator (seeFig. 3.2) producing X-rays. The X-rays are guided through the monochromator and re-focusing optics onto the sample studied. In this schematic picture a XES spectrometer(see Chapter 4.2.1) is used.

A typical design of a beamline is schematically shown in Fig. 3.5, in thisfigure an X-ray Emission Spectrometer (see Chapter 4.2.1) is used to recordspectra.

3.3.1 Grazing incidenceGrazing incidence (sometimes called Glancing incidence) is when the anglebetween the reflective surface and the incident photon is small, in Fig. 3.7 thiscorresponds to the angle i being a small angle. Grazing incidence is needed asthe reflectivity is low for soft X-rays for most incident angles except grazingangles where it is high. In Fig. 3.6 I show how the reflectivity for a perfectplanar gold mirror varies with different incident energies and different grazingangles. In Fig. 3.6 it is evident that for higher photon energies the angle mustbe smaller than for low energies to achieve good reflectivity.

3.3.2 MonochromatorThe photons from the undulator are somewhat monochromatized, centered atthe wavelength specified by the undulator equation (Equ. 3.6) with an energyresolution of ∆λ ≈ λ

N as written in Chapter 3.2.1.This resolution is far from from what we need in our experiments, therefore

most beamlines has an additional monochromator. In the soft X-ray regime the

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Figure 3.6: Left The reflectivity of a flat perfect gold mirror as a function of photonenergy and grazing incidence angle [3]. It is evident that for most energies small an-gles are needed. Right The same information but displayed in a contour plot. Whitecorresponds to high reflectivity and black corresponds to low reflectivity.

monochromators are grazing incidence grating monochromators for the samereflectivity reasons as the mirrors. These monochromators usually consists ofa grating and a/some mirror(s). The grating will disperse different wavelengthsin different directions according to the grating formula

mλ = d [sin(90−u)− sin(90− i)] (3.7)

where d the groove spacing of the grating, m is the diffraction order, i is theincident angle and u the angle of the diffracted wavelength λ , the angles aredefined in Fig. 3.7. By using a small slit after the monochromator it is pos-sible to select only a certain bandpass of energies. This is a short simplifiedexplanation of how a grazing incidence grating monochromator works.

Figure 3.7: A schematic picture of a reflection grating. In the figure the incident radi-ation of two different wavelengths hits the grating. These different wavelength will bereflected in different angles according to Equ. 3.7. Note that the distance d has to besmall compared to the illuminated area. The grating is well explained in most opticstextbooks, e.g. Ref. [2].

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3.4 End stationsThe experiments are (usually) done in what is called the end station. The endstation contains the experimental equipment needed to perform the experi-ment, e.g. detectors or spectrometers. At the beamlines I have been perform-ing most of my experiments the end stations have been in constant change,usually an experiment will start with re-building the end station from bits andpieces. Many experiments have been done using the ARPES end station atElettra, but what is inside has differed greatly between each experiment. Theend station used for the XETECO experiments is described in Chapter 6 whilethe other end stations are briefly described in the corresponding paper, and, tosome extent, in Chapter 7.

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4. Experimental equipment

Experiments at synchrotrons requires a lot of experimental equipment, oneneeds power supplies, pumps (to obtain vacuum), vacuumtight chambers,electronics and much, much more. In this Chapter I will present some ofthe detectors and spectrometers we use to detect photons or particles in ourexperiments.

4.1 DetectorsWhen performing this type of experiments at a synchrotron one can detectemitted particles, e.g. ions, electrons, metastable particles and photons (someof this is discussed in Chapter 5.3). To detect these particles there are severaltypes of detectors developed, these are just a few of them.

4.1.1 Multi Channel PlatesA Multi/Micro Channel Plate (MCP) are used to detect charged particles, orparticles with a significant internal or translational energy. In the left part ofFig. 4.1 I show a schematic picture of an MCP. When an X-ray photon hitsthe MCP surface several electrons will be emitted from the MCP surface. Dueto the applied potential these electrons will be accelerated into the channels(also called pores) of the detector where they will create a cascade by hittingthe surface of the channel several times, as shown in the right part of Fig. 4.1.Each time an electron hits the surface of the channel a multiplication of theelectron is done, see Fig. 4.1. This is called a cascade process and the totalmultiplication typically reaches values of 103 - 104 [4].

An MCP detector usually consists of several of these plates stacked on topof each other, giving a significant amount of electrons at the end of the MCPstack. The electrons produced will then hit a conductive surface producing asmall change in the potential detectable by standard equipment. MCPs alsohave a very fast response time, that is the time from the X-ray hits the surfaceuntil a signal can be detected is small (< 100 ps [4]) and the jitter (how muchthis time response varies from time to other) in this signal is small.

MCPs work in a similar way when detecting ions and electrons, with theonly exception of how the initial electron is created. A picture of an MCP1

1This MCP is broken, a crack can clearly seen in the upper right part of the MCP.

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Figure 4.1: Left A schematic cross-section of an MCP showing the incident X-raysproducing electrons that are multiplied in the channels. Right A schematic drawing ofthe multiplication process the channels. These figures are included with permissionfrom Ref. [5].

Figure 4.2: Left A picture of a channeltron in its holder, the channeltron looks a littlebit like a trumpet. The funnel shaped entrance is hidden from view in this figure. RightA typical MCP, the round shape is most common. The holes in the plate are so smallthey cannot be seen in a photograph of this quality. The diameter of the MCP is 4 cm.The MCP has a visible crack in it, i.e. it is broken.

can be seen in the right part of Fig. 4.2, the left part depicts a channetron in itsholder.

It is possible to increase the quantum efficiency (QE) of MCPs with dif-ferent techniques. I will present two techniques here that enhances the QE ofMCPs for most X-ray photons in the soft X-ray regime.

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1. By putting a mesh in front of the first MCP plate and applying ∼ −1000V/cm compared to the MCP plate, electrons that are emitted away from thepores will be diverted back toward the MCP, hence increasing the probabil-ity of them being multiplied in a channel. This voltage is optimized so thatthe electrons emitted away from the MCP will have a high probability ofbeing accelerated down into one of the MCP pores while keeping the timeresolution fairly accurate.

2. By adding a material on top of the first MCP that has a higher probabilitythan the MCP itself of emitting one or several electrons for each incomingX-ray photon the QE of the detector will increase. For this we use CsI, butit is also possible to use other materials e.g. KBr and KCl., see Refs. [6–9]and references therein.

4.1.2 ChanneltronsIn the left part of Fig. 4.2 a photo of a channeltron is shown, a channeltron canbe seen as a single channel in an MCP, but with a funnel in one end increasingthe collection-angle of the channeltron. The funnel part is hidden from viewin Fig. 4.2.

4.1.3 PhotodiodesThe photodiode is a small device, typically less than 1 cm2 that can be usedto detect a wide range of photon energies as well as charged particles. Thereexists many different models of photodiodes, each slightly different from theother in its characteristics. A photodiode is what is called a p-n junction, whena photon of sufficient energy is absorbed by the photodiode material it will ion-ize an atom, hence create a photo current. The principle of a photodiode canbe found in many places, I can recommend the technical descriptions avail-able at the homepage of Hamamatsu [10] for the interested reader as a goodintroduction.

4.1.4 Advantages and disadvantagesEach of these detectors has their own advantages and disadvantages. Typicallythe MCP detectors are fast while at the same time they can be rather large.The channeltrons are usually smaller than an MCP but has similar time char-acteristics. Photodiodes are usually only a fraction of the cost of MCPs andchanneltrons, but then they also lack the fast time response possible to obtainwith an MCP and a channeltron. There are fast photodiodes for sale, but theyare often very small, or very expensive if they have a large sensitive area. Onthe other hand photodiodes are usually much sturdier than channeltrons andMCPs.

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For each experiment the choice of detector is not easy, for simple fluores-cence yield (see Chapter 5.3) measurements a photodiode is probably the bestchoice. If you on the other hand need high time accuracy an MCP/channeltronis probably your best option, or maybe an avalanche photodiode.

There are also a great many detectors not covered here that might well bea better choice for experiments, one option might be the photon detector weare currently developing, it is based on the same principle as the detector inRef. [11].

4.2 SpectrometersMuch of the work in this thesis has been done using spectrometers, e.g. thephotoelectron spectrometer and a photon spectrometer. A spectrometer is adevice that not only detects electrons/ions/photons but that also analyzes theenergy of these particles. Here I just present some of all types of spectrometersthat are available.

4.2.1 The XES spectrometerThe XES (X-ray Emission Spectroscopy) spectrometer used by my group iswell described in many places, I can recommend a few, such as Refs. [12–15],in fact the XES spectrometer is well described in most theses written in the lastyears in this research group. The principle behind our design of a XES spec-trometer is the Rowland geometry, shown in Fig 4.3. A mathematical discus-sion regarding the Rowland circle is available in e.g. Ref. [16], the Rowlandcondition can be summarized as follows.

If you have a spherical grating with a radius 2R, you can inscribe a circlewith a radius R having a common intersect as shown in Fig. 4.3. A smallsource (S) originating somewhere on a circle with a radius R will be focusedas a line back onto the same circle after the grating. Since the grating willdiffract different wavelengths in different angles each wavelength (energy)will be focused onto a different point after the grating, as shown in Fig. 4.3.

By putting a detector on the Rowland circle where the different energies arefocused you can detect a certain range of energies, this range depends on thesize of your detector and the diffraction in the grating. The acceptance anglefor the XES spectrometer is very small, this makes it possible to study angleresolved emission.

As we are using soft X-rays the incident angles must be grazing to obtainreflectivity as discussed in Chapter 3.3.1.

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Figure 4.3: The Rowland geometry implies that a small source (S) on the Rowlandcircle will be focused as a line onto the Rowland circle if the Rowland conditionis fulfilled (see text). If the reflective surface is a grating (as in the figure) differentwavelengths will be diffracted in different angles (see Equ. 3.7) and it will be possibleto detect the different wavelengths separately. The focusing properties is important asit will be possible to detect wavelengths close to each other. The incidence angle andthe grating size are exaggerated to make the figure easier to understand.

4.2.2 The photoelectron spectrometerParts of my work has been done using a Gammadata Scienta SES-2002 X-rayphotoelectron spectrometer. This type of electron spectrometers can be calledXPS spectrometers, where XPS is an abbreviations for X-ray photoelectronspectroscopy. The XPS spectrometers has been well described in many papersand theses and I do not intend to go into details in this thesis as only parts ofmy studies were done using this apparatus.

One design of the XPS spectrometer is described in Ref. [17] and othermore general descriptions can be found in many doctoral theses from the de-partment of physics at Uppsala University, such as Refs. [18, 19].

The function of an XPS spectrometer is very similar to that of an XESspectrometer. The XES spectrometer separates photons of different energiesby means of a diffraction grating while the XPS spectrometer separates elec-trons of different kinetic energies by means of electron optics. These electronoptics can crudely be separated into an electron lens and a hemispherical sec-tion. From the kinetic energy it is possible to calculate the binding energyusing Equ. 5.6. The acceptance angle for the XPS spectrometer is very small,this will be important as you can study photoemission angle resolved (alsocalled ARPES - angle resolved photoemission spectroscopy).

As already stated charged particles will be affected by external fields (seeEqu. 3.1), hence it is important to shield the spectrometer, and the vacuum

37

chamber, from external fields as they will affect the trajectories (and energies)of the electrons. The chamber itself shields well from electric fields, whileµ-metal2 shields are used to shield the experiment from external magneticfields.

Threshold photoelectron spectrometerThe threshold photoelectron (TPE) analyzer can be described as a photoelec-tron spectrometer optimized for electrons with a very low kinetic energy (∼= 0eV). The kinetic energy of these electrons is so low that an electrostatic fieldthat accelerates the electrons toward the TPE analyzer has to be applied. Asthe TPEs are accelerated into the analyzer the collection angle is close to 4π .One design of a TPE analyzer is presented in Ref. [20].

When the electrons enter the TPE analyzer they are focused and energyselected so that only threshold photoelectrons (electrons with Ekin

∼= 0 eV)make it to the detector. In Fig. 4.4 I show a simulation of the trajectoriesof threshold photoelectrons emitted from a point source through parts of theelectron lens.

Figure 4.4: A simulation of the trajectories for threshold electrons in the first part ofa threshold photoelectron analyzer. The analyzer is represented by the crossed patternin the figure, the electron trajectories are more or less horizontal lines and the moreor less vertical lines are electrical field lines. The solid piece to the left in the figurerepresents a surface that can be biased with a potential.

It is also important to shield this experiment from external fields, for thesame reasons as described above for the XPS spectrometer.

2µ-metal is an alloy that has a high magnetic permeability, therefore µ-metal can "divert" mag-netic fields to a large extent.

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4.2.3 Advantages and disadvantagesFor light atoms, such as the atoms studied in this thesis, the Auger decayusually dominates over the radiative decay. As so few photons are emittedcompared to photoelectrons the statistics using the photoelectron analyzer will(usually) be better than with a photon spectrometer.

As electrons will be affected by external fields the photon spectrometer hasa great advantage if one wants to study atoms or molecules in external fields.

The X-ray emission spectroscopy is typically more bulk sensitive than pho-toemission. Soft X-rays can penetrate several hundred nanometers before be-ing absorbed in a solid material while electrons will loose their kinetic energywithin a few nanometers. This is related to the mean-free-path, the mean-free-path is the average distance a particle (e.g. an electron or photon) can travelbefore it interacts with another particle.

By increasing the photon energy the kinetic energy of the photoelectronswill also increase and then they will have a longer mean-free-path than elec-trons with a lower kinetic energy, the incident photons will also (due to theirhigher energy) penetrate deeper into the sample. XPS is usually called a sur-face sensitive technique while XES is called a bulk sensitive technique. Withthe advancement for high kinetic energy electron XPS it is possible to probethe bulk using XPS, see e.g. Ref. [21].

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5. The physics studied

My research has been centered around the electronic structure of atoms andmolecules in gas phase; or more specific the core (inner shell) electron proper-ties. The electronic structure determines a great deal of the atomic/molecularproperties. In this Chapter I will present the basics of the physics I have stud-ied and also some of the methods used.

To study these core electrons there are a great deal of methods available tothe interested researcher. I will present only a few of them here, namely theones that have been used in my experiments.

5.1 The atomTo understand the atom, or to understand it as much as we do today, will takeseveral years of studies - and is clearly beyond the beyond the scope of thisthesis.

Quantum mechanics and the electronic structure of atoms and moleculesare the subject of a great many books, for the interested reader I will recom-mend a few, see e.g. Ref. [22–28]. This chapter is not intended to make youunderstand these concepts, as it takes years of study to do that. However, asthe electronic structure of the atom is a central piece of my research, I willpresent a simplified theory of the electronic structure.

An atom consists of a nucleus and electron(s) around the nucleus. The nu-cleus consists of positively charged protons and neutral neutrons. The elec-trons have a negative charge and are orders of magnitude lighter than bothprotons and neutrons. The electrons will interact with each other, but also withthe nucleus - this interaction describes how strongly the electron is bound tothe atom. I have studied these relationships, how strong the different interac-tions for the electrons are.

5.1.1 The orbital pictureThere are certain quantum mechanical states in an atom/molecule that elec-trons can occupy. An electron can be uniquely described using four quantumnumbers - in one representation we call these quantum numbers n, l, ml andms [22–25]. Another representation of these quantum numbers are n, l, j andmj.

41

It is important to note that ml , ms and mj are projections of the l, s and jquantum numbers.

These quantum numbers define the states available for the electrons. ThePauli principle states that two fermions [e.g. electrons] cannot occupy the samestate at the same time - i.e. no two electrons (in the same atom/molecule) canhave the same set of quantum numbers. This follows from symmetry reasons,see e.g. Ref. [27].

To each atom we assign shells, it is important to understand that these arequantum mechanical shells. The quantum mechanical shells have nothing incommon with the shells of e.g. an onion. They were introduced in the begin-ning of the 20:th century and given a theoretical explanation by the Danishscientist Niels Bohr [29]. We now label these shells with the n quantum num-ber (also called the main/principal quantum number) starting from n = 1 rang-ing up to n = ∞. For n = 1 we refer to as the K shell, n = 2 the L shell, n = 3the M shell and so on.

To each shell we assign subshells, each shell has as many subshells as itsmain quantum number; the shell n = 1 has one subshell, n = 3 has threesubshells and so on. These subshells are labeled by the l quantum numberand are called orbitals. The l quantum number ranges from 0 to (n− 1), i.e.l = 0,1,2, ...,(n−1). These orbitals also have names• l = 0 is called s (for sharp)• l = 1 is called p (for principal)• l = 2 is called d (for diffuse)• l = 3 is called f (for fundamental)• l = 4 is called g• l = 5 is called h and it follows the alphabet from here on...The l quantum number is associated with the orbital angular momentum ofthe electron.

The last two quantum numbers are the ms and the ml quantum number. ms

can take the value ±1/2 (±s), while ml = −l,(−l + 1), ...,(l − 1), l. Both ml

and ms can further split the orbitals into even finer structures.The electrons can be seen as standing waves in the atomic system. If the

electronic wave function meets certain criteria it will be a standing wave andwill then correspond to one set of the four quantum numbers above. If thewave function is slightly different the amplitude will rapidly decay to zerodue to negative interference.

It is possible to draw an analogy between the standing wave of an electronto something as common as a guitar string. A guitar can only produce toneswhere the strings are standing waves with a node at each end of the string.If this condition is not met the tone will either change into a tone that corre-sponds to a standing wave or rapidly die out.

42

5.2 Couplings and selection rulesThe transitions between orbitals (as described in Chapters. 5.3) follow certainrules. To avoid having to calculate transition matrices for each atom we haveintroduced approximations. I will briefly present the electric dipole approxi-mation and some electronic coupling schemes below.

The electric dipole approximation states that if the wavelength of the X-rayphoton is sufficiently long with respect to the atomic dimensions the electricfield from the photon can, at any time, be approximated by a dipole field overthe entire atom, see e.g. Refs. [26,27]. The electric dipole approximation givesthe selection rules ∆l = ±1 and ∆ml = 0,±1 in a one-electron system [28].

The different coupling schemes comes from how strong or weak differentinteractions are, weakly coupled levels can be separated from each other whilestrongly coupled cannot be.

In the LS coupling scheme the coupling between the spin and orbital angu-lar momentum is weak compared to the electrostatic interaction between theelectrons. Therefore we can decouple the L and S vectors as described below.The LS coupling is mostly valid for light atoms while the jj-coupling is usedfor heavier atoms.

In the jj-coupling the electrostatic interaction is weak compared to the spin-orbit interaction. In the jj-coupling scheme the spin and orbital angular mo-menta of each electron couple to an electronic angular momentum j and the jvectors of each electron couple into a total angular momentum J.

The jk-coupling occurs in an atom with one electron excited into a highn quantum number. Then the Coulomb interaction is weak, but it is strongcompared to the spin-orbit coupling of the outer electron, see Ref. [30]. Thecoupling is done according to the following scheme:For the inner electrons the spin and orbital angular momenta are coupled intoa total J, then this J is coupled with the outer electron’s orbital angular mo-mentum into K, and in the end K is coupled to the spin of the outer electron.

As the LS coupling is a good approximation for most of my studies I wantto present it in some detail here. In the LS coupling scheme the electronicangular momenta l and s couple separately to form L and S. L is the totalorbital angular momentum and S the total spin angular momentum. Thesevectors couple to form a total angular momentum J as J = L + S.

L and S are calculated as L = ∑i

li and S = ∑i

si. This is the same as saying

that one can treat the spin as decoupled from the orbital angular momentum,hence one can add the spin angular momenta separately and the orbital angularmomenta separately and then add the two sums into a total angular momen-tum.

The vectors L and S can also be expressed as quantum numbers ML andMS, which are projections, just as, for a single electron, ms is a projection of

43

s and ml is a projection of l. These projections are calculated as ML = ∑i

mli

and MS = ∑i

msi .

There is also the quantum number L, in a three electron system where theelectrons have the orbital angular momenta l1, l2 and l3 the possible values ofL is calculated as

L′ = |l1 + l2| , |l1 + l2 −1| , . . . , |l1 − l2| (5.1)

furtherL =

∣∣L′ + l3∣∣ , ∣∣L′ + l3 −1

∣∣ , . . . , ∣∣L′ − l3∣∣ (5.2)

The L quantum number determines, along with S, the possible terms of theatom. And at last there is the quantum number J that can take the values

J = |L+S| , |L+S−1| , . . . , |L−S| (5.3)

Figure 5.1: (a) If there are no external fields the L and S vectors will precess aroundthe J vector [24]. In the figure the S vector is translated in order to emphasize thevector sum J = L+S. (b) In the presence of a strong external magnetic field the L andS vectors will precess around the external field B instead of around the total angularmomentum J [24], hence leading to a breakdown of the LS coupling. In a strongmagnetic field this is called the Paschen-Back effect. In weak external magnetic fieldsthis will cause an additional split of the orbitals, this is called the Zeeman effect.

An easy way to visualize how the LS coupling works is to see both the Land S as vectors precessing about the total angular momentum J, as shown inFig. 5.1 (a). In Fig. 5.1 (a) the S vector is translated to emphasize the vectorsum J = L+S.

In a strong external magnetic field both the L and S vector will start precess-ing around the external magnetic field, making the total angular momentum Jundefined - leading to a breakdown of the LS coupling, as shown in Fig. 5.1(b). In a strong magnetic field this is called the Paschen-Back effect and in a

44

weak magnetic field it is called the Zeeman effect. In the Paschen-Back casethe LS coupling breaks down internally, while in the Zeeman case the energylevels will split while preserving parts of the LS coupling.

In an electric field a similar effect is seen, this effect is called Stark effect.The Stark effect leads to a split and shift of the internal energy levels [24].The presence of both electric and magnetic external fields can also lead tostate mixing, I will present results from this in Chapter 7.6.2.

In the LS coupling scheme we denote levels as 2S+1LJ . The LS coupling istypically good as long as the external fields are weak and the atom is not tooheavy.

A photon is usually categorized by its spin quantum number S = 1. Photonsare bosons, meaning that they have integer spin quantum numbers, which setsthem apart from fermions with half integer spin [27] (e.g. electrons with s =12 ).

When an atom absorbs a photon the momentum of the photon will also beabsorbed. As the energy is conserved (in a closed system) also the momentumis conserved, which implies that the total angular momentum of the atom mustchange by ±1 when a photon is absorbed (and similar for the emission ofa photon). The photon’s angular momentum couples to the orbital angularmomentum of the electrons, which implies that the orbital angular momentumquantum number l must change by ±1. In the electric dipole approximationthis means that an electron can only change its l quantum number by ±1 whena photon is absorbed or emitted. If two, or more, electrons are involved in theexcitation one has to look to the change of L instead.

From the discussion above follows that in LS coupling the total spin of theelectrons is not allowed to change. The selection rules (in the electric dipoleapproximation and the LS coupling scheme) for a many electron system canbe summarized as:∆L = 0,±1 1

∆S = 0and from this follows∆J = 0,±1. However if J=0 then ∆J = 1 and if L=0 then ∆L = 1.In a one electron system the selection rules are straightforward:∆l = ±1∆ml = 0,±1

5.2.1 Metastable statesThere exists excited states in both atoms and molecules that are calledmetastable states. These states are excited states that must break one, ormore, of the selection rules (there are also other selection rules not mentioned

1Readers of Physics Handbook [31] should be careful to note the selection rule ∆L = 0,±1(if L=0 then ∆L = 1) [24, 28] that is wrongly labeled as ∆L = ±1 is all versions of PhysicsHandbook [31] I have seen.

45

here) in order to decay, the easiest example is He 1s2s 1,3S. Although thesestates can be excited from the ground state by a photon, the cross-sectionfor this process is very small, as the transition is forbidden according to theelectric dipole approximation. Let us see why these two states are metastable.

Metastable heliumThe internal energy of He 1s2s 1S state is not sufficient for the atom to decaythrough an Auger process. The selection rules presented in Chapter 5.2 statethat in the electric dipole approximation ∆l = ±1 in the emission of a photon,but as the decay is 2s → 1s ⇒ ∆l = 0, this decay is forbidden in the electricdipole approximation.

The same is true for He 1s2s 3S but, according to the Pauli principle (seeChapter 5.1.1), this state must also change the spin of one of the electrons inorder to decay. This makes the transition not only forbidden in the electricdipole approximation, but it is also forbidden according to the LS coupling, asthe transition violates the selection rule ∆S = 0.

It is reasonable to assume that it will take much longer for the He 1s2s 3S todecay compared to the He 1s2s 1S, as the He 1s2s 3S is forbidden twice, andthis is indeed the case. The lifetime of He 1s2s 1S is ∼20 ms [32,33] while thelifetime of He 1s2s 3S is about 9000 seconds (!) [34]. This value is typicallyquoted as 8000 seconds in the literature, see e.g. Refs [35–37] which mightcome from theoretical calculations in Ref. [38] giving a lifetime of ∼7900 sec.The term lifetime is further discussed in Chapter 5.5.

5.3 Probing the orbitalsThe orbitals can be separated into occupied and unoccupied orbitals, they bothcontain information about the atom. Partly (or fully) occupied orbitals haveat least one electron in them, while (partly or fully) unoccupied orbitals areorbitals that can potentially be filled by one or several electrons. It is possibleto use soft X-rays to probe both the occupied and unoccupied orbitals usinga vast number of spectroscopic techniques. I will briefly present some of thetechniques I have used to study atoms and molecules.

If all electrons (with any kinetic energy) are detected (i.e. both the pri-mary emitted electron and all AE emitted subsequent to the ionization) themeasurement is called total electron yield (TEY). If the kinetic energy of theelectrons can be distinguished the technique is typically called X-ray photo-electron spectroscopy or Augerelectron spectroscopy (AES).

If on the other hand the emitted photons are detected, the measurement iscalled fluorescence yield (FY). Likewise if it is possible to separate the en-ergies of the photons, the technique is typically called X-ray emission spec-troscopy (XES).

46

Name AbbreviationParticle Energy Angular

Resonantstudied resolution resolution

Total electron yield TEY/EY Electrons None No Both

Partial electron yield EY Electrons Maybe Maybe Both

Total ion yield TIY/IY Ions None No Both

Partial ion yield IY Ions Maybe Maybe Both

X-ray photoelectron spectroscopy XPS Electrons High Yes No

Auger electron spectroscopy AES Electrons High Yes Both

Fluorescence yield FY Photons Maybe Yes Both

X-ray emission spectroscopy XPS Photons High Yes Both

X-ray-emission threshold-electron coincidence XETECOPhotons &

High Some -electrons

Table 5.1: A summary of some of the properties for the spectroscopy techniquespresented in this thesis.

It is also possible to detect partial electron yield, as well as FY and IY canbe divided into total FY/IY or partial FY/IY. The meaning of partial is not welldefined, it can either be a part of the solid angle that is studied, or it can be onlycertain energies of photons/electrons/ions that are studied. In Table 5.1 someof the properties of the techniques presented in this Chapter are summarized.

Depending on the orbitals involved in the transition the emitted photoelec-tron as well as the Auger electron (AE) and/or the emitted X-ray photon (seeChapter 5.3.1) will have different angular distributions. I will write more aboutthe angular distributions in Chapter 7.6.1, see also Refs. [39, 40].

5.3.1 X-ray Absorption SpectroscopyX-ray Absorption Spectroscopy (XAS) is typically used to map out the partlyor fully unoccupied orbitals in an atom/molecule. It is possible to record ab-sorption spectra either above or below the ionization threshold. Above thresh-old XAS can give informations about e.g. shape resonances see e.g. Ref. [41],below threshold XAS can give information about unoccupied states.

The process studied in XAS is schematically shown in Figs. 5.2 and 5.3.Fig. 5.2 shows both the resonant (below threshold - (a)) and non-resonant(above threshold - (b)) case, the shaded area corresponds to the ionizationcontinuum. Fig. 5.2 (c) presents a possible XAS spectrum from this modelatom. We see a peak right at the resonance and an extended structure abovethreshold. The XAS spectrum is, as can be seen in Fig. 5.2 (c), a "map" of theunoccupied orbitals available for the the excited electron.

In Fig. 5.3 I show how this atom can relax (decay). Fig. 5.3 (a) shows aresonant excitation (but the same discussion can be held for excitations abovethreshold, where the electron is excited into the continuum and the atom ion-ized), Fig. 5.3 (b) shows the Auger decay and 5.3 (c) shows the radiativedecay.

The Auger decay (usually) has much higher probability than the radiativedecay (for lighter elements), the Auger decay corresponds to one electron fill-ing the core hole and the excess energy is released by emitting an (Auger)

47

Figure 5.2: A schematic explanation of X-ray absorption spectroscopy showing a (a)resonant excitation, (b) non-resonant (above threshold) excitation and (c) possibleXAS spectrum with the resonance showing as a peak.

electron, see Fig. 5.3 (b). Due to the conservation of energy the kinetic energyof the Auger electron can be calculated.

The excited state in 5.3 (a) can also decay by emission of a photon (calledradiative decay or fluorescence decay) as pictured in 5.3 (c). In the radiativedecay a photon is emitted instead of an Auger electron when the core hole isfilled by an electron. Also the energy of the emitted photon can be calculateddue to the conservation of energy.

If an electron is emitted subsequent to each excitation the absorption willbe proportional to the electron yield (EY). As a photon can be emitted insteadof an electron the true absorption will not be exactly proportional to the EYnor the FY. We make the approximation that the absorption will be propor-tional to each yield, therefore it is possible to measure XAS using a variety oftechniques. These techniques will give slightly different results as the EY canbe different from FY.

The most common techniques are FY, IY and EY. EY and IY are usuallythe easiest ways to study XAS from gas phase; but the competing fluorescencedecay can give important information not available through EY or IY, see e.g.Ref. [42]. When XAS spectra are recorded the photon energy is scanned whileemitted particles are detected; examples of FY XAS can be seen in Figs. 7.1,7.3, 7.8, 7.11 and 7.14.

48

Figure 5.3: A model of the (a) resonant excitation, and (b) Auger decay and (c) ra-diative decay that can happen after the resonant excitation. The model works just aswell if the excitation in (a) is an ionization with the only difference that the excitedelectron has left the system. In this model there will not be enough electrons for theion to decay through an Auger decay, but in a more complex atom (having more than3 electrons before the ionization) it can usually decay through Auger decay.

5.3.2 X-ray Emission SpectroscopyWe call photon spectroscopy in the soft X-ray regime X-ray emissionspectroscopy. The X-ray emission spectrometer used in my research groupis briefly described in Chapter 4.2.1. In XES we study the energies of thephotons emitted in a core hole decay, this corresponds to measuring theenergy of the emitted photon in Fig. 5.3 (c), XES can be measured after bothresonant and non-resonant excitations. An example of a resonant excitationand emission is shown in Fig. 5.3 (a)+(c).

In a more complex atom/molecule than the one shown in Fig. 5.3 there willbe several decay paths and using the X-ray spectrometer we can differentiatebetween the different decay channels by studying the energy of the emittedphoton. From this it is then possible to draw conclusions about which orbitalswere involved in the transition and understand the atom/molecule better.

49

This can be exemplified by considering the sulfur atom resonantly excitedby a photon

1s22s22p63s23p4 +hν → 1s12s22p63s23p44p1 (5.4)

if the excited state decays radiatively the electrons from the three orbitals thatcan be involved are, according to the selection rules in Chapter 5.2, the porbitals.

1s12s22p63s23p44p1 → 1s22s22p53s23p44p1 +hν1 (5.5)

1s12s22p63s23p44p1 → 1s22s22p63s23p34p1 +hν2

1s12s22p63s23p44p1 → 1s22s22p63s23p44p0 +hν3

The photons emitted in each of these decays (hν1,2,3) will have different ener-gies. Therefore knowing the energy of the emitted photon gives us informationon which orbital was involved in the decay. The energy separation betweenhν1, hν2 and hν3 are rather large, the XES measurements I have done canseparate photons of a much more similar energy.

As it is possible to study angle resolved emission (see Chapter 4.2.1) itwill become even easier to separate different orbitals from each other. Oneexample that can be mentioned is that the decay np → ms does not radiateparallel to the polarization vector of the (linearly polarized) exciting photon,something we made use of in Paper IV. I will write more about this in Chapter7.6.1.

When an XES spectrum is recorded the incident photon energy is kept con-stant and all photon energies reaching the detector (see Chapter 4.2.1) will bedetected.

5.3.3 X-ray Photoelectron SpectroscopyPhotoemission is called XPS when the kinetic energy of the electron emittedin the non-resonantly excitation is studied (see Fig. 5.2 (b)). XPS spectra aremeasured with a photoelectron spectrometer, already mentioned in Chapter4.2.2. The main principle behind XPS can be summarized with the simpleformula

EB = hν −Ekin (5.6)

where EB is the binding energy of the electron, hν is the photon energy andEkin the kinetic energy of the emitted electron. This relation is called Einstein’sphotoelectric law. As both the incident photon energy and the kinetic energyof the emitted electron are known, it is possible to calculate the binding en-ergy2. In Fig. 5.2 XPS would correspond to measuring the kinetic energy ofthe emitted electron in Fig. 5.2 (b).

2Equ. 5.6 is only valid in gas phase where there is no work function.

50

It is also possible to detect the kinetic energies of the Auger electrons emit-ted in the core hole decay, the spectroscopy is then called Auger electron spec-troscopy (AES). This would correspond to measuring the kinetic energy of theAuger electron emitted in the Auger decay in Fig. 5.3 (b).

It is also possible to record angle resolved spectra with a typical photo-electron spectrometer. Therefore it is possible to measure the asymmetry pa-rameter (β ) in atoms and molecules. The β parameter defines the angulardistribution of the emitted electrons, see Chapter 7.4.

In XPS and AES the photon energy is kept constant while the spectrometerscans over a range of kinetic energies for the electrons. At any determinedtime only "one" kinetic energy is being detected.

If Ekin = 0 in Equ. 5.6 then hν = EB and XPS is then referred to as thresholdphotoelectron (TPE) spectroscopy, see Chapter 4.2.2 for a brief discussionabout a TPE spectrometer.

5.4 MoleculesI mentioned earlier that I have studied core electrons. In a molecule core elec-trons are localized to the site of the corresponding nucleus, while the valenceelectrons can be shared between the nuclei. One example is the linear N2Omolecule that has the ground state electronic configuration and term

1σ22σ23σ24σ25σ26σ21π47σ22π4 1Σ+ (5.7)

Here 1σ , 2σ and 3σ correspond to the O1s, NC1s and NT1s orbitals, respec-tively. NC is the central nitrogen atom and NT the terminal nitrogen atom inN2O (NTNCO). These orbitals are primarily localized to one nucleus. σ and πorbitals are defined as the projection of the orbital angular momentum on themolecular axis, a definition that is valid only in linear molecules.

The term for a molecule is obtained in a similar way compared to atoms.Following Ref. [28] the quantum numbers λ for the molecular orbitals arecombined to form a total orbital angular momentum Λ. These states are thenassigned as Σ (Λ = 0), Π (Λ = 1), ∆ (Λ = 2) etc. The axial component ofthe total electronic spin S is denoted Σ and can take 2S+1 different values. Σcouples to Λ to form Ω = |Λ+Σ|. The molecular term has the notation ΣΛΩ.

If the molecular wave function is symmetric with respect to coordinate in-version (with the coordinate systems origin at the molecular center of mass)it is called gerade (denoted Λg), and if it is asymmetric it is called ungerade(denoted Λu) - this is called the parity of the state. For many molecules geradeand ungerade has no meaning as they are not symmetric with respect to coor-dinate inversion. The notation Λ+ or Λ− is associated with symmetry duringa reflection in any plane through all atomic nuclei. This notation has meaningonly for "flat" molecules. Molecular terms and orbitals are well described inmany books, see e.g. Refs. [25, 28].

51

For non-linear molecules the molecular orbitals and terms are denoted dif-ferently using standard point group labels, see e.g. Ref. [22].

5.4.1 Molecular vibrationsThere are many molecules, from the simple hydrogen molecule (H2) tosomething as complicated as DNA that consists of millions and millionsof atoms. The more atoms a molecule consists of the more complex thevibrations becomes. To simplify the problem let us limit this discussion todiatomic molecules (such as O2, N2, H2, HF etc.) in one dimension.

Diatomic moleculesIn a simple model each atom in a molecule can be seen as a solid sphere, andthe bond between the atoms as a quantum mechanical spring, see Fig. 5.4.In this model the strength of the spring together with the atomic masses will

Figure 5.4: The two atoms are shown as spheres and the bond between them as aquantum mechanical spring. Two atoms connected with a quantum mechanical springwill never be at complete rest, this means that the molecule will always perform smallmovements, even when the molecule is in the lowest possible energetic state.

determine the frequency of the vibrations. The vibrational modes would, inthe harmonic oscillator approximation, be equally spaced in energy. This isof course a simplification; in reality the vibrational frequency is determinedby a more complex molecular potential. A good approximation for diatomicmolecules is the Morse potential

V (r) = De

(1− e−a(r−re)

)2(5.8)

where r is the inter atomic distance, re is the inter atomic equilibrium distance,De the dissociation energy and a is related to the width of the molecular po-tential, see e.g. Ref. [25]. The corresponding energy levels can be calculatedas:

Ev = ωe

(v+

12

)−ωexe

(v+

12

)2

(5.9)

where ωe is the vibration frequency and v is the vibrational quantum number.We can also define the anharmonicity constant xe that is a small positive num-ber [25, 28]. The Morse potential is not necessarily a good approximation forlarge values of v [28].

In Fig. 5.5 a Morse potential is shown with some of its corresponding en-ergy levels and the dissociation energy De.

52

15

10

5

0

Ene

rgy

(arb

. uni

ts)

1086420Interatomic distance (arb. units)

De=10a=0.85Re=1

E0

E1

E11

De

Figure 5.5: The Morse potential of a diatomic molecule showing energy levels E0 →E11 and the dissociation limit De. Note that the energy needed for dissociation is De−E0 as the molecule in its ground state has an internal energy E0.

Triatomic moleculesEqu. 5.9 is also a good approximation for larger molecules and have success-fully been applied to many triatomic molecules. In Papers II, VII and VIII wehave applied this model for N2O. The Morse potential have also been used tomodel vibrations in small atoms in the literature with great success, see e.g.Refs. [43, 44] to mention a few.

In a diatomic molecule there is only one vibrational mode, in a triatomicmolecule there are four vibrational modes. The four vibrational modes for atriatomic linear molecule are shown in Fig. 5.6, where I show the:

a Ground state (which is not a vibrational mode, it is included for clarity)

b Symmetric stretch

c Antisymmetric stretch

d Bending mode (the bending mode is doubly degenerated)

One should note that the molecule has a vibrational energy even in itsground state, this is also evident in Fig. 5.5, where the E0 level is above theminimum of the molecular potential. One way of understanding the this zero-point energy is to consider the Heisenberg uncertainty principle, which canbe written ∆x∆px ≥ h

2 . If the molecule did not vibrate we would have ∆x = 0

53

Figure 5.6: The four different vibrational modes in a triatomic linear molecule. I showthe (a) ground state of the molecule - this is not a vibration but is shown for compari-son, (b) symmetric stretch vibration where the bonds contract and elongates in phase,the (c) antisymmetric stretch vibration where the bonds contract and elongates out ofphase, and the (d) doubly degenerate bending mode vibration where the atom bends onthe middle. The bending mode is degenerate as the molecule can perform the bendingmotion along two orthogonal axes.

which would give ∆p = ∞ which would imply that we have no idea of themomentum and the kinetic energy, hence is not consistent with ∆x = 0.

5.5 Peak shapesWhen interpreting the recorded spectra I make use of different peak shapesto model the observed peaks. In the XETECO data I have approximated thepeak shape as a Voigt profile. For some of the Helium FY measurements Ihave used a Gaussian profile and for others a Voigt profile, and for the N2OXPS data I used PCI shifted Voigt profiles (PCI is explained in Chapter 6.1.2)convoluted with a Gaussian.

These different peaks reveals information about the physics studied, it istherefore important to understand why and when to use what peak shapes tomodel the recorded spectra. I will give a brief introduction to the peak shapesand why they are used. The peaks I will introduce in this section are:1. The Gaussian profile2. The Lorentzian profile3. The Voigt profile4. The PCI distorted Voigt profile

The experimental equipment has many uncertainties, the sum of these un-certainties contributes to a statistical spread in energies. Such a spread canusually be approximated by a Gaussian broadening in energy space. The math-

54

Figure 5.7: Normalized Gaussian, Lorentzian, Voigt and PCI distorted Voigt profiles.As expected the broader a peak is the less is the maximum peak value. The totalintensity (integral) is the same for all these peaks.

ematical expression for a normalized Gaussian is

G(x) =1

σ√

2πe−

12(

x−x0σ )

2

(5.10)

where σ is the standard deviation of the Gaussian and x0 is the center. Wetypically use the full width at half maximum (FWHM) to specify the width ofa curve, the FWHM is related to σ as FWHM =

√8∗ ln2×σ ≈ 2.355×σ .

Excited atoms will decay according to an exponential decay N = N0e−2γt ,where N0 is the number of excited atoms at time t = 0. 1

2γ is the time t0 it

takes for N excited atoms to decay to Ne excited atoms [24], t0 is called the

lifetime of the excited state. Transforming the exponential decay from thetime domain into energy space gives a Lorentzian function [24], therefore thelifetime broadening of an excited state is Lorentzian. A normalized expressionfor the Lorentzian is

L(x) =1π

(γ

(x− x0)2 + γ2

)(5.11)

where x0 is the center and γ = FWHM2 .

If a lifetime broadened state is excited and then detected the Gaussianbroadening from the experimental equipment will further broaden the detectedpeak, such a peak can be described by a Voigt peak. The width of the recordedpeak will be affected by the widths of both the Gaussian and the Lorentzianfunction. A Voigt function is a convolution of a Gaussian and a Lorentzian as

V (x) =∫

G(y)L(x− y)dy (5.12)

55

where G(x) is the Gaussian profile, L(x) the Lorentzian and V (x) the Voigtprofile. It is also possible to approximate the Voigt function to avoid having tocalculate it each time.

The mathematical expression for a PCI shifted Voigt profile is a bit morecomplex and I refer the interested reader to Ref. [45]. In Figs. 5.7 and 5.8 Ishow two different PCI shifted Voigt profiles, the curve PCI is a PCI shiftedVoigt profile while the curve PCI Convoluted is the same curve convolutedwith a Gaussian with a FWHM of 0.05.

Figure 5.8: The five peaks discussed here shown on different axes to facilitate com-parisons between the peak shapes. See the text for details on how these peaks werecreated. The peaks are all normalized to the same area.

The peak shapes discussed are shown in Figs. 5.7 and 5.8 where they arenormalized to have the same area. All peaks have been made with the sameLorentzian width (0.05), the same Gaussian width (0.05) (except for the curvesLorentzian and PCI 1 that are not affected by the Gaussian width) and the samecenter position (10.5). In Fig. 5.7 all peaks are normalized to the same area,while in Fig. 5.8 they are plotted separately for an easier comparison of thepeak shape.

56

6. XETECO

During my period as a Ph.D. student I have been involved in developing a newtype of spectroscopy that we call X-ray-Emission-Threshold-Electron Coinci-dence (XETECO) [46–49]. Much of my work during my Ph.D. studies havebeen centered around this interesting and novel technique (see e.g. Papers I -III). As it is a new technique I want to present it in some more detail comparedto the more established techniques discussed in Chapter 4.

It turns out that the results from XETECO are very similar to the resultsfrom XPS. An X-ray photoelectron spectrum is excited using one specificphoton energy and electrons of different kinetic energies are detected, i.e. thephoton energy hν is kept constant while the kinetic energy of the photoelec-trons are scanned. In XETECO the kinetic energy of the electrons is keptconstant (∼=0 eV) while the photon energy is scanned over threshold. I hopeto show that it is possible to interpret XETECO as TPE spectra free from PostCollision Interaction (PCI).

6.1 The physicsXETECO spectra gives information about threshold ionization dynamics.Threshold ionization has been studied for a long time using a technique calledthreshold photoelectron spectroscopy, see e.g. Refs. [50–55]. To understandthe benefits of XETECO one must first understand TPE spectroscopy.

6.1.1 Threshold photoelectron spectroscopyTPE spectroscopy can be used for valence electrons with great success. Fig.6.1 shows a TPE spectrum of the argon atom [56]. Many sharp narrow linesappear and they can all be assigned to different valence ionization thresholdsin the argon atom.

In Fig. 7.2 I show a TPE spectrum from core ionized neon (Ne 1s−1). Theionization energy obtained in Paper II is 870.11 eV. Naively one would ex-pect a symmetric peak centered at the ionization energy, but instead the TPEpeak is shifted toward higher photon energies and it is asymmetrically broad-ened. This is due to the PCI effect [45,57,58], which puts great limitations onwhat information can be extracted from a core electron TPE spectrum, as itdegrades the effective resolution.

57

Figure 6.1: A threshold photoelectron spectrum from the valence electrons in ar-gon [56]. A great many narrow symmetric lines appear showing a wealth of valenceionization thresholds.

6.1.2 Post Collision InteractionIn this thesis I refer to PCI as PCI induced on photoelectrons by Auger elec-trons unless otherwise specified. The theoretical aspect of PCI is well de-scribed in Ref. [45], but as PCI (or rather the removal of PCI) is essentialfor XETECO I will explain PCI briefly using a concrete example from PaperI (see also Chapter 7.1).

The ground state configuration of the neon atom is 1s22s22p6. The 1s bind-ing energy is 870.11 (870.17) eV, determined using XETECO (XPS) - in thisexample I will assume that the value from XETECO is correct. If the neonatom is ionized by a photon with the energy 871.11 eV the emitted electronwill have a kinetic energy of 1 eV (see Equ. 5.6). If this atom decays througha radiative decay the whole process can be described as

Ne 1s22s22p6 +hν → Ne 1s12s22p6 + e−PE (6.1)

Ne 1s12s22p6 + e−PE → Ne 1s22s22p5 + e−PE +hν ′

where the kinetic energy of e−PE is 1 eV directly after the ionization and hν ′

is the photon emitted in the core hole decay. If the excited ion decays throughAuger decay the whole process can be written as

Ne 1s22s22p6 +hν → Ne 1s12s22p6 + e−PE (6.2)

Ne 1s12s22p6 + e−PE → Ne 1s22s02p6 + e−PE + e−AE

In this process a 2s electron has filled the 1s hole while emitting another 2selectron (e−AE). It is also possible to imagine other Auger decays involving the2p orbital. The Auger electron will have a kinetic energy of ∼800 eV [59] and

58

it is obvious that the velocity of the AE is much higher than the velocity of thePE.

In a simple model it is possible to assume that the AE is emitted alongthe same path as the PE, then the AE will soon pass the PE. Before the AEpasses the PE, the PE exists in a field from a singly charged neon ion (if oneimagines that the screening the AE produces is perfect). The AE on the otherhand exists in a field from a doubly charged neon ion. After the AE has passedthe PE the screening will be reversed and the kinetic energies of the electronswill change accordingly as they now will be affected by different fields fromthe neon ion.

How much energy the PE looses in favor of the AE is determined by thedistance between the ion and the PE when the AE passes the PE. This distancedepends on the kinetic energy of the AE and the PE and how long time it takesfor the Auger decay to happen. What is difficult here is that the time it takesfor the Auger decay to happen is not constant, far from it. It depends on thelifetime of the excited state; the Ne 1s−1 lifetime is ∼ 15 fs. This spread intime of Auger electrons determines the asymmetry of the TPE peak. If theAuger decay always happens after a set amount of time the TPE peak wouldbe shifted, but not asymmetric nor broadened.

This is a very simplified model, in a more complex picture the PCI shiftdepends on what angles (with respect to each other) the electrons are emittedin and other factors, this is all well thought through in Ref. [45].

6.2 Principle of operationAfter a threshold ionization the atom/molecule will decay, mostly throughAuger decay or radiative decay. Very seldom will the decay yield both anAuger electron and an X-ray photon. By detecting the threshold electron emit-ted in the ionization in coincidence with the X-ray photon emitted in the sub-sequent core hole decay it is possible to detect only the TPEs that were notaffected by the (Auger decay induced) PCI effect. If the emitted photoelec-tron does not interact with its parent ion it is possible to see this as a two stepprocess where the threshold electron is emitted in the first step and an X-rayphoton in the second step, see also Chapter 6.3.

The coincidence spectra of threshold photoelectrons and X-ray photonsemitted in the core hole decay constitutes the XETECO signal. The photonenergy is scanned over threshold while TPEs are detected using a penetrationfield analyzer and the X-ray photons emitted in the subsequent core hole decayare detected using MCP detectors.

The TPE analyzer is described in Chapter 4.2.2, the principle of the MCPsused in the FY detectors is described in Chapter 4.1.1.

59

6.2.1 Fluorescence detectorsThe FY detectors are MCP detectors (see Chapter 4.1.1). To make sure thatonly photons are detected by the MCPs, and not ions, electrons or metastableparticles, several meshes are mounted in front of the detector. In Fig. 6.3 aschematic picture of the experimental setup is shown.

As described in Chapter 4.1.1 a high voltage is applied to the MCPs, typi-cally several thousands of volts. Therefore the MCPs needs to be contained bya material that shields the interaction region from the electrical fields from theMCPs. Otherwise these leak fields would affect the emitted photoelectrons,see Equ. 3.1.

This is done by mounting the MCP in an aluminum cylinder where thesensitive area of the MCP are facing toward the interaction region, see Fig. 6.3.In front of the MCP several meshes are mounted, starting from the interactionregion going toward the MCP detector these are:

1. Two grounded meshes. These meshes are there to minimize any leak fieldsfrom the MCP and the other meshes into the interaction region.

2. A mesh biased with ± 200 V. This mesh is used to deflect ions/electrons.3. A mesh biased with ∓ 200 V. This mesh is used to deflect electrons/ions.4. A 1100 Ångström thick polyimide filter. This filter is meant to stop any

charged or metastable particles from being detected my the MCP. It has ahigh transparency for X-ray photons, typically above 50%.

5. A biased mesh to increase the QE of the MCP, see Chapter 4.1.1.

6.2.2 Threshold photoelectron analyzerTPEs are detected using a TPE analyzer based on the penetration-field tech-nique [20], see also Chapter 4.2.2. Inside the chamber is a double set of µ-metal shields that shields the whole experiment from external magnetic fields.No magnetic materials are mounted in the chamber, hence there will be ex-tremely small magnetic fields in the interaction region. The interaction regionis also shielded from all electric fields created by the MCPs and the TPE ana-lyzer itself. The shielding from electric fields is done by enclosing all all com-ponents that can create an electric field in metallic containers. This shieldingis necessary to not affect the threshold electrons, see Equ. 3.1.

6.2.3 Detecting coincidences∼150 ns after a photon is detected by an MCP an ∼80 ns long time-windowis opened. If a TPE is detected in this time-window it is considered to be incoincidence with the photon that triggered the measurement.

This time-window is experimentally determined by ionizing helium to the2p threshold, this ionization will give many coincidences between TPEs andphotons emitted in the 2p decay. The time settings will vary depending on thesetup used, but has in our measurements been approximately these numbers.

60

As mentioned; the electron detected in this time-window is considered to bein coincidence with the photon that triggered the measurement, that means thatthey came from the same atom/molecule. There is however a probability thatthese events were in fact not related at all, that they did not at all emerge fromthe same atom/molecule. Such events can come from noise in the detectors orother uncorrelated events.

To compensate for this statistical deviation we measure false-coincidencesas well, these are measured in an equally long time-window opened 864 nsafter the first time-window. This time delay corresponds to one ring revolutionof the synchrotron. This time delay is chosen to:1. Make sure that the photon and electron detected as false coincidences can-

not be real coincidences.2. Record the false-coincidence spectra under similar conditions compared to

the coincidence spectra. This is an attempt to compensate for a possibleinhomogeneous filling of the synchrotron storage ring.

The true coincidence spectra are then obtained by subtracting the false co-incidences from all coincidences. Experience shows that the amount of falsecoincidences can be tuned to almost zero by increasing the resolution of theTPE analyzer and making sure that the time-windows are not unnecessarilylong.

6.2.4 Experimental setupThe axis of the lens in the TPE analyzer is mounted perpendicular to the po-larization and to the axis of propagation of the incident radiation. The FYdetectors are mounted at an angle of ∼ 115 with respect to the electrons pathin the lens of the TPE analyzer, perpendicular to the axis of propagation ofthe incident radiation and at an angle of ∼ 25 with respect to the polarizationvector of the radiation. A photograph of the actual layout can be seen in Fig.6.2 and a schematic drawing of the layout can be seen in Fig. 6.3.

6.3 End RemarksIn a simple model XETECO can be described as a two-step process

hν +A → A+ + e−TPE

A+ → A+′+hν

′(6.3)

where A is an atom/molecule in the ground state, A+ is a core-ionized stateof A and e−TPE is a threshold electron, while A+′

is a state of A+ after the corehole decay in which the photon hν ′

is emitted. If the two-step model is correctit implies that there is one unique way to each final state and there will beno interference in the XETECO spectra (and indeed no interference is seen inXETECO).

61

Figure 6.2: A photo of the internal chamber during a XETECO experiment. At thetop is the lens to the threshold photoelectron analyzer and the needle that is used tolet gas into the chamber comes from the bottom. The two fluorescence detectors aremounted from the sides enclosed in aluminum boxes. The "nozzle" at the front holdsthe meshes discussed in Chapter 6.2.1. The circle in the middle of the picture is wherethe X-ray photons will later enter the chamber. The polarization vector E is horizontal(parallel to the text) in this figure.

According to the simple two-step model the peak shape would be Voigt like,I have recently discovered that this is not the case which means that the simpletwo-step model is not perfect. Although the quantitative agreement betweenthe simple two-step model and XETECO spectra implies that the simple two-step model is probably a rather good approximation.

In the framework of the simple two-step model it is possible to compare theresults from XETECO with the results from XPS. The differences between theresults from XPS and XETECO have so far mainly been attributed to changesin cross-section close to threshold and errors in the calibration of the energyscale. It is possible that theoretical calculations might identify other sourcesfor these discrepancies, but for this we need a well founded theory for theXETECO process. It has recently been found by Scheit et al. [60] that a coin-cidence spectrum can be quantitatively different from a non-coincidence spec-trum, this new knowledge might help us to extract new additional interestinginformation from XETECO measurements.

So far the binding energy observed in XETECO is usually lower than valuesreported from XPS, in the case of O2 the difference is 150 meV (see Chapter7.3). So far we have attributed this to calibration errors of the energy scale.

62

It should be noted that the XETECO spectrum is well calibrated using closelying resonances in FY, therefore the energy scale for the XETECO spectrumis very accurate (as long as the energy scale of the monochromator is linear).

In each XETECO spectrum there are weak structures below threshold (seee.g. Fig. 7.12), these structures coincides (in energy) with the peaks seen inthe corresponding TPE and FY spectrum. The below threshold peaks in TPEspectra are assigned to Rydberg excitations, see e.g. Ref. [61] and referencestherein. As false coincidences are subtracted from the XETECO spectrum Ibelieve that these structures are real coincidences, they might come from pro-cesses such as:

Figure 6.3: A schematic drawing showing a cross-section of the layout in Fig. 6.2. TheMCP detectors are schematically shown as rectangles inside their aluminum shielding,photons emitted from the interaction region goes through a set of meshes (see Chapter6.2.1) before they are detected by the MCPs. The electron lens in the TPE analyzeris schematically shown as a rectangle, after the lens is a hemispherical element thatguides electron with the correct kinetic energy to the channeltron where they will bedetected. The figure also shows a schematic drawing of the needle used to let gas intothe chamber. The polarization vector of the incident photons is indicated by E.

63

• Radiative Auger - In radiative Auger the molecule decays emitting anAuger electron and an X-ray photon [62, 63]. If the energy is assumed tobe randomly distributed between the emitted particles some of them willbe detected as coincidences in the XETECO measurements.

• Emission of a slow electron subsequent to the radiative decay. This couldcorrespond to valence excited state with a highly excited Rydberg electrondecaying by emitting a slow electron.

Assuming that the structures below threshold in the XETECO spectra arenot real coincidences but due to bad resolution of the TPE analyzer, improp-erly settings of the time-windows etc. it would be reasonable to assume thatthe intensity of the XETECO structures would be proportional to the multipli-cation of the intensities of the TPE and FY peaks.

As the intensity of the XETECO structures are not proportional to the mul-tiplication of the intensities of the TPE and FY peaks (and also the fact thatthese coincidences have been observed in threshold-electron-singly-charged-ion spectroscopy in neon [64]) these peaks hints toward that this is a realphysical process giving a TPE and a singly charged ion/X-ray photon in coin-cidence below threshold.

This argument is valid under the assumption that the lifetime and decayprocesses of each excited state discussed above is similar. If the processesgiving rise to the different peaks in TPE spectrum and FY are vastly differentfor different resonances this argument is not necessarily correct and then thestructures below threshold in XETECO spectra might come from bad experi-mental resolution.

64

7. Results

In this chapter I will briefly present some of the results from the papers in-cluded in this thesis. This summary is not a complete summary of the papers,but instead I have tried to select parts from each paper. For the molecules stud-ied I refer to the innermost orbitals as 1s orbitals. As the orbitals in a moleculeare molecular orbitals they should be referred to as such, but as that can causesome confusion (e.g. 1σ , 2σ and 3σ in N2O all correspond to 1s-like orbitals)I will refer to the innermost core orbitals in molecules as 1s orbitals.

7.1 Neon - Ne

Inte

nsit

y (a

rb. u

nits

)

871870869868Energy (eV)

TPE

XETECO

FY

Figure 7.1: The FY (top), TPE (bottom) and XETECO (middle) spectra of neon nearthe 1s threshold. The vast amount of points in the spectra are an artifact from inter-polation, the real energy step is much larger, therefore narrow structures are not to betrusted.

Neon is a noble gas, neon has no vibrations nor rotations, which makes theobserved XETECO peak intuitively easy to understand. In Fig. 7.1 I show the

65

FY, XETECO and TPE spectra from neon. The TPE spectrum show an asym-metric peak with its maximum value at 870.65 eV, the XETECO spectrumshows a symmetric Voigt shaped peak centered at 870.11 eV. The FY spec-trum clearly shows the 1s−14p resonance at 868.75 eV, the additional struc-tures corresponds to the 1s−1np Rydberg series converging to threshold. The1s−14p resonance is also seen in the TPE spectrum, as discussed in Chapter6.3.

I studied neon 1s ionization using FY, TPE and XETECO, these results areshown in Paper I. The simple two-step model of XETECO (as discussed inChapter 6.3) predicts a single Lorentzian peak in the XETECO spectrum ofneon 1s ionization. In the two-step model the excitation can be described as

Ne 1s22s22p6 1S+hν → Ne 1s12s22p6 2S+ e− (7.1)

Ne 1s12s22p6 2S → Ne 1s22s22p5 2P+hν ′

where e− is a threshold photoelectron and hν ′ an X-ray photon emitted in thesubsequent core hole decay.

The XETECO peak in Fig. 7.1 is well described by a Voigt peak (see Chap-ter 5.5) giving a Ne 1s binding energy of 871.11 eV and a lifetime broadeningof ∼250 meV. This can be compared to previously published values of the Ne1s binding energy as 870.1 [65], 870.17 eV [66] and references therein, andlifetime broadening 270±20 meV [67].

Inte

nsit

y (a

rb. u

nits

)

871.5871.0870.5870.0Energy (eV)

250 meV 270 meV 300 meV TPE spectrum

Figure 7.2: A detailed investigation of the neon TPE spectrum shows a visible con-tribution of the threshold photoelectrons originating from atoms decaying through ra-diative decay as a shoulder on the low energy side of the peak. It was also possible toperform fits using the theory from Ref. [45] to estimate the lifetime broadening of theionized state.

In Fig. 7.2 I show the TPE spectrum of neon together with a theoreticalmodel for the threshold peak, the model is based on the theory in Ref. [45].

66

Below the main peak there is a shoulder, this shoulder corresponds to thresh-old photoelectrons where the parent ion decayed radiatively. By fitting oneVoigt peak (centered at hν = 870.11 eV) to the shoulder and a PCI shiftedVoigt peak to the main TPE peak it is possible to determine that ∼2% ofthreshold ionized neon decays radiatively. From these simulations it is alsopossible to say that the lifetime broadening should be in the order of 250 meV,which is in good agreement with the fitted Lorentzian width of ∼250 meVobtained from the XETECO spectrum.

7.2 Nitrogen - N2

411.0410.5410.0409.5409.0Energy (eV)

Inte

nsit

y (a

rb. u

nits

)

XETECO

TPE

FY

Figure 7.3: The FY (top), XETECO (middle) and TPE (bottom) spectra of N2. TheXETECO spectrum shows two peaks at 409.82 and 409.93 eV, these peaks are as-signed to the gerade and ungerade core hole states. The first vibration is seen as anasymmetry on the high energy flank in the XETECO spectrum, these states can alsobe seen in XPS, see Fig. 7.4. The high amount of data points comes from interpola-tion, the real energy step is larger, therefore narrow structures are not to be trusted.The intensity at the low energy flank is discussed in Chapter 6.

Neon is a "simple" system, for which a single Voigt peak at threshold can beexpected. In the nitrogen dimer (N2) one would expect several peaks. First ofall the N2 molecule will exhibit vibrations (see Chapter 5.4.1) that we expectto see in XETECO and, in addition, the core ionized state of N2 can be either

67

gerade or ungerade. Indeed both the vibrations and the gerade/ungerade corehole states were seen as shown in Papers I and II.

411.0410.5410.0409.5409.0Energy (eV)

XETECO

XPS460 eV

Inte

nsit

y (a

rb. u

nits

)

Figure 7.4: A comparison of the XPS (top) and XETECO (bottom) spectra of N2. Thegerade/ungerade components are seen as an asymmetry in the peak shape in XPS whilethey are resolved in XETECO. The first vibrations are seen in both XPS and XETECO.The high amount of data points comes from interpolation the real energy step is larger,therefore narrow structures are not to be trusted. The difference in relative intensitiesfor the gerade and ungerade components in XETECO and XPS are evident in thefigure.

In Fig. 7.3 the XETECO spectrum together with FY and TPE spectra fromthe N 1s excitations of N2 is shown. The XETECO spectrum shows two dis-tinct peaks corresponding to the gerade and ungerade core hole states. Thesestates have also been studied using state-of-the-art XPS [68] where they can beseen as an asymmetric broadening of the peak in the photoelectron spectrum,see Fig. 7.4. It is interesting to note that the SAC-CI calculations in Ref. [68]predict an almost equal intensity distribution between the ν = 0 gerade andungerade component, which is not seen using XPS in the same reference, butis seen in the XETECO spectrum.

The fact that the ratio νg=0νu=0 is different in XPS and XETECO is attributed

to cross-section differences at threshold compared to above threshold.

68

7.3 Oxygen - O2

The oxygen (O2) molecule is very similar to the N2 molecule, but in O2 Iconsider four O 1s thresholds. The ground state of molecular oxygen is a3Σ−

g , but in O2 there are two main thresholds besides the gerade and ungerade,giving a total of four O 1s thresholds to consider. The XETECO measurementsfrom the O2 molecule are presented in Paper II.

Core ionizing O2 can give a 2Σ−g,u or a 4Σ−

g,u state, the doublet(

2Σ−g,u

)and

quartet(

4Σ−g,u

)have different ionization potentials, hence they will be seen as

two thresholds in XPS and XETECO spectra, see Fig. 7.5. As both of thesethresholds will have gerade and ungerade symmetry I consider four thresh-olds, just that only two of them will be clearly resolved. According to the-ory [69] the gerade-ungerade states are separated by 50 meV in the quartetand 7 meV in the doublet.

545.5E545.0544.5544.0543.5543.0

Energy (eV)

Figure 7.5: The XPS (top) and XETECO (bottom) spectra of O2. The spectra showsthe doublet and quartet threshold (see text for details) and the fit shows the gerade andungerade components. In XETECO the vibrations in the quartet are better resolvedthat in in XPS, the relative intensities between the two thresholds is significantly dif-ferent between the two measurements.

In molecular oxygen the value of the O 1s binding energy obtained fromXETECO is vastly different from the binding energy obtained from XPS, asshown in Fig. 7.5. The ν=0 component in the quartet has a binding energy of543.19 eV in XETECO while it is 543.34 eV in XPS. This is a difference of150 meV, which is a large discrepancy; as I cannot explain these discrepanciesat the moment, I have to attribute them to calibration errors, in either XPS orXETECO.

69

In a simple theoretical approach the intensity ratio4Σ2Σ should be close to 2,

since the quartet has 4 possible spin-states while the doublet only 2. In XPSit is determined to about 2.2 while in XETECO it is closer to 6 (see Fig. 7.5).Also this I attribute to differences in cross-section close to threshold.

One possible explanation of this difference in the intensity ratio is a spin-flip in the core. Consider a Rydberg resonance (Rd) near the 2Σg,u threshold. Ifthe excitation energy for Rd is the same (or slightly higher) as the ionizationenergy for the 4Σg,u these states would be energetically degenerate (or neardegenerate). This is schematically shown in Fig. 7.6.

The electronic configuration for O2 in its ground state can be written as1σ22σ23σ24σ25σ21π42π2 3Σ−

g . In Fig. 7.6 I show a schematic picture ofhow this spin-flip in the core can occur. In order to make the picture easier tounderstand I will not show the filled shells that are not involved in the spin-flipin the core.

Figure 7.6: A schematic energy diagram of a possible spin-flip-effect in O2. Severalorbitals are left out to simplify the picture. Left An electron with the same spin asthe electrons in the 2π orbital is excited into a Rydberg orbital Rd , the term of the"core contribution" can then be written as 2Σ. Right If the excited electron would beof opposite spin with respect to the electrons in the 2π orbital the the term of the corecontribution can then be written as 4Σ and as the figure shows the molecule wouldthen be ionized. I propose the possibility that the electron excited into Rd state in the"core 2Σ configuration" can change its spin, while at the same time changing the spinof the remaining 1σ electron (or one of the 2π electrons). If this happens the moleculewould have the term 4Σ and then the molecule would be ionized. This process wouldincrease the relative signal of the 4Σ. A relative increase (compared to above thresholdXPS measurements) of the 4Σ intensity is evident in Fig. 7.5.

If the states are energetically degenerate the electron excited to the Rydbergorbital Rd could auto-ionize. However this would imply that the ion now is inthe 4Σg,u state, as it is ionized with a photon energy that matches the ionizationenergy for the 4Σg,u threshold. In order for this to happen both the remaining1σ electron (or one of the 2π electrons) and the auto-ionized electron must

70

invert their spin. This process is shown in Fig. 7.6 and in the formulas 7.2 and7.3. Consider first a resonant excitation into the Rydberg orbital Rd

O23Σ+hν → O∗

22Σ (7.2)

where O∗2 denotes the Rydberg excited state Rd . Here the notation 2Σ refers

the the core-contribution of the oxygen molecule, i.e. taking all electrons intoaccount - except the excited electron.If the excited electron (and at the same time also the remaining 1σ or one ofthe 2π electrons) changes its spin the process can be written as

O∗2

2Σ spin− f lip−→ O+2

4Σ+ e− (7.3)

and as the energy of the O∗2 state is nearly degenerate with the ionization en-

ergy for the O24Σ the emitted electron will be detected as a TPE.

Such a process could contribute to the intensity of the 4Σg,u, especially ifthere are several states in the 2Σg,u that are near degenerate with the ionizationof the 4Σg,u. As the TPE analyzer has a limited (albeit good) resolution elec-trons with a low kinetic energy (∼ 10 meV) will be detected as TPEs, hencethe resonance Rd does not have to be exactly degenerate with the ionizationenergy in the 4Σg,u state, but it can also be near degenerate as described above.The lifetime broadening of the excited state will further decrease the demandson exact energetic degeneracy.

7.4 Nitrous oxide - N2ODue to the proximity of the electronegative oxygen atom in N2O the two ni-trogen atoms in N2O are chemically different. Among other things they willhave different binding energies, this is what is called the chemical shift. Thechemical shift was a discovered by Kai Siegbahn and co-workers while work-ing with electron spectroscopy, this work later lead to Kai being awarded aNobel prize in 1981.

I have studied the influence of a N 1s core hole in N2O using differentmethods. In Paper VII I experimentally determined the vibrational constantsfor both the terminal (NT) and central (NC) nitrogen site by recording N2OXPS spectra far above threshold. The XPS spectrum of NC and NT are shownin Fig. 7.7 together with the experimental fits. These results are compared totheoretical calculations in Table 7.1.

The experimental parameters are obtained by fitting PCI shifted Voigt pro-files [45] to each vibrational envelope. NC is well described using only onevibrational progression called the quasi-symmetric stretch (v1), while two pro-gressions are needed to fit the data for NT, called quasi-symmetric stretch (v1)and quasi-antisymmetric stretch (v3).

As N2O is not symmetric under coordinate inversion (NT −NC −O vs.O−NC −NT) it is impossible to talk about symmetric and antisymmetric

71

Inte

nsity

(ar

b. u

nits

)

42403836Kinetic energy (eV)

4x103

3

2

1

0

Inte

nsity

(ar

b. u

nits

)

42.041.641.240.8Kinetic energy (eV)

Data Fit v1 = v3 = 0 v1 = 1 – 3; v3 = 0 v1 = 0; v3 = 1 v1 = 1, 2; v3 = 1

5x103

4

3

2

1

0

Inte

nsity

(ar

b. u

nits

)

38.037.637.236.8Kinetic energy (eV)

Data Fit v1 = 0 – 4

Figure 7.7: Bottom A photoemission spectrum of N2O recorded with a photon energyof 450 eV. Top left The central nitrogen can be well described using one vibrationalprogression of PCI peaks. Top right The terminal nitrogen can be well described us-ing two vibrational progressions of PCI peaks, only the most intense components areshown. The same Gaussian width, lifetime broadening (Γ) and energy of the Augerelectron was used for both thresholds. See the text and Table 7.1 for details.

stretch (see Chapter 5.4.1). But, as the vibrational modes are strongly relatedto the symmetric and antisymmetric stretch in a linear molecule such as CO2

that is symmetric under coordinate inversion (O1 −C−O2 vs. O2 −C−O1)they are called quasi-symmetric and quasi-antisymmetric.

The two vibrational modes in NT and the single vibrational mode in NC

were fitted using PCI profiles [45] (see also Chapter 5.5) and assuming thatthe molecular potential can be approximated by a Morse potential (see Chapter5.4.1). The energies of the vibrational components can then be described byEqu. 5.9, but slightly modified to account for an offset in energy by adding aconstant energy E0.

Ev = E0 +ωe

(v+

12

)−ωexe

(v+

12

)2

(7.4)

if the vibrational modes are uncoupled it is straightforward to express Equ.7.4 to deal with two vibrations simultaneously

Ev1,v3 = E0 +ωe1

(v1 +

12

)−ωe1xe1

(v1 +

12

)2

+ (7.5)

+ωe3

(v3 +

12

)−ωe3xe3

(v3 +

12

)2

72

If the two vibrational components excited are (ν1,0,0) and (0,0,ν3), thenthe (ν1,0,ν3) vibrations will most likely also be excited. Further, if the two vi-brational modes are uncoupled the energies of these vibrations can be writtenas

E (v1,v3) = Ev1 +Ev3 −Ev1=0,v3=0 (7.6)

and the intensity of the vibrational combination components (v1 = 0,v3 = 0)can be approximated as

I (v1,v3) =Iv1Iv3

Iv1=0,v3=0(7.7)

If Equs. 7.5, 7.6 and 7.7 are used when performing a curve fit for NT it turnsout that ωexe = 0 for one of the vibrational progressions. The calculations donein Paper VII showed that I (v1,v3) = Iv1 Iv3

Iv1=0,v3=0. By not imposing the restriction

set by Equ. 7.7 in the experimental fit it was possible to fit also NT withoutanharmonicity; these are the results presented in Paper VII.

The final results of the experimental fit and calculations are presented inTable 7.1. The column Opt refers to an optimized geometry whereas ECACCSD(T) and CCSD refers to a non-optimized geometry. As the XPS spec-trum used here was recorded using an excitation energy of 450 eV it is stillinfluenced slightly by the shape-resonance (see Fig. 7.9 and discussion be-low), hence the computed geometry is not correct and an optimization wasdone.

As this spectrum is influenced of the shape-resonance the geometries ob-tained in Paper VII are not necessarily accurate. We tried to take this into ac-count by optimizing the ECA CCSD(T) 2D potential, these results are shownin Table 7.1, column Opt. In short this optimization was done using the inter-atomic bond lengths as a fitting parameter and changing them in order to getthe calculated relative intensity of the first vibrational peak(s) to match the ex-perimental intensity of these peaks. The optimized geometry is an optimiza-tion of the ECA CCSD(T) 2D potential surface as we predicted this model togive the best results.

In Paper II we present XETECO data from N2O. Using information aboutthe vibrational energies from Paper VII it was possible to fit vibrational pro-gressions to the terminal (NT) and the central (NC) nitrogen site, as shown inFig. 7.8. The 1s binding energy of the adiabatic component in NT was deter-mined to be 408.43 (408.44) eV using XETECO (XPS) and for NC=NT+4.01(+4.02) eV in XETECO (XPS).

It was also possible to extract the relative intensities for the two vibrationalenvelopes, and I obtained NT

NC≈ 2.5, see Fig. 7.8. In XPS excited far above

threshold the same value is close to 1, this difference is interpreted as changesin cross-section near threshold. The cross-section (σ ) of both NT and NC can

73

Experimental Fit ECA CCSD(T) ECA CCSD Opt

NC 1s−1

Γ (meV) 118(2) - -

ωe1 (meV) 136(2) 125 114 125

ωe3 (meV) - 225 249 225

R(1,0,0) 0.60(1) 0.467 (0.472) 0.367 0.592 (0.597)

R(2,0,0) 0.20(6) 0.110 (0.111) 0.043 0.179 (0.182)

R(0,0,1) - 0.002 (0.004) 0.059 0.007 (0.009)

R(1,0,1) - 0.000 (0.002) 0.003 0.003 (0.005)

∆RNN (Å) - +0.010 -0.007 +0.0125(3)

∆RNO (Å) - +0.043 +0.045 +0.0485(6)

NT 1s−1

Γ (meV) 118(2) - -

ωe1 (meV) 178(1) 175 186 175

ωe3 (meV) 303(2) 295 304 295

R(1,0,0) 0.82(1) 0.840 (0.819) 1.052 0.840 (0.817)

R(2,0,0) 0.29(2) 0.301 (0.287) 0.497 0.300 (0.286)

R(3,0,0) 0.05(2) 0.061 (0.057) 0.141 0.060 (0.057)

R(0,0,1) 0.31(2) 0.276 (0.289) 0.365 0.301 (0.314)

R(1,0,1) 0.21(2) 0.192 (0.194) 0.331 0.207 (0.208)

R(2,0,1) 0.07(2) 0.055 (0.054) 0.133 0.059 (0.058)

∆RNN (Å) - -0.008 -0.007 -0.0068(9)

∆RNO (Å) - -0.065 -0.071 -0.0661(9)

Table 7.1: The experimental parameters were obtained by fitting PCI shifted Voigtpeaks [45] to the XPS spectrum shown in Fig. 7.7. The table also shows results fromdifferent theoretical models as presented in Paper VII. The model Opt refers to an op-timized geometry as the experimental results are still affected by the shape resonance(see Fig. 7.9) and will therefore not be comparable to calculations not taking the shaperesonance into account, see text for details.

be seen in the upper part of Fig. 7.9 but it was impossible to measure σ closeto threshold in that experiment.

Calculating the oscillator strengths (shown in the bottom part of Fig. 7.8) forNT and NC and extrapolating to threshold gave a value of NT

NC≈ 1.8. The dif-

ference between the calculations and experiment could perhaps be attributedto high Rydberg states excited at NC auto-ionizing to the threshold of NT, ina similar fashion as discussed for O2 already. This auto-ionization process forN2O could be described as

NNO+hν → NN∗O (7.8)

74

413.0412.0411.0410.0409.0408.0Photon Energy/ eV

-4 -2 0

0.03

0.02

0.01

0.00

fν3

-4 -2 0

Nt Nc

FY

XETECO

TPE

XPS

sσ sσ

pπ

pσpσ

pπdσdπ

E - Eion (eV)

Figure 7.8: Top XPS, TPE, XETECO and FY spectra from N2O The relative intensi-ties of the two thresholds differ between XPS and XETECO. Also for N2O the bindingenergies for XETECO is lower than the binding energies obtained from XPS (abovethreshold) measurements. Bottom Calculated oscillator strengths for both NT and NC

scaled by the energy density for the corresponding Rydberg series.

where the star (∗) denotes a core hole, here it is located on NC. If this excitationnearly overlaps (in energy) with the ionization energy for NT one can imaginethat the core hole jumps from one atom to the other. This could be describedas

NN∗O → N∗NO (7.9)

75

but as the excitation energy of NN∗O was only slightly higher than the ion-ization energy for N∗NO this state will be in an ionized state, this can be seenas

N∗NO → N+NO+ e− (7.10)

and as the energy of the excited state NN∗O is very close to the ionizationenergy for N+NO the emitted electron can be detected as a TPE. We label this"core hole jump" auto-ionization and the spin-flip auto-ionization discussedfor O2 core vacancy rearrangement (CVR).

1.2

1.0

0.8

0.6

0.4

0.2

0.0

Cro

ss s

ectio

n (M

Bar

n)

460450440430420410

Excitaton energy (eV)

NC

Schmidbauer et al. Our data Theory

1.2

1.0

0.8

0.6

0.4

0.2

0.0

Cro

ss s

ectio

n (M

Bar

n)

460450440430420410

Excitaton energy (eV)

NT

Schmidbauer et al. Our data Theory

2.0

1.5

1.0

0.5

0.0460450440430420410

Excitaton energy (eV)

NC

Schmidbauer et al. Our data Theory

2.0

1.5

1.0

0.5

0.0460450440430420410

Excitaton energy (eV)

NT

Schmidbauer et al. Our data Theory

Figure 7.9: Upper part The cross-section σ for NC (left) and NT (right) in N2O. Lowerpart The asymmetry parameter β for NC (left) and NT (right) in N2O. The cross-section is normalized to the values from Schmidbauer et al. [70] at 450 eV from NC

and scaled by a factor 0.6, as suggested by Schmidbauer et al. Included in the figureis also theoretical results.

In Paper VIII I investigated the cross-section σ and asymmetry parameterβ in N2O as function of photon energy to further investigate the possibility ofthis auto-ionization process. I could however not find any changes in σ thatcould strengthen the possibility of CVR.

With the setup used it was impossible to measure close to threshold, at thelowest measured energy (∼2 eV above the NT and NC 1s thresholds) the ratioNTNC

≈ 1.5. With the results from the XETECO measurements it is possible to

predict a significant change inσNTσNC

for low energies. This could be possible

to measure using existing techniques, such as a magnetic bottle where the

76

transmission function is flatter (compared to the transmission function in XPS)for low kinetic energy electrons.

In N2O there are two shape resonances (one for each nitrogen site) abovethreshold, they are clearly seen in the upper part of Fig. 7.9. The measurementsof the cross-section (σ ) and the angular distribution parameter (β ) in PaperVIII are compared to previous measurements by Schmidbauer et al. [70] andrecent theory.

In the upper part in Fig. 7.9 I show the cross-section of NT and NC as afunction of photon energy and comparisons to theoretical results. The theoryquantitatively predicts the shape resonances and the agreement with the datafrom Schmidbauer et al. is fair.

In the electric dipole approximation it is possible to calculate the angulardistribution of photoelectrons as depending on one parameter β (called theasymmetry parameter). β will be different for different elements and differentorbitals, β is also sensitive to the chemical environment as shown in the lowerpart of Figs. 7.9. One way of defining β is

I (θ) =σ4π

[1+

β2

(3cos2 θ −1

)](7.11)

where I (θ) is the relative intensity in angle θ . θ is the angle between the out-going electron and the polarization vector of the (linearly polarized) ionizingphoton and σ is the angle integrated cross-section [39, 40].

In Paper VIII we could measure the outgoing electrons parallel and perpen-dicular to the polarization vector, it is then possible to calculate β as

β = 2× I (0)− I (90)I (0)+2I (90)

(7.12)

and σ asσ = I (0)+2I (90) (7.13)

where I (0) and I (90) are the intensities measured parallel and perpendic-ular to the polarization vector. The greatest discrepancy when comparing ourdata to the data from Schmidbauer et al. is a discrepancy in β for the centralnitrogen atom (NC) for energies below ∼416 eV (shown in the lower left partof Fig. 7.9). The theory presented in Paper VIII reproduce our findings in thatregion well.

In the left part of Fig. 7.10 the vibrationally resolved cross-section as afunction of photon energy for NC is shown together with theoretical predic-tions. The maximum of the shape resonance shifts toward higher excitationenergy with an increase in the vibrational quanta ν1. This upward shift can,in analogue to the findings in Ref. [71], be interpreted as an elongation ofthe equilibrium N −N and N −O bond lengths in the NC core-ionized state(compared to the ground state), which agrees with the results in Table 7.1.

The vibrationally resolved cross-section for the quasi-symmetric and quasi-antisymmetric stretch in NT can be seen together with theoretical predictions

77

Figure 7.10: The vibrationally resolved cross-section of NC and NT as a function ofphoton energy. The theory qualitatively reproduces both the shape and upwards shiftof the maximum of the shape resonance. The notation (v00) corresponds to ν1 - thequasi-symmetric stretch and (00v) corresponds to ν3 - the quasi-antisymmetric stretch.Note that the y-scale is logarithmic. The parameters used in the experimental fit for Γand ωx are the same as the experimental parameters in Table 7.1.

in the middle and right part of Fig. 7.10. The quasi-symmetric stretch hasthe highest cross-section, and the maximum of the shape resonance for thequasi-symmetric stretch shows a shift toward lower excitation energy with in-creasing ν1. The quasi-antisymmetric stretch has a lower cross-section, andthe maximum of the shape resonance shows a slight shift toward higher exci-tation energy with increasing ν3. Again, analogue to the findings in Ref. [71],the shift in ν1 can interpreted as a contraction of both the N −N and N −Obond lengths in the NT core-ionized state.

7.5 Carbon dioxide - CO2

CO2 is a triatomic linear molecule, just as the molecules discussed in Chapter5.4.1 and will therefore have the same vibrations as in Fig. 5.6. As for N2Othe symmetric stretch is called ν1 while the antisymmetric stretch is called ν3.

In Paper III the CO2 molecule was studied using XETECO, this is one of thelongest molecular XETECO measurements ever did (the effective acquisitiontime is ∼85 hours for this spectrum), hence the spectrum has relatively goodstatistics.

In Fig. 7.11 I show the FY, XETECO and TPE spectra from CO2. Thevertical line at 541.17 eV represents the ionization energy for CO2 O 1s−1

obtained from the XETECO data. The other vertical lines are there to assistthe reader to align the three spectra with respect to eachother.

The XETECO spectrum were compared to theoretical calculations fromRef. [72] giving a surprisingly good agreement between results based on bothSDCI and ECA SDCI and the experimental data. I have also compared the

78

542.5542.0541.5541.0540.5540.0Photon energy (eV)

Inte

nsity

(ar

b. u

nits

)

XETECO

FY

TPE

Figure 7.11: The FY (top), XETECO (middle) and TPE (bottom) spectra of CO2. Thevertical line at 541.17 eV represent the O 1s−1 threshold obtained from the XETECOdata. The first vibrational peak can just be seen in the TPE spectrum. The other verticallines are just guides for the eye to show that the structures in FY, TPE and XETECOcorresponds to each other.

XETECO data to recent calculations by Hatamoto et al. [43] where they usedECA CC-SD(T) which also gave a good agreement. In Fig. 7.12 the compari-son between SDCI [72] and XETECO is shown, the other theories (not shown)gave similar results although the intensity of the individual components varies.These theories were not calculated for XETECO, but for above threshold XPSmeasurements. In the simple two-step model I employ for XETECO this the-ory would be applicable for all excitation energies. Since the emitted photo-electron interacts with the parent ion (e.g. CO2 has shape-resonances) this isnot the case.

Studying the shape-resonance in CO2 vibrationally resolved (through curvefitting XPS data) shows that the relative ratio of each vibrational componentremains more or less the same, see Ref. [73]. This helps to explain whytheoretical models for the intensities far above threshold (above the shape-

79

Inte

nsity

(ar

b. u

nits

)

542.5542.0541.5541.0540.5540.0Photon energy (eV)

XETECO SDCI Adiabatic transition Asymmetric stretch Symmetric stretch Combination

Figure 7.12: A comparison of the SDCI [72] theory with the XETECO data, a similaragreement was found using both the ECA SDCI [72] and CC-SDT(T) [43] theories(not shown). The theoretical values are broadened with a Voigt function using a life-time broadening of 165 meV and a Gaussian width of 90 meV. The theoretical spec-trum is normalized to have no background and the same max value as the experimentaldata, a flat background has been removed from the experimental data. The structuresbelow threshold corresponds, in energy, to the resonances seen in both the FY andTPE spectra.

resonance) can be applied to XETECO data close to threshold and still givequalitatively good agreements. Note that in Ref. [73] the authors assumedone vibrational progression, therefore it is not evident that the results fromRef. [73] can be applied if two vibrational progressions are considered.

In Fig. 7.13 I show a comparison of XETECO and XPS data [43]. Thewidth of the second peak at ∼541.5 eV is similar in both measurements whichsuggests that the experimental resolution is the similar in both experiments.The peak at ∼541.65 eV and the additional intensity at ∼541.36 eV in theXETECO spectrum (as indicated by arrows in Fig. 7.13) corresponds well inenergy to vibrational components in the symmetric stretch [72].

The XETECO peak has a low energy flank not visible in the XPS spectrum,we attribute this peak to highly excited Rydberg states giving intensity in theXETECO signal (see Chapter 6). If this assumption is correct it is likely thatall vibrational peaks would have a similar asymmetry. Here it is worth to notethat no hints of this asymmetry was seen in the XETECO spectrum of neon(see Fig. 7.1). I speculate that it could perhaps be associated with the increaseof internal degrees of freedom in molecules compared to atoms.

80

Inte

nsity

(ar

b. u

nits

)

542.5542.0541.5541.0540.5540.0Energy (eV)

XETECO XPS

Figure 7.13: A comparison between XPS [43] and XETECO from CO2. The peak at∼541.5 eV shows that the experimental resolution is similar for both XETECO andXPS (about 90 meV in XETECO). The low energy tail in the XETECO spectrumis discussed in the text, both the peak at ∼541.65 eV and the additional intensityat ∼541.36 eV in the XETECO spectrum (indicated by arrows) corresponds well inenergy to vibrational components in the symmetric stretch [72]. As no binding energywas given in Ref. [43] the XPS spectrum is aligned by eye to reproduce the bestoverlap of the two spectra. To facilitate comparisons to Fig. 7.12 a flat background hasbeen removed from the XETECO spectrum.

7.6 Helium - HeSome of the research presented in this thesis is about doubly excited helium,namely Paper IV, V and VI.

Even though helium seems to be such a simple system, at first sight onemight think that it is almost as simple as hydrogen, that is not the case. Theelectrons in helium are so strongly correlated that it is a rather difficult atom tounderstand. Double excitations in helium was seen already in the 1920:ies byCompton et al. [74], in the 1960:ies Madden and Codling [75] saw a featurerich absorption spectrum from doubly excited helium, which was later studiedin detail by Domke et al. [76].

The series I have studied are the series (excited from the GS) converging tothe second ionization threshold (N=2 threshold). Strictly speaking there is notone threshold but three, namely the 2s1/2, 2p1/2 and 2p3/2 thresholds. In theLS coupling scheme and electric dipole approximation there are three allowedseries converging (from the GS) to the N=2 threshold(s), they can be labeledas n+, n− and n0, this notation qualitatively follows the notation of Cooper etal. [77].

In a simplified model for the n+ and n− series the excited states can be seenas a linear combination of s and p orbitals. The excitation can be written as:

He 1s2 1S+hν → He (|2s〉 |np〉± |2p〉 |ns〉) 1P (7.14)

81

The n+ series corresponds to ± ⇒ + and the n− series to ± ⇒ −. There isalso the n0 series, the excitation into a n0 state can be described as:

He 1s2 1S+hν → He 2pnd 1P (7.15)

Here we see that the selection rules from Chapter 5.2 are valid since ∆L = 1for all excitations (see Chapter 5.2).

I have studied the fluorescence decay of doubly excited states in helium.I employ a two-step picture when describing these transitions where the in-cident photon excites helium into a doubly excited state, this state will thendecay radiatively. As for the two-step model used in XETECO this impliesthat, if the model is correct, there will be no interference effects in the FYspectrum of helium. This two-step model can be written as

He 1s2 +hν → He∗ (7.16)

He∗ → He∗′ +hν ′

where He∗ is a doubly excited state below the N=2 threshold, see formulas7.14 and 7.15. The doubly excited state will decay to the state He∗′, that canbe written as He 1sn′l, while emitting a photon. Here n′ and l defines thefinal state; n′ = 1,2, . . . and l = 0,2 (s or d) according to the selection rulesin Chapter 5.2. This is a simplified model, the doubly excited states are notexactly described by formulas 7.14 and 7.15, nor can all final states be writtenas He 1sn′l, but if the energy of hν ′ is ∼40 eV the final states can be writtenHe 1sn′l.

7.6.1 Field free environmentIn Paper IV I studied the fluorescence from doubly excited helium in a fieldfree environment. Fig. 7.14 shows the FY from some of the first doubly ex-cited states, these can be compared to previously published spectra, see e.g.Refs. [76, 78–80]. The spectra discussed here are recorded in a geometry thatstrongly favors detection of 1D2 final states while minimizing detection of 1S0

final states. All other final states are forbidden in LS coupling and the electri-cal dipole approximation.

For high n the spin-orbit interaction of the inner electron becomes non-negligible, causing a breakdown of the LS coupling, leaving the only remain-ing selection rules to be ∆J = 1 and the change of parity [78]. This leads to newseries being observed in the FY spectrum, where the 3D series is one [78]. InFig. 7.14 one member of the 3D series is seen at a slightly higher in excitationenergy than 6+.

For all states except the 3D, 60, 7−, 70 and 8− states the solid line corre-sponds to theoretical calculations [81] with only 1D2 final states. The dashedline corresponds to an estimated maximum contribution of 1S0 final statesfrom the same theoretical calculations, this estimate is discussed below. For

82

63.72063.620 64.14064.120 64.48564.445

64.65664.645 64.83564.805 64.92064.905

65.01064.995 65.06065.045Photon energy (eV)

65.15065.135

x10 x10

x5

x5

30

40

50

60

70

3+

4+

5+

6+

4-

5-

6-

7-

8-

3D

Figure 7.14: The FY from some of the first resonances in the series converging to theN=2 threshold in helium. The solid and dashed curves correspond to theoretical cal-culations [81]. For the 3D, 60, 7−, 70 and 8− no theoretical predictions were available,therefore the solid line is a best fit using well known resonance energies. The solid linecorresponds to only 1D2 final states while the dashed line has some contribution from1S0 final states as well (Pv = 0.07). The relative normalization between experimentand theory is done using the 40 resonance.

the resonances where no theory was available a fit was done as seen in Fig.7.14. The 40 resonance is used to calibrate the intensity scale between theoryand experiment in Figs. 7.14, 7.16, 7.17 and 7.18.

The fluorescence was detected using a grazing incidence Rowland spec-trometer (see Chapter 4.2.1) with a small acceptance angle mounted almostparallel to the polarization axis of the incident radiation, as schematically pic-tured in Fig. 7.15. It was possible to estimate the maximum contribution of1S0 final states through simple geometry. The major part of the contribution of1S0 final states does not come from the spectrometer’s acceptance angle, nora possible misalignment with the polarization vector (as this misalignment

83

would have to be ∼ 5 to contribute significantly). Instead we attribute this toa vertical component in the incident radiation.

Figure 7.15: A schematic picture of the setup during the field free measurements.Helium is contained in a gas cell with three ultra thin aluminum windows; two forthe incident photons and one for the scattered photons. The polarization vector of theincident radiation is almost parallel to the direction of the scattered photons towardthe spectrometer, schematically shown here. A photodiode is mounted behind the gascell to measure transmission.

Equ. 7.11 shows the angular distribution of not only electrons but also ofphotons. β takes different values depending on what orbitals are involved inthe transitions, see e.g. Ref. [79]. With the spectrometer aligned as it is in Fig.7.15 the 1D2 final states will have a much higher probability of being detectedthan the 1S0 final states.

The component of 1S0 final states detected can be estimated using the for-mula Γ∆Ω

na→ml ∝ [(0.9+0.15Pv)Γna→md +1.5PvΓna→ms] where the vertical frac-tion of polarization Pv relates the intensity of the horizontal (Ih

in) and vertical(Iv

in) polarization direction in the expression for the total incident intensityIin = PvIv

in +(1−Pv) Ihin. Γ∆Ω

na→ml is the scattering in the small solid angle mea-sured in the experiment. We estimated Pv ≤ 0.07 and Figs. 7.14, 7.16, 7.17and 7.18 shows the two extreme case where Pv = 0 (solid curve) and Pv = 0.07(dashed curve).

The fluorescence yield spectra in Fig. 7.14 were recorded using the inte-grated signal from the spectrometer in the excitation energy interval 63.58-65.16 eV. As the X-ray emission spectra (see Figs. 7.16, 7.17 and 7.18) aremeasured using the same spectrometer the intensity of the FY peaks will beproportional to the intensity of the measured X-ray emission spectra.

In Fig. 7.14 the FY for the n+ series is shown, the FY is almost constantwith increasing n. The low lying n+ states are also significantly energeticallybroadened (compared to the monochromator bandpass) by their lifetime [76]hence the peak maximum will be lower due to the increased width (see Fig.5.7 where the integral is the same for both the Gaussian and Voigt profile,but the Voigt profile has a much lower maximum due to the extra broadeningintroduced by the Lorentzian). In Fig. 7.14 a hint of the 3+ resonance can

84

maybe be seen while the 4+, 5+ and 6+ resonances are clearly visible. TheFY for higher n can be seen in e.g. Refs. [78–80].

The fluorescence yield for the low lying n− and n0 series are also shown,for the n0 series the fluorescence yield goes down with increasing n whilethe fluorescence yield is almost constant for the n− series. For higher n thefluorescence yield for both the n− and n0 series keeps decreasing, see e.g.Refs. [78–80].

The theory predicts the relative intensities well, with the exception of then+ series where the theory seem to underestimate the experimental data.

By tuning the photon energy to the maximum to each of the resonancesin Fig. 7.14 it was possible to record resonant X-ray emission spectra (seeChapter 5.3.2) from each of these resonances. As the X-ray emission spectra isintegrated over a much longer time than a typical FY spectrum it was possibleto record X-ray emission spectra even from the low lying n+ states that arebarely visible in FY.

Figs. 7.16, 7.17 and 7.18 shows the X-ray emission spectra from each reso-nance, the emission spectra are labeled according to the resonance they wereexcited on. As seen in Fig. 7.14 it is impossible to resolve the 60,7− states(with this resolution), therefore the X-ray emission spectrum from each ofthese two states will not be "pure", but will have contaminations from the nearlying state.

The solid and dashed lines in Figs. 7.16, 7.17 and 7.18 corresponds to thesame theoretical calculations used in Fig. 7.14 (from Ref. [81]), the solid linehas only 1D2 final states while the dashed line has some contribution from 1S0

final states as well (Pv = 0.07).The y-scales in Figs. 7.16, 7.17 and 7.18 are logarithmic, this is to empha-

size the final states with low relative intensity visible in Figs. 7.16 and 7.17.The spectra from 30 and 40 were measured with a better resolution than the re-maining spectra, that is why the peak shape is different for 30 and 40 comparedto the other spectra in Figs. 7.16, 7.17 and 7.18.

By determining the energy of the photon hν ′ (the photon emitted in thecore hole decay) in formula 7.16 it is possible to determine what final statethe excited helium atom is in after the decay.

Both the n′ and the l quantum number (see discussion in connection withformula 7.16) can be different in each decay - i.e. there are several final statesavailable for each resonance, yielding several peaks of different intensity inthe X-ray emission spectra. This is clearly seen in the X-ray emission spectrafrom 30, 40, 3−, 4− and 5− in Figs. 7.16 and 7.17. Some final states cannot beresolved but can instead be seen as an asymmetric broadening of the peaks,this is clearly visible in 3+ in Fig. 7.18.

The reader should note that the energy scale is final state energy, whichis related to the emission energy by the simple relation final state energy =excitation energy - emission energy. A summary of the final state energies in

85

46

0.1

2

46

1

2

25.024.524.023.523.022.522.0Final State Energy (eV)

2

46

0.1

2

46

1

2

46

1

2

46

2

4

6

1

2

4

30

40

50

60

21.020.5

21.020.5

Figure 7.16: Experimental n0 → 1sml scattering spectra compared to theoretical pre-dictions [81]. The 1s2s final states are shown as inserts. The solid vertical lines corre-spond to 1D2 final states while the dashed vertical lines correspond to 1S0 final statesstarting with 1s3l around 23 eV and ending with 1s6l at about 24.2 eV. The experi-mental spectra are normalized to the integrated FY for each resonance. The solid anddashed lines correspond to theoretical predictions where the solid line has only 1D2 fi-nal states and the dashed line has some contribution of 1S0 final states (Pv = 0.07). Therelative normalization between experiment and theory is done using the 40 resonance.

86

4

0.12

4

1

25.024.524.023.523.022.522.0Final State Energy (eV)

4

0.12

4

1

4

0.12

4

1

4

0.12

4

1

68

0.1

2

4

6

3-

4-

5-

6-

7-

Figure 7.17: Experimental n− → 1sml scattering spectra compared to theoretical pre-dictions [81]. The solid vertical lines correspond to 1D2 final states while the dashedvertical lines correspond to 1S0 final states starting with 1s3l around 23 eV and end-ing with 1s6l at about 24.2 eV. The experimental spectra are normalized to the inte-grated FY for each resonance. The solid and dashed lines correspond to theoreticalpredictions where the solid line has only 1D2 final states and the dashed line has somecontribution of 1S0 final states (Pv = 0.07). The relative normalization between exper-iment and theory is done using the 40 resonance. Note that the normalization for 3− isarbitrary.

87

4

68

0.1

2

4

6

25.024.524.023.523.022.5Final State Energy (eV)

6

80.1

2

4

6

6

80.1

2

4

6

0.1

2

3

456

3+

4+

5+

6+

Figure 7.18: Experimental n+ → 1sml scattering spectra compared to theoretical pre-dictions [81]. The solid vertical lines correspond to 1D2 final states while the dashedvertical lines correspond to 1S0 final states starting with 1s3l around 23 eV and end-ing with 1s6l at about 24.2 eV. As the integrated FY for each resonance is low it wasimpossible to normalize the experimental spectra in the same way as for the n0 andn− series. Instead a method that takes the integrated photon flux, lifetime broadeningof the state and acquisition time into account was adopted. The solid and dashed linescorrespond to theoretical predictions where the solid line has only 1D2 final statesand the dashed line has some contribution of 1S0 final states (Pv = 0.07). The relativenormalization between experiment and theory is done using the 40 resonance.

88

singly excited helium can be found in the NIST database [82]; the energies forthe doubly excited states can be found in e.g. Ref. [76].

The relative intensity of these final states have earlier been studied by us-ing the photons from the secondary decay [81,83] (the secondary decay is thedecay of He∗′ in formula 7.16, in formula 7.17 the secondary photon corre-sponds to hν ′′) to determine the relative intensities of the corresponding finalstates.

7.6.2 Helium in weak external fieldsDoubly excited states in helium close to the N=2 threshold has recently gotsome attention in the literature, see e.g. Refs. [42,78–81,83–85]. I have studiedthe influence of weak static electric and magnetic fields on doubly excitedstates close to the N=2 threshold.

Figure 7.19: The two different setups used to study helium in magnetic fields (B-fields) and static electrical fields (ε-fields), the MCPs are shown as cylinders. For theelectric field experiment there are two MCPs mounted, one that measures FY fromhelium in an electric field and one that measures FY from helium in a field free re-gion. This setup was used to facilitate the comparison of the two cases as accuratelyas possible. In both experiments the measurements were done "perpendicular" to thepolarization vector of the incident photons as shown in the figure. In this case perpen-dicular is not that well defined as the acceptance angle is large.

As shown in Fig. 7.19 the helium gas is contained in a different gas cell foreach experiment. On the gas cell one or two (depending of what setup is used)ultra thin membranes are mounted. Close to each membrane a MCP detectoris mounted. In both experiments the sensitivity to both S and D final stateswere estimated to be similar.

89

The ultra thin membranes (∼1800 Ångström thick) separate the gas cellfrom the vacuum chamber. The membranes are composed of aluminum andcarbon, the materials were chosen to give high transmission around 40 eV (thisenergy corresponds to the decays shown in Figs. 7.16, 7.17 and 7.18 or hν ′

in formula 7.17) while giving a low transmission below 25 eV (this energycorresponds to the photon hν ′′ emitted in the decay of the He∗′ in formula7.17). The full excitation and radiative decay process can be thought of as(similar to formula 7.16):

hν +He → He∗ (7.17)

He∗ → He∗′ +hν ′

He∗′ → He∗′′ +hν ′′

where He is the ground state of helium, He∗ is a doubly excited state and He∗′

is a singly excited state in helium. He∗′′ can be any state with lower energythan He∗′, including the ground state. As long as He∗′′ is an excited state itwill decay further. The primary radiation corresponds to hν ′ (∼40 eV) and thesecondary radiation to hν ′′ (<25 eV). This is a simplified model, the primarydecay can also give a doubly excited state or the photon can be elasticallyscattered.

The main effect of both the electric and magnetic field is state mixing. He-lium has an abundance of states [86] not possible to excite from the groundstate (using a photon) within the electric dipole approximation and the LS cou-pling scheme (see Chapter 5.2). Excitation of forbidden states has a negligiblecross-section compared to the allowed 1P1 states. However, the fluorescencebranching ratio (FBR) may be much higher for some forbidden states com-pared to the allowed states.

Due to the presence of an external field the forbidden and the allowed stateswill be intermixed with each other. Hence it is possible to excite an electroninto an allowed state (with a relatively low FBR). This state is mixed (dueto the external field) with a forbidden state (that might have a relatively highFBR). Due to state mixing it is therefore possible to get a relatively high FBRfrom states in helium when an external field is applied compared to the FBRin the field free case.

An easy way to see this is by calling ground state |GS〉, the excited allowedstate |A〉 and the excited forbidden state |B〉. In the field free case the excitationcan be described as

〈A|D |GS〉 (7.18)

which will then decay primarily through Auger decay as the FBR is low forthe |A〉 state. In an external field the excitation can be seen as

〈aA+bB|D |GS〉 (7.19)

where a and b defines how much the states mixes. D is the electrical dipoleoperator, which corresponds to the photon making the excitation. This means

90

that the excited state might, as the excited state is not a pure |A〉 state any morebut a linear combination as |aA+bB〉, have a significant higher fluorescence,as the state |B〉 can have a significantly higher FBR than |A〉. This discussioncan of course be held "the other way around" resulting in a lower fluorescencewhen an external field is present.

Helium in weak static electric fieldsHarries et al. [87] showed the influence of strong static electric fields on thedoubly excited states near the N=2 threshold, with the lowest field being 9170V/cm and the highest 84.4 kV/cm.

In Paper V we show that even weak external fields (11 - 10440 V/cm) havean influence on highly doubly excited states in helium. A similar study wasalso done by Prince et al. [85]. In the FY there is a significant differencealready at fields as low as 44 V/cm compared to the field free situation, this isevident in the dip at ∼65.39 eV that has vanished at 44 V/cm, see Fig. 7.20.

The vanishing of the dip at ∼65.39 eV is a clear indication of field inducedstate mixing as described below where I discuss the influence of a magneticfield on doubly excited states of helium.

Figs. 7.20 and 7.21 shows the influence of weak static electric fields ondoubly excited helium near the N=2 threshold. The field strength start fromthe field free case and is increased to a maximum field of 10440 V/cm. For then+ series the field mixes in states with a higher FBR, thereby increasing thetotal fluorescence for the n+ series. For the n0 and n− series the field mixesin states with a lower FBR thereby decreasing the total fluorescence from then0 and n− series. Note that the electric field strength is calibrated using thefrequency of the oscillations in FY above threshold at high field strength, seeFig. 7.21 and discussion below.

The theoretical models does not predict the exact intensities of the res-onances below threshold, but it predicts the general behavior of helium inweak static electric fields with good accuracy. One possible explanation ofthe difference between theory and experiment can be pressure effects, theseare known to influence the field free spectrum at these relatively high targetpressures (∼10−3 Torr). Another possibility is that the theoretical atomic de-scription is not fully converged.

The oscillations above threshold are expected for excitation spectra of Ry-dberg atoms in an external field [88], and can quantitatively be understood asfollows. The applied electrical potential will tilt the potential of the heliumion, as schematically shown in Fig. 7.22. The electron emitted in the ioniza-tion can be represented by its de Broglie wavelength (λ = h/

√2m0Ekin [24]),

in Fig. 7.22 this wavelength is schematically shown above the tilted atomicpotential well.

If an electron is emitted "against" the potential it will loose kinetic energyin favor of potential energy, hence the de Broglie wavelength will also change,as schematically shown in Fig. 7.22. The outgoing electrons fighting the uphill

91

Figure 7.20: The experimental data and theoretical predictions of the influence ofweak static fields on doubly excited helium. The field strength is indicated in the rightpart of the figure. The theoretical predictions describe the general increase in intensityfor higher fields, although the exact intensity might differ from the experimental data.The Stark shifted thresholds are indicated by arrows in the figure.

92

Figure 7.21: The experimental data and theoretical predictions of the influence ofweak static fields on doubly excited helium. The field strength is indicated in theright part of the figure. The theoretical predictions describe the general increase inintensity for higher fields, although the exact spectral shape and intensity differ fromthe experimental data. The Stark shift of the threshold is clearly seen. The oscillationsabove threshold in high fields are explained in the text. The Stark shifted thresholdsare indicated by arrows in the figure.

93

1086420 Kinetic energy (arb. units)

Potential well de Broglie wavelength

Figure 7.22: A schematic figure of the potential well in an external electric field.A schematic model of how the de Broglie wavelength varies with kinetic energy isshown above the potential well. This wavelength shown corresponds to the de Brogliewavelength at certain kinetic energies, if the outgoing electron is emitted against thepotential it will be retarded and thereby increasing its wavelength. When the electronreaches 0 kinetic energy it will be reflected back by the applied potential. The deBroglie wavelength will be affected by the potential well, such effects are not includedin this picture - this is a schematic model shown here only to give a quantitativeunderstanding. As this figure shows two different things the axis are cannot be labeled.The only label is the kinetic energy of the electron which is related to the de Brogliewavelength of the electron.

potential will be reflected at a certain distance, due to the tilted potential (atEkin = 0). Depending on if the electronic wavelength is in phase or out ofphase with itself after the reflection an intensity minimum or maximum in theFY will be observed.

Helium in weak static magnetic fieldsIt was for a long believed that weak magnetic fields (below 5 T) would haveno influence on the dielectronic recombination [89] cross-section. In Paper VIwe show that weak static magnetic fields (below 1 T) have large impact on theFY signal from doubly excited helium near the N=2 threshold. This effect iswell described using the multichannel quantum defect theory, where the maininfluence of the magnetic field is due to the diamagnetic interaction.

The numbers 1/2, 1, 3/2 and 2 in Fig. 7.23 corresponds to ∆ν = νLS −νJK

from Ref. [84]. In short it can be said that the effective quantum number νJK isdetermined using (all) experimental N=2 threshold values while the effectivequantum number νLS is determined using only the LS-allowed 2p1/2 threshold[84]. When ∆ν is an integer the FY is low in the field free case, as predicted byLS coupling. Whereas when ∆ν is a half-integer the maximum deviation frompure LS coupling is predicted in the field free case, and therefore a maximumin the enhancement of the FY in the field free spectrum is expected here [84].

94

Inte

nsity

(ar

b. u

nits

)

65.4065.3865.3665.3465.32 Energy (eV)

13

1/2

+

130 14-/

1 3/2 2

140 15/

14+ 15+

-

1 T 0.8 T 0.6 T 0.4 T 0.2 T 0 T

Figure 7.23: Fluorescence yield spectra of helium close to the N=2 threshold in dif-ferent weak magnetic fields. The numbers 1/2, 1, 3/2 and 2 refers to ∆ν = νLS −νJK

from Ref. [84]. The top spectra shows FY spectra for different magnetic field strengths0-1 Tesla. In the bottom part I show the same spectra where I have subtracted the fieldfree spectrum to emphasize the differences from the field free case. The field freespectrum has a dip at ∆ν = 1 while the spectrum recorded at 1 Tesla has no dip there.The variations in the difference-spectra, near the n+ resonances might be due to non-linearities of the monochromator and not real effects due to the applied field.

In the top part of Fig. 7.23 I show the FY near the N=2 threshold fromhelium in different magnetic fields. The bottom part of Fig. 7.23 shows thedifference-spectra, where the field free spectrum is subtracted from the spec-tra where an external field is present. The experimental spectra have beennormalized to have the same intensity above threshold, i.e. in Fig. 7.23 it isassumed that the FY above threshold is independent of field strength.

For the Rydberg states near the N=2 threshold the LS coupling fail to de-scribe the observed spectrum and additional LS-forbidden states must be takeninto consideration to explain the experimental data [84]. From this it can quan-titatively be understood that the maximum in the difference-spectra (lower partof Fig. 7.23) will be where ∆ν is an integer. In this region the FY predicted bythe LS coupling is retrieved, which implies that no LS-forbidden states willbe populated in the excitation (in the field free case). In the presence of anexternal field the allowed states might be mixed with forbidden states havinga larger FBR, a mixing that is not as available where ∆ν is a half-integer.

At a field strength of 1 Tesla the paramagnetic shift of the thresholds in-duced by the magnetic field is of the same order as the 2p1/2-2p3/2 splitting(727 µeV). This 2p1/2-2p3/2 splitting determines the ∆ν parameter which iscrucial for the understanding of the field free spectrum. Therefore one canintuitively expect that ∆ν looses its meaning at these field strengths and that

95

Inte

nsity

(ar

b. u

nits

)

65.4065.3865.3665.3465.32Energy (eV)

13 14 15+ + +

1 T0.8 T0.6 T0.4 T0.2 T 0 T Exp. 1 T Exp. 0 T

Figure 7.24: Theoretical spectra taking the paramagnetic shifts of the N=2 thresholdsinto account. The experimental spectra for 0 and 1 Tesla are included as a reference.The agreement between experiment and theory is good in the field free case but poorwhen a magnetic field is applied.

65.4065.3865.3665.3465.32Energy (eV)

Inte

nsity

(ar

b. u

nits

) 13 14 15+ + + 1 T0.8 T0.6 T0.4 T0.2 T 0 T Exp. 1 T Exp. 0 T

Figure 7.25: Top Theoretical spectra taking the paramagnetic and diamagnetic shiftsof the N=2 thresholds into account. The experimental spectra for 0 and 1 Tesla isincluded as a reference. Bottom The theoretical difference-spectra (compare to Fig.7.23), the figure also shows the experimental difference-spectra for 1 Tesla for com-parison.

there will be significant spectral changes. As shown in Fig. 7.24 the param-agnetic shift gives only minor spectral changes, the paramagnetic shift alonedoes not describe the experimental results well.

96

In Fig. 7.25 the full theory from Paper VI is included, particularly the dia-magnetic l mixing, this shows a much better agreement with the experimentaldata. The structures near the ends in the theoretical spectra in Figs. 7.24 and7.25 are artifacts from the convolution process of the theoretical data.

7.7 End remarksI consider the future development of XETECO to be very interesting. Byincreasing the QE of the FY detectors it will be possible to perform XETECOmeasurements on a more routine basis. With a descriptive theory of theXETECO peaks we will be able to say much more about the ionizationdynamics at threshold, I believe there is a wealth of interesting informationavailable there.

It would be extremely interesting to combine XETECO with a magneticbottle, a schematic design of a magnetic bottle is show in e.g. Ref. [90]. Ibelieve that might make it possible to use the magnetic bottle even duringmulti bunch mode at a synchrotron - normally single bunch mode is neededfor the magnetic bottle. This would also change XETECO into XEPECO -X-ray-emission-photoelectron coincidence, it would be possible to performthese measurements for electrons with a kinetic energy of several eV. Thismight be a straightforward implementation, or it might require some work -but I believe it has great potential.

Although helium has been studied for such a long time there are still inter-esting experiments to do, even below the N=2 threshold. To repeat the exper-iment in Paper IV in electric fields would be interesting. As would angle re-solved FY be, both with and without external fields applied, see e.g. Ref [91].Some of these studies, not only should - but must be done using the parabolicspectrometer being built by Prof. Joseph Nordgren (well, must in a sense as "Imust eat" - it can be done using the good old Rowland geometry spectrome-ter), I envy the people who will be privileged to do that (and I also hope to beone of them).

Finishing my Ph. D. studies does not mean that I will forget these ideas.And if I ever get the chance to realize them I intend to. For now I hope thatthis thesis can serve as a source of inspiration for new Ph. D. students - Iencourage you to measure better than I have, to find more interesting effectsand to prove my interpretations wrong if you have to.

Then there is of course the development of free electron lasers - a dauntingnew field for researchers using synchrotron light. For photon hungry tech-niques (as all my experiments are) the use of long, in vacuum, cooled undula-tors is an interesting development. For XETECO I would like to hint towardthe fact that if the QE of the photon detector can be increased by a factorof 5 (which is not unreasonable) and the photon flux from the undulator can

97

be increased by a factor of 10, then the CO2 spectrum in Chapter 7.5 can beobtained in about 1 hour.

The best of luck to all of you - whatever you want to try!

98

8. Acknowledgments

The last few years has been extremely hectic for me, so much to do and somuch to learn - and no matter how much you do and learn there is alwaysmore to do and more to learn. But at the same time this has been a wonderfulride, even though I have been cursing and doubting myself from time to timethe fact that I have discovered the pleasure with research has made it all worthit.

I would not be where I am today without the help and support of many peo-ple, people I now call not only my colleagues, but also my friends. The mostimportant among them is of course my supervisor Jan-Erik Ruben Rubens-son who guided me through my first steps toward becoming a researcher, whomade me realize that research is indeed fun and interesting. I cannot say howmuch you have meant to me, as a supervisor, but also as a colleague and friend.

I have also a great many colleagues in Uppsala, with whom I spent too littletime as I was living abroad for so long during my Ph. D. studies. They have allbeen great fun to take breaks in the coffee room with, or just chitchat about thisand that - too little of that while writing this thesis I am afraid. I’d like to saythank you to (I choose the alphabetical order) Marcus Agåker, Egil Andersson,Joakim Andersson, Andreas Augustsson, Sergei Butorin, Laurent Duda, Carl-Johan Englund, Raimund Feifel, Johan Forsberg, Håkan Hollmark, Leif Karls-son, Anne Kronquist, Kristina Kvashnina, Anders Modin, Joseph Nordgren,Anders Olsson, Jan-Erik Rubensson, Magnus Ström, Conny Såthe, ThorstenSchmitt and Lars Werme. And of course everybody else at Fysikum - thankyou for everything!

I did quite many experiments together with Marcus Agåker, and wouldtherefore like to mention him a bit extra - thanks for the times in Italy (coldas they might be) and also for the times in Lund (that can be even colder, Iam referring to my horrible night at Tåget). Marcus also made some of thefigures used in this thesis, thank you for allowing me to use them, they are allavailable in his thesis [13].

I want to say thank you to Joseph Nordgren, for insightful discussions andcomments, and also for heading the USX group and giving all us knowledgehungry youths an opportunity to start learning more.

I also want to mention some of my colleagues again who put in a tremen-dous effort in reading a draft of this thesis and finding a wealth of mistakesthat are now corrected. All remaining mistakes are of course entirely my ownfault. Thank you Ruben, Leif and Marcus!

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I have spent a long time abroad, both living abroad and doing experiments. Ihave many colleagues to whom I own a great debt. Thank you Jinghua Guo forallowing me to work together with you at the ALS for one year, I learned a lotduring that period. During my time at ALS I worked together not only withJinghua, but also with Aran Guy, Timothy Learmont and Per-Anders Glanswhom I want to thank for company and scientific discussions.

I also want to thank all my colleagues at BESSY II in Berlin, it was a lot offun!

As you might have seen many of my experiments have been done at thegasphase beamline at Elettra in Italy. I owe more than anyone know to thegreat people working there, whom were present at my first beamtime and haskept inspiring me each time I go there. I want to extend my deepest gratitudeto Robert Richter, Michele Alagia and Stefano Stranges with whom I spent themost time in Italy. But I do not want to forget to mention Monica de Simone,Marcello Coreno and Kevin Prince. I have said it before but I want to say itagain, I always have fun when I do experiments with you - thank you.

Other than the people mentioned there are all my friends here in Swedenand abroad, from my time in Uppsala, USA, and Germany, whom I want tothank. It is not often that one gets to think about how important friends reallyare and how boring my life would have been without all of you. I am veryhappy that I can still count you as my friends.

It would take up a whole book in itself to let you know what all namedand un-named persons here have meant for me - but I hope that you all knowwhat you have meant for me, both personally and at work. Should you not bementioned by name in this thesis you are not forgotten and you still mean asmuch to me as the named persons.

And of course I want to thank my family, whom might not have understoodwhat I was doing, or why. I love and cherish them above everything else.

∼Johan

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Acta Universitatis UpsaliensisDigital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology 297

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A doctoral dissertation from the Faculty of Science andTechnology, Uppsala University, is usually a summary of anumber of papers. A few copies of the complete dissertationare kept at major Swedish research libraries, while thesummary alone is distributed internationally through theseries Digital Comprehensive Summaries of UppsalaDissertations from the Faculty of Science and Technology.(Prior to January, 2005, the series was published under thetitle “Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology”.)

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