Spectrum and energy levels of six-times-ionizedmolybdenum (Mo VII)
Joseph Reader
National Institute of Standards and Technology, Gaithersburg, Maryland 20899
Uri Feldman
E. 0. Hulburt Center for Space Research, Naval Research Laboratory, Washington, D.C. 20375-5000
Received August 31, 1989; accepted November 14, 1989
The spectrum of the kryptonlike ion Mo VII was observed from 140 to 2274 A with sliding-spark discharges on 10.7-m normal- and grazing-incidence spectrographs. Experimental energies were determined for all levels of the4s24p6, 4s24p54d, 4f, 5s, 5p, 5d, 5f, 5g, and 4s4p64d configurations. A few levels of the 4s24p44d2 configuration werealso found. A total of 399 lines were classified as transitions between 86 observed levels. The observed configura-tions were theoretically interpreted. The energy parameters determined by least-squares fits to the observed levelsare compared with Hartree-Fock calculations. A revised value of the ionization energy was obtained by using theenergy of the 4p55g configuration together with an isoelectronically extrapolated value of the effective quantumnumber n*(5g). The adopted limit is 1013 340 + 200 cm 1 (125.64 + 0.02 eV).
Resonance lines of the kryptonlike ion Mo VII were original-ly investigated by Charles,' who reported transitions to the4p6 So ground state from the two J = 1 levels of the 4p55sconfiguration. Later, Chaghtai2 added transitions to theground state from the 4p5 4d 3P1 and 3D1 levels. Reader etal.3 further expanded the list of resonance lines to includetransitions from levels of the 4p5 4d, 5d, 6d, 5s, 6s, 7s, 8s, 9s,10s, and 4s4p6 5p configurations. Tauheed and Chaghtai 4
investigated transitions between the excited configurationsof Mo VII. They classified approximately 300 lines as tran-sitions between the 4p 55s, 6s, 7s, 5p, 6p, 4d, 5d, 6d, and4s4p64d configurations.
Recently the present authors proposed a scheme for a soft-x-ray laser at 600 A based on photopumping a 4p56s level ofMo vii by a strong line of the galliumlike ion Mo XII.5
Lasing would take place from the 4p56s level to levels of the4p55p configuration. In order to quantify this proposal,spectrograms taken at the National Institute of Standardsand Technology (NIST) were examined to try to locate the4p55p-6s transitions given in Ref. 4. These transitionscould not be found. Further comparisons of the NIST spec-tra with data of Ref. 4 made it clear that it would be neces-sary to reinvestigate the spectrum of Mo VII in order toproceed with the soft-x-ray laser study. We present herethe results of this investigation. The previous analysis4 ofthis ion has been completely revised.
EXPERIMENT
Our data for the region from 140 to 900 A were taken fromspectra obtained previously in connection with investiga-tions of Mo IX (Ref. 6) and Mo X.7 The spectra were record-ed on the 10.7-m normal- and grazing-incidence spectro-graphs at the NIST. The angle of incidence of the grazing-incidence spectrograph was 80°. Both spectrographscontained gratings ruled with 1200 lines/mm. The first-
order plate factor of the normal-incidence spectrograph was0.78 A/mm. The plate factor of the grazing-incidence spec-trograph at 340 A was 0.25 A/mm. The light source was alow-voltage sliding spark between molybdenum electrodeswith a quartz spacer, operated as described by Reader et al.
3
Capacitance ranged from 24 to 80 ,F. Assignment of linesto ionization stages was accomplished by comparing intensi-ties at various peak currents in the spark. A strong spec-trum of Mo VII was observed at a peak current of 2000 A.Further details, especially concerning wavelength-calibra-tion spectra, are given in Ref. 6.
For the region above 900 A new spectrograms were takenon the 10.7-m normal-incidence vacuum spectrograph at theNIST. The light source was a sliding-spark discharge simi-lar to that used previously. Peak currents in the sparkranged from 700 to 4000 A, with a well-developed spectrumof Mo VII again appearing at a current of 2000 A. Forexposures above 1200 A a magnesium fluoride window wasused to eliminate second- and higher-order lines. Spectrafor wavelength calibration consisted of separate exposures ofsliding sparks of yttrium at a peak current of 1000 A. Mostof the calibration lines were either Y III (Ref. 8) or Y IV.9
Shifts between reference and unknown spectra were takeninto account by using known wavelengths of Mo v (Ref. 10)as well as impurity lines"1 of oxygen, carbon, and silicon.
The wavelengths, intensities, and classifications of theobserved lines of Mo VII are given in Table 1. All wave-lengths are in vacuum. The intensities are visual estimatesof plate blackening. The estimated uncertainty of the wave-lengths is +0.005 A.
SPECTRUM ANALYSIS
Analysis of the spectrum was begun by making calculationsof the level structures of the 4p5 (4d + 5s), 4p55p, and 4p5 (5d+ 6s) configurations with the Hartree-Fock (HF) code of
1 Wavelengths are in vacuum. Except for the 4p6, 4s4p64d, and 4p44d2
configurations, the levels are based on the 4p5 2P parent and are designated in
J1l coupling. The 4p6, 4s4p6 4d, and 4p 44d2 configurations are designated in
LS coupling. For the 4p 44d2 configuration only the 3 P parent term is shown.b Symbols: c, complex; d, double; m, mashed by a line of oxygen, a lower
stage of ionization of molybdenum, or a stronger line of the Mo vii, wave-length and wave number calculated from optimized energy level values; p,perturbed by close line; 1, asymmetric, shaded to longer wavelength; w, wide;u, unresolved from close line.
I Doubly classified line.
Cowan.12 The calculations were performed in a nonrelativ-istic mode that provided energy parameters equal to those ofthe Froese-Fischer code.13 Scale factors for the parameterswere estimated by extrapolating known scale factors for thekryptonlike ions Rb j,14 Sr III,15 Y IV,9 and Zr V.16 Theknown J = 1 levels of the 4p5 (4d + 5s) and 4p5(5d + 6s)configurations were then used to develop levels of 4p55phaving J = 0, 1, 2. These 4p 55p levels were used to extendthe 4p5 (4d + 5s) and 4p5 (5d + 6s) levels to higher J values.All levels of these configurations were thus located. Thelevels of the 4s4p64d configuration, which are interleavedwith levels of 4p 55p, were next similarly located.
Continuation of the analysis in this manner to try to locatelevels of the 4p54f and 5f configurations proved unsuccess-ful. Levels could not be found that corresponded to predic-tions of the HF calculations. Further considerations sug-gested that these configurations were probably perturbed bythe 4s24p4 4d2 configuration. This configuration lies high atthe beginning of the isoelectronic sequence but drops rapid-ly in relative energy as the sequence progresses. A newcalculation was thus made in which the entire complex ofeven configurations including 4s24p44d2 was treated togeth-er. The Cowan code was used with relativistic Hartree-
a Fixed at scaled HF value (scale factors: 0.85 for electrostatic parameters, 0.95 for spin-orbit parameters).b Fixed at HF ratio to G3(4p5g).
exchange (HXR) wave functions. Scale factors for the ener-gy integrals were the commonly used values17 "18 of 0.85 forthe elecrostatic parameters and 0.95 for the spin-orbit pa-rameters. Energy levels, wavelengths, and intensities werecalculated for the 4s24p6 + 4s24p5(5p + 4f + 5f) + 4s4p6 4d +4s24p4 4d2 and 4s24p5 (4d + 5s + 5d + 6s + 5g) configurations.The levels obtained with this calculation closely resembledthe level structures that had been observed. The calculatedeigenvectors further confirmed the importance of the inter-action with 4s24p4 4d2. With this calculation as a guide, alllevels of the 4p5 4f and 5f configurations could be identified.* Considerable difficulty was again encountered in trying tolocate the 4p55g levels. The 4p54f-5g transitions were pred-icated to fall in the midst of a group of oxygen lines in the540-590-A region, and, because of the purity of the Jl1 cou-pling for these configurations, only a few transitions wereexpected to be observable. Possible confirming transitionsfrom the 4p55f-5g array were predicted to lie above ourregion of observation. Thus not many recurring differencescould be expected.
The line identifications were made by comparing the cal-
culated spectrum in this region with the observed spectrum.Because of the similarity of these spectra we could in factidentify most of the lines and establish all the 4p5 5g levels.As is common for this transition array, many of the 5g levelsare based on only one line, the strong transition betweenterms of pair-coupled levels. For some levels this strongtransition was found to be masked by an oxygen line, and aline of lesser intensity was used to establish the 5g level.
In the course of locating the 4p55g levels as just described,several strong lines in the region remained unassigned.These could be identified as transitions from 4p55g to levelsof 4p44d2, which is strongly mixed with levels of 4p5 4f. Con-firmation of these identifications was obtained through ob-servation of several 4p54d-4p44d2 transitions in the 300-Aregion. This established two levels of 4p44d2 . A third levelof 4p44d2 was located solely from its transitions to 4p54d.The 4p4 4d2 configuration contains 110 levels, and furtherinvestigation of its level structure was considered to be out-side the scope of the present study. However, it is clear fromour spectrograms that the region near 300 A contains manystrong transitions of the type 4p54d-4p4 4d2 .
J. Reader and U. Feldman
260 J. Opt. Soc. Am. B/Vol. 7, No. 3/March 1990
Table 5. Calculated Energy-Level Values (in cm-') and Percentage Compositions for the 4p5(5d + 6s)Configurations of Mo villa
PercentageJ E (obs) E (calc) Obs - Calc (LS) Percentage Composition (J1)
Table 7. Calculated Energy-Level Values (in cm-') and Percentage Compositions for the 4p 6, 4p5 5p, 4s4p6 4d, 4p54f,4p 44d 2, and 4p55f Configurations of Mo VII
LeadingJ E (obs) E (calc) Obs - Calc Percentage Percentage Composition by Configurationa
The 4p44d2 configuration is denoted 4d2; the 4s4p64d configuration is denoted 4s4d. Percentages for levels of 4p4 4d2 are given only for observed levels.b Not included in least-squares fit.
The energy levels of Mo VII are given in Table 2. The levelvalues were determined by an iterative procedure in whichthe observed wavelengths were weighted according to theiruncertainties.' 9 The uncertainties of the level values asgiven by this procedure are also listed. Except for 4p6,4s4p64d, and 4p44d 2, all the levels are given in J1l coupling.The levels of these three configurations are given in LScoupling. High levels determined only by resonance lines3
are not included in Table 2.
THEORETICAL INTERPRETATION
4p5(4d + 5s) ConfigurationsThe 4p5(4d + 5s) levels are plotted in Fig. 1. The results offitting the energy parameters to the observed levels by aleast-squares calculation are given in Table 3. The fittedvalues of the parameters along with the HF values are givenin Table 4.
As is shown in Fig. 1, the 4p 54d configuration in Mo VII issomewhat more tightly bound than 4p55s, and there is nooverlapping of levels. According to the percentage composi-tions, there is practically no mixing of 4p 54d and 4p55sstates. As a result, the configuration interaction integralshad to be fixed at the scaled HF values in the least-squarescalculation. The fitted/HF ratios are generally close to theadopted scale factors. Although we have used Jil couplingto denote the levels, the coupling is not very pure in eitherthe Jl or the LS scheme.
4p5 (5d + 6s) ConfigurationsThe levels of the 4p 5(5d + 6s) configurations are plotted inFig. 2. The percentage compositions are given in Table 5,the parameters in Table 4. As with the 4p54d and 5s config-urations, the two configurations are well separated, andthere is not much mixing. The configuration interactionintegrals were thus fixed at the scaled HF values. Thefitted/HF ratios are again close to the adopted scale factors.The coupling is fairly pure in the Jl scheme.
4p55g ConfigurationThe 4p55g levels are plotted in Fig. 3. The percentage com-positions are given in Table 6, the parameters in Table 4. Inthe least-squares fit G5(4p5g) did not take a well-definedvalue and was thus fixed at its HF ratio to G3(4p5g), which isnot well defined itself. The spin-orbit coupling constant V5gis small and was fixed at its scaled HF value. As expected,
the coupling is nearly pure Jl. The deviations betweenobserved and calculated energies in Table 6 indicate thatthis configuration is slightly perturbed. Nevertheless, thefitted value of 4p of 15 412 cm-' is close to the value of15 516 cm-' found in the 4p 5 2
P core of Mo VIII.20
4p 6 ConfigurationThe 4p 6 SO ground level of Mo Vii is significantly mixedwith levels of the 4p44d2 configuration. Although the ad-mixture of the 4p44d2 state into 4p 6 So is only 2%, as shownin Table 7, the ground state is depressed by 18 000 cm-' bythis interaction. This effect may be important for accurate
580
E0
a)CD
560 -
5400 1 2 3
J Value
Fig. 4. Structure of the 4 p55p and 4s4p64d configurations ofMo VII. Heavy lines, 4p5p; dashed lines, 4s4p64d. Levels of 4p55pare designated in Jl coupling; levels of 4s4p 64d are designated in LScoupling.
1 [2 6
4p 5p + 4s4p 64d
1/2 [3/21
13/2 13/2]
k ~/- 312 [51
1/2 [1/2]-
3/2 [1/2]_
I I I I
l
J. Reader and U. Feldman
Vol. 7, No. 3/March 1990/J. Opt. Soc. Am. B 263
Table 8. Fitted and HF (HXR) Parameters (in cm-') and Mean Error A of Least-Squares Fit for the EvenConfigurations of Mo VII
4s4p64d-4s24p44d2 R1(4p4p, 4s4d) 108 399 92 1 3 9 b
A 473
a Fixed at HF ratio to G2(4p4f).b Fixed at scaled HF value (scale factors: 0.85 for electrostatic parameters, 0.95 for spin-orbit parameters).
ab initio calculations of the energies of resonance transitionsof rare-gas-like ions or other ions with analogous structures.
4p55p and 4s4p'4d ConfigurationsThe levels of the 4p 55p and 4s4p 64d configurations are plot-ted in Fig. 4. Although the 4s4p64d configuration lies highin the early part of the isoelectronic sequence, it drops rapid-ly in energy relative to the other excited, even configurationsas the sequence progresses and in Mo VII is nearly the firstexcited even configuration. Clearly, it will be the lowestexcited even configuration for succeeding ions of the se-quence. In the theoretical interpretation, the 4p 55p and4s4p64d configurations were treated together with the othereven configurations 4p6 , 4p 54f, 4p55f, and 4p44d 2. As theentire group of even configurations is complicated, we havenot attempted to give detailed percentage compositions forthe levels. Instead, Table 7 gives the percentage composi-tion for the leading eigenvector component and a summaryof percentage composition by configuration. It can be seenthat, although 4p 55p is nearly pure, there are small admix-tures of other even configurations, mainly 4s4p64d. The4s4p64d levels are grouped as two distinct LS terms. Theyare considerably mixed with levels of the 4 24p 44d2 configu-ration through the large np2-nsnd interaction. The radialintegral for this interaction, given near the end of Table 8, isthe largest of those for the even levels. The configurationpurities of the 4s4p64d levels are -70% on the average.
4p54f + 4p 44d 2 + 4p 55f ConfigurationsThe remaining group of even configurations constitutes acomplex set of highly mixed levels. Figure 5 shows theexperimental positions of the 4p 54f levels. The three levelsof 4p 4d2 that were observed are shown as bold dashed lines.The calculated positions of 4p 44d2 levels that fall in thisgeneral region are shown as light dashed lines.
The designations of the two J = 4 levels at 610 000 cm-'are ambiguous. The calculated positions of these levels areclose, and the observed intensities of their transitions tolevels of 4p54d and 4p 55g are nearly identical. It is thus notpossible to distinguish them experimentally, and they havebeen omitted from the least-squares fit. Since the J = 4level at 610 908 cm-' lies close to the calculated position of4p 54f 32[9/2]4, it was so designated. The other J = 4 levelwas designated as 4p 44d2.
The results of the least-sqaures calculations are given inTables 7 and 8. Inasmuch as only a few levels of 4p44d2 havebeen located experimentally, it was necessary to fix all inter-nal and configuration interaction integrals for 4p 44d2 at
their scaled HF values in the fit. Only Eav(4p 44d 2) wasallowed to vary. As can be seen from the percentage compo-sitions in Table 7, all 4p 54f levels contain large 4p44d 2 ad-mixtures. Although we have designated the J = 2 level at645 812 cm-' as a 4p 54f level on the basis of its leadingeigenvector component, it actually has a 60% 4p 44d2 charac-ter. The designation thus has little physical significance.
The 4p 55f levels are plotted in Fig. 6. The calculatedpositions of 4p44d 2 levels that lie in this general region areagain shown as thin dashed lines. Many calculated levels of4p44d 2 lie between the 4p 54f and the 4p55f configurationsand do not appear in the figures. Two levels of 4p44d2 arepredicted to lie well above 4p 55f, a J = 0 level at 863 000cm'1 and a J = 2 level at 843 000 cm-'.
In the least-squares calculations an exceptionally largeresidual was obtained for the J = 3 level of 4p55f at 775 781cm-'. This level was thus omitted from the fit. As this
650 _
E000
0I
C'Q
r_LU
630 -
I I _ _ _ _ __ _ _ ___ _
1/2 (5/2 __
4p54f + 4p44d2 \ --
1/2 [7/2]
3/2 5/2]
\ =-3/2 [7/21
3/2 [3/21
_ ___
_ I I
610 -
0 1 2 3J Value
I__ - --:- - 3/2 [9/2] _
I I I I
4 5 6
Fig. 5. Structure of the 4p 54f and 4p 44d2 configurations of Mo VII.Heavy lines, 4p 54f; dashed lines, 4p 44d2. Predicted positions ofunobserved levels of 4p 44d2 are shown as thin dashed lines. Onlylevels of 4p 44d2 occurring in the general vicinity of 4p 54f are shown.Levels of 4p 54f are designated in J11 coupling.
J. Reader and U. Feldman
Vol. 7, No. 3/March 1990/J. Opt. Soc. Am. B 265
800 1h2 /L"I2]
1/2 [5/2]
4p 55f + 4p 44d2
780 - 3/2 [7/2]
3/2 [5/2]
WLI N...........3/2 [9/2]
312 [312]
760 ----
I I I I I0 1 2 3 4 5
J Value
Fig. 6. Structure of the 4p55f and 4p44d2 configurations of Mo VII.Heavy lines, 4p55f; dashed lines, 4p44d2. Predicted positions ofunobserved levels of 4p44d2 are shown as thin dashed lines. Onlylevels of 4p44d2 occurring in the general vicinity of 4p55f are shown.Levels of 4p 55f are designated in Jil coupling.
level is calculated to lie somewhat higher than its observedposition, it is likely that the interaction with 4p44d2 has beenoverestimated by the ab initio configuration interaction pa-rameters.
The structure of 4p55f is clearly distorted compared withthat of an unperturbed p5f configuration. In particular, the1/2[5/212 level is much lower than normally found. This iscaused by interaction with 4p4 4d2 .
It should be pointed out that, although only three levels ofthe 4p44d2 configuration were observed in this investigation,to our knowledge this is the first observation of a configura-tion of this type in any atom.
IONIZATION ENERGY
A previous value for the ionization energy of Mo VII of1 013 550 + 150 cm'1 was derived by Reader et al.3 from theseries of 4p5 ns(n = 5-9) resonance lines. This value wasconsistent with the value 1 013 483 cm-' obtained by Clarket al.21 by fitting the differences between experimental andHF values for kryptonlike ions to a straight line. An inde-pendent value can be derived form our present data for the4p55g configuration. If we consider the center of gravity ofthe pair of levels 4p5(2P3/2)5g[11/2]5,6 in Rb II,14 Sr III,15 YIV,9
and Zr V,'6 we extrapolate an effective quantum number forthis pair in Mo VII of n*(5g) = 4.9600 + 0.0020. This yields alimit of 1 013 120 180 cm-', which is in fairly good agree-ment with the previous value.3 For the ionization energy weadopt an average value of 1 013 340 200 cm-' (125.64 +0.02 eV).
ACKNOWLEDGMENTS
We thank Craig Sansonetti for extensive assistance in usingthe Cowan codes and Marcel Klapisch for several helpfuldiscussions. This research was supported in part by Inno-vative Science and Technology/Strategic Defense Initiativeunder direction by the Naval Research Laboratory. It wasalso supported in part by the Office of Fusion Energy of theU.S. Department of Energy.
REFERENCES AND NOTES
1. G. W. Charles, "A study of the spectra of columbium and molyb-denum in the extreme ultraviolet," Phys. Rev. 77, 120 (1950).
2. M. S. Z. Chaghtai, "Vacuum spark spectra of zirconium, niobi-um, and molybdenum," Phys. Scr. 1, 31 (1970).
3. J. Reader, G. L. Epstein, and J. 0. Ekberg, "Spectra of Rb II,Sr III, Y IV, Zr v, Nb VI, and Mo VII in the vacuum ultraviolet,"J. Opt. Soc. Am. 62, 273 (1972).
4. A. Tauheed and M. S. Z. Chaghtai, "The spectrum of six-timesionised molybdenum (Mo VII)," J. Phys. B 17, 179 (1984).
5. U. Feldman and J. Reader, "Scheme for a 60-nm laser based onphotopumping of a high level of Mo6+ by a spectral line ofMoll+," J. Opt. Soc. Am. B 6, 264 (1989).
6. J. Reader and N. Acquista, "4s24p4-4s4p5 transitions in Zr VII,Nb VIII, and Mo Ix," J. Opt. Soc. Am. 66, 896 (1976).
7. J. Reader and N. Acquista, "4s24p3-4s4p4 and 4s24p3-4s24p 25stransitions in Y VII, Zr VIII, Nb IX, and Mo x," J. Opt. Soc. Am.71,434 (1981).
8. G. L. Epstein and J. Reader, "Spectrum of doubly ionized yttri-um (Y III)," J. Opt. Soc. Am. 65, 310 (1975).
9. G. L. Epstein and J. Reader, "Spectrum and energy levels oftriply ionized yttrium (Y IV)," J. Opt. Soc. Am. 72, 476 (1982).
10. M. I. Cabeza, F. G. Meijer, and L. Iglesias, "A revision of theanalysis of the fifth spectrum of molybdenum (Mo V)," Phys.Scr. 34, 223 (1986).
11. R. L. Kelly and L. J. Palumbo, Atomic and Ionic EmissionLines Below 2000 Angstroms-Hydrogen through Krypton,Naval Research Laboratory Rep. No. 7599 (U.S. GovernmentPrinting Office, Washington, D.C., 1973).
12. R. D. Cowan, The Theory of Atomic Structure and Spectra (U.California Press, Berkeley, Calif., 1981).
13. C. Froese-Fischer, "A multi-configuration Hartree-Fock pro-gram with improved stability," Comput. Phys. Commun. 4,107(1972).
14. J. Reader, "Spectrum and energy levels of singly ionized rubidi-um (Rb II)," J. Opt. Soc. Am. 65, 286 (1975).
15. W. Persson and S. Valind, "The spectrum of doubly ionizedstrontium (Sr III)," Phys. Scr. 5, 187 (1972).
16. J. Reader and N. Acquista, "Spectrum and energy levels of four-times ionized zirconium (Zr V)," J. Opt. Soc. Am. 69,239 (1979).
17. U. Litzen and J. Reader, "Spectra and energy levels of thegalliumlike ions Rb vII-Mo xII," Phys. Scr. 39, 73 (1989).
18. E. Bi6mont and J. E. Hansen, "Magnetic-dipole and electric-quadrupole transitions in the ground-state configurations of thegermanium and arsenic isoelectronic sequences," Phys. Scr. 33,117 (1986).
19. Optimization of the level values was done with the computercode ELCALC written by L. J. Radziemski, Jr. (Department ofPhysics, New Mexico State University, Las Cruces, New Mexico88003). The procedure and definition of the level value uncer-tainties are described by L. J. Radziemski, Jr., and V. Kaufman,J. Opt. Soc. Am. 59,424 (1969).
20. J. 0. Ekberg, J. E. Hansen, and J. Reader, "Analysis of thespectrum of seven-times-ionized molybdenum (Mo VIII) andisoelectronic comparison of the spectra Y V-Mo VIII," J. Opt.Soc. Ain. 62, 1143 (1972).
21. C. W. Clark, M. G. Littman, R. Miles, T. J. McIlrath, C. H.Skinner, S. Suckewer, and E. Valeo, "Possibilities for achievingx-ray lasing action by use of high-order multiphoton processes,"J. Opt. Soc. Am. B 3, 371 (1986).
