KSU August 27, 2003
1
QuasiQuasi-free electron scattering from-free electron scattering from highly charged ionshighly charged ions
Theo J.M. ZourosTheo J.M. ZourosUniversity of Crete – HeraklionUniversity of Crete – Heraklion
GREECEGREECE
The MediterraneanThe MediterraneanCrete
CIA map
The island of CreteThe island of Crete
250 km
50 k
m
Heraklion
Area ~ 8200 km2 (3200 mi2)Population ~ 600 000 winter
> 1 000 000 summer
Two mountains ~ 2450 m
Heraklion population ~ 220 000
CreteCreteHeraklion
University of Crete - HeraklionUniversity of Crete - Heraklion
UoC ~ 5000 studentsPhysics Dept ~ 600 under grads
50 grads 30 faculty
Physics DeptUoC campus
From my living room
Physics &Biology
Medical school
University Hospital
Recent collaboratorsRecent collaborators
Dr. Manolis Benis PhD 2001
Univ. of Crete & JRM
Prof. Tom GorczycaWestern Michigan Univ.
R-matrix calculations
Pierre Auger1899-1993
Auger effect1923-1925
J.R. Macdonald LabKansas State Univ.
Prof. Pat
Richard
Prof. (Emeritus)Chander Bhalla
Mikhail Zamkov Grad Student
Teck Lee Grad Student
Ion – atom/electron collisionsIon – atom/electron collisions
Ion beamZ ~ 1-12I ~ 1-100 nAq ~ 1-12E ~ 0.5-2 MeV/uV ~ 3-6 a.u.gs or metastable
t = -t = -∞∞ t = -t = -∞∞∆∆t = 10t = 10-17-17 s sPreparationPreparation
Ionization ExcitationTransfercombinations
RelaxationRelaxation
e-
e-
e-
γ
γ
Black box?!
Non radiative: Auger electronsRadiative: Photon decay
Atom/Molecule Targetq = 0 (neutral)Gas/Solidgs or excited staten ~ 1012-1020 #/cm3
InteractionInteraction
Detectorsprojectile, recoil, photon, electroncoincidencesΔΩ – solid angleε - efficiency
e- beam Targetq = -1 I ~ 1-50 μAn ~ 106-108 #/cm3
Ion-atomIon-atom//electron interactions: electron interactions: Investigation of the Coulomb forceInvestigation of the Coulomb force
• Force is Coulomb:Force is Coulomb: Potential usually known - can write down a HamiltonianPotential usually known - can write down a Hamiltonian• Calculate emission or interaction cross sectionsCalculate emission or interaction cross sections• Difficulties: many particles, long range force, correlation effectsDifficulties: many particles, long range force, correlation effects• Model calculationsModel calculations• Develop theoretical and experimental techniquesDevelop theoretical and experimental techniques• Test approximationsTest approximations
Mature field – more than 40 years old – negative population growth!Mature field – more than 40 years old – negative population growth!
Interest in ion-electron/atom collisions Interest in ion-electron/atom collisions ApplicationsApplications
• Tokomak and AstrophysicalTokomak and Astrophysical PlasmasPlasmas• Accelerator technology - Storage ringsAccelerator technology - Storage rings• Radiation damage – cancer therapyRadiation damage – cancer therapy• Basic atomic collisionsBasic atomic collisions
Recent review:Electron-Ion scattering, I. Williams, Rep. Prog. Phys. 62 (1999) 1431
• Use HCI and simple targets – few-electron systems• Study ion excitation rather than target excitation:
Control charge state q of ion – N number of electrons Isoelectronic sequence study – same N different Z
Presentation SummaryPresentation Summary
• Resonant electron scattering (RES)Resonant electron scattering (RES)• Long range – short range potential treatmentLong range – short range potential treatment• Electron – ion collision techniquesElectron – ion collision techniques• Impulse Approximation – Electron scattering Impulse Approximation – Electron scattering
modelmodel• Advantages of quasi-free electron scatteringAdvantages of quasi-free electron scattering• RES applications: He-like and H-like ions, triply RES applications: He-like and H-like ions, triply
excited states isoelectronic sequence studyexcited states isoelectronic sequence study• Future plansFuture plans
Electron - ion collisions: Electron - ion collisions: Production and decay of Production and decay of
doubly excited statesdoubly excited states
capture of a (quasi-) free electron + excitation inverse autoionization
radiative stabilizationrecombinationDR or RTEX
autoionizationResonant electron
scatteringRES or RTEA
EEee
(quasi-)free (quasi-)free electronelectron
EE11-E-E00
EE11
EE00
EEnn
BBnn
EEe e + B+ Bn n = E= E11-E-E00
fi Eqqq
E eAAAe )1s()'l1snln'()1s( 2)1(2
EE11
EE00
EEnn
AAq+q+
EE11
EE00
EEnn
h
AAq-1+q-1+
AAq+q+
EE11
EE00
EEnn
doubly-excitedintermediate state
RTE
AAq-1+q-1+
Electron-ion scattering Electron-ion scattering twotwo-amplitude formula-amplitude formula
+q
e-
Ion
2*22 ||]Re[2|||~| SSq
Rq
RSq
Rdd ffffff
{2
2)(RrV
Rr
Srqe
rqe
rV
Rutherford Short-rangeInterference
Rr
VS short range potential
Sum of Rutherford and Short Sum of Rutherford and Short Range amplitudesRange amplitudes
RangeShortRutherfordfi fff
Griffin & PinzolaPRA42 (1990) 248
160 161 162 163 164 165 166 167 168 169 170-5
-4
-3
-2
-1
0
1
2
3
4
5
R-matrix
e- + B3+(1s2) e-(1800) + B3+(1s2)
d/d
(x 1
0-18 c
m2 /s
r)
Electron energy (eV)
|fR|2 (Rutherford)
Elastic scattering: Rutherford termElastic scattering: Rutherford term
Non resonant scatteringBinary Encounter Peak
Elastic scattering: Rutherford & Short-Elastic scattering: Rutherford & Short-rangerange
160 161 162 163 164 165 166 167 168 169 170-5
-4
-3
-2
-1
0
1
2
3
4
5
R-matrix
e- + B3+(1s2) e-(1800) + B3+(1s2)
d/d
(x 1
0-18 c
m2 /s
r)
Electron energy (eV)
|fR|2 (Rutherford)
|fS|2 (Short-range)
Resonant contributions
160 161 162 163 164 165 166 167 168 169 170-5
-4
-3
-2
-1
0
1
2
3
4
5
R-matrix
e- + B3+(1s2) e-(1800) + B3+(1s2)
d/d
(x 1
0-18 c
m2 /s
r)
Electron energy (eV)
|fR|2 (Rutherford)
2Re|fR
*fS| (Interference)
|fS|2 (Short-range)
Elastic scattering: All 3 termsElastic scattering: All 3 terms
Resonant contributions
Elastic scattering: Sum of 3 termsElastic scattering: Sum of 3 terms
160 161 162 163 164 165 166 167 168 169 170-5
-4
-3
-2
-1
0
1
2
3
4
5
R-matrix
e- + B3+(1s2) e-(1800) + B3+(1s2)
d/d
(x 1
0-18 c
m2 /s
r)
Electron energy (eV)
|fR|2 (Rutherford)
2Re|fR
*fS| (Interference)
|fS|2 (Short-range)
Sum
Sum of resonant, non-resonant and interference contributions
R-matrix results R-matrix results ee-- + B + B3+3+ (1s (1s22) ) [B [B2+2+ (1s2l2l (1s2l2l'')] )] B B3+3+ (1s (1s22) + e) + e--
(all terms!)
DifferentialDifferential scattering at scattering at largelarge angles provides the angles provides the most stringent tests most stringent tests of theoryof theory
Merged beam experiments at storage ring
Aq+
Circulatingion beam
Aq+
A(q-1)+
A(q+1)+
1.5m
TSR electron cooler:Merged beam setup for charge-changing electron-ion collisions
16O7+ H-likeEion = 8.9 MeV/u Ee=8-9keV
Eecm=500 eV ΔEecm=±0.6 eVIion= 4 E7 ion stack 7 min
16O7+ H-likeEion = 8.9 MeV/u Ee=8-9keV
Eecm=500 eV ΔEecm=±0.6 eVIion= 4 E7 ion stack 7 min
Kilgus et al PRL 1990
Differential electron scatteringDifferential electron scattering
J. Phys. B29 (1996) 4443
Ion beam
e- beam
Elastic scatteringEcm=20.69eV e- + Xe6+
Rutherford
Hartree-Fock
2sin16 42
2
eE
q
UoC HEMISPHERICAL ANALYZER UoC HEMISPHERICAL ANALYZER WITH 2-D PSD 0WITH 2-D PSD 0oo ELECTRON SPECTROMETER ELECTRON SPECTROMETER
UoC HEMISPHERICAL ANALYZER UoC HEMISPHERICAL ANALYZER WITH 2-D PSD 0WITH 2-D PSD 0oo ELECTRON SPECTROMETER ELECTRON SPECTROMETER
Ion Beam
Gas in Pressure Gauge
Gas Cell
PSDX-PositionY- Position
Timing
4-element lens
Faraday Cup
Inner hemisphere
electrons
Outerhemisphere
θ e-
IonResolution ~ 0.1%ΔΩ = 1.8 x 10-4 sr
00 dgrs
Experimental setup at J R Macdonald Laboratory
Electron Scattering Model/Impulse ApproximationElectron Scattering Model/Impulse Approximation
Vp >> v
I2
zpI2
pe E)vV(2
1E)vV(
2
1E
zp
z
freee
freequasie
2
vV
)J(v)(E
dΩ
dσ
dEd
σd
Free e--Ion Bound e--Ion
Z-axisIone-
vAtom
vz
Vp
Vp + vz
Compton Profile J(vz)
11
2 e
V
H2
0
25
50
75
100
125
150
175
-650
-600
-550
-500
-450
-400
-350
-300
-250
-200
-150
-100
1s3l1snl
2l2l'nl"
2l3l'nl"
1s2lnl'
B2+ B3+ B4+
(1s2)1S
(2s22p)2P
(1s2s)1S(1s2p)3P(1s2p)1P
2l2l'
(2s2p2)2D
2l3l'
(1s22p)2P
1s
(1s22s)2S
(1s2s)3S
Energy Level diagram of boronB
indi
ng E
nerg
y (e
V)
A
uger
ele
ctro
n en
erg
y (e
V)
Sliding the Compton profile Sliding the Compton profile across the resonancesacross the resonances
I2
pze EV2
10)(vE
I2
zpe E)v(V2
1E
Changing the ion velocity Vp slides the Compton profile across the doubly-excited states bringing them into resonance!
Ee =
184
eV(4
.0 M
eV)
RES
Auger decayΔ
ΕΕe = ΔΕRES
Com
pton profile
Ee
Comparison of signal ratesComparison of signal ratesR (#/s) = NR (#/s) = NII n nee L L σσ
Merged beams (Heidelberg TSR)
Crossed Beams (CEA – Grenoble)
Quasi-free e- beams (UoC - JRM)
Electrons: ne (#/cm3) 1 E 7 (1 A) 1.2 Ε 8 (4 μΑ) 3 Ε 14 (10 mTorr)
Overlap: L (cm) 150 0.20 5
Ions: NI (#/s) 3.7 E 12 (50 μA) 8.9 E 12 (10 μA) 7.8 E 10 (100 nA)
R (#/s) 5.5 E 21 σ 2.1 E 20 dσ/dΩ ΔΩ 1.3 E 26 dσ/dΩ ΔΩ
Electron beam ΔΕe (eV) 0.004 0.500 120
Chamber Vacuum (Torr) 1 E -11 1 E -10 1 E -7
e- Analyzer: ΔΩe (sr)
Resolution (%)
Only ions
measured
4 E -4
2
1.8 E -4
0.1
What’s the use of a quasi-free electron?
1. >106 higher luminosity compared to crossed electron-ion beam experiments!2. Measure scattering at 1800 (very sensitive)!3. Include also resonances
(e- energy dependence – d2/dEd)!4. No UHV5. Spectrum in 30 minutes!
Sounds great but is it really electron-ion scattering???
Elastic scattering of quasi-free electrons on BElastic scattering of quasi-free electrons on B4+4+ ions ions
180 190 200 2100
1
2
3
4
5
6
230 240 250 2600
1
2
3
Electron Energy (eV)
2l2l'
d2
/dd
(10
-20 c
m2 /e
V s
r)
2p2
1 S
2s2p
1P
2s2p
3P
2s2
1 S
2p2
1 D
220
2lnl
' Ser
ies
Lim
it
2l5l'
2l4l'
2l3l'
3.91 MeV B4+ + H2
180 190 200 210 220 230 240 250 260
1
10
R - Matrix
e- + B4+
d/d
(10 -
18 c
m2 /s
r)
Electron Energy (eV)
Doubly Excited stateszp
z
freee
freequasie
2
vV
)J(v)(E
dΩ
dσ
dEd
σd
Elastic scattering of quasi-free electrons on BElastic scattering of quasi-free electrons on B4+4+ ions ions
Zouros et al PRA 2003 RC
Elastic scattering of quasi-free electrons on BElastic scattering of quasi-free electrons on B3+3+ ions ions
150 155 160 165 170 1750
3
6
9
12
15
180 185 190 195 200 2050
1
2
3
4
5
6
7
1s2p
2 2 S
1s2l2l'
Electron Energy (eV)
1s2lnl' (n>2)
1s2s
2 2 S
1s(2
s2p
1 P) 2 P
1s(2
s2p 3 P
) 2 P 1s2p
2 2 D
1s2s
2p 4 P
d2 /dd
(10 -
20 c
m2 /e
V s
r)
4.0 MeV B3+ + H2
Doubly Excited states
----
- 2s
2p 3 P
----
- 2s
2p 1 P
150 155 160 165 170 175 180 185 190 195 200 2050.1
1
10
100
R - Matrix
e- + B3+
d/d
(10 -
18 c
m2 /s
r)
Electron Energy (eV) Zouros et al PRA 2003 RC
First Z-dependence study First Z-dependence study of a triply-excited stateof a triply-excited state
0
50
100
150
200
250
300
0
25
50
75
100
125
150
175
-650
-600
-550
-500
-450
-400
-350
-300
-250
-200
-150
-100
1s3l1snl
RES
2l2l'nl"2l3l'nl"
1s2lnl'
RES
B2+ B3+ B4+
(1s2)1S
(2s22p)2P
(1s2s)1S(1s2p)3P(1s2p)1P
2l2l'
(2s2p2)2D
2l3l'
(1s22p)2P
1s
(1s22s)2S
(1s2s)3S
Energy Level diagram of boron
Bin
din
g E
ne
rgy
(eV
)
11
2 e
V
H2
Ee-=
18
4 e
VE
e-=
18
4 e
V
Au
ge
r e
lect
ron
en
erg
y (e
V)
188 190 192 194 196 198 200 202 204 206 208 210
0
2
4
6
8
10
12
14
f3S=25%
g
f
e
d2s
2p 1 P
4.00 MeV B3+
370 375 380 385 390 395 400 405
0
1
2
3
4
5
f3S=25%
e
dc
b
a
10.14 MeV N5+
475 480 485 490 495 500 505 510 515
0.0
0.5
1.0
1.5 f3S=25%
c
b
a
14.35 MeV O6+
590 595 600 605 610 615 620 625 630 635 640
0.0
0.2
0.4
0.6
f3S=25%
20.18 MeV F7+
Benis et al JPBL submitted 2003
quasi-free electronquasi-free electron scattering is scattering is real electron scatteringreal electron scattering!! (remember Compton scattering – electrons there also really quasi-free!)(remember Compton scattering – electrons there also really quasi-free!)
• quasi-free electronquasi-free electron scattering provides the scattering provides the only only wayway to presently observe to presently observe differentialdifferential RES! RES! (particularly at the large scattering angles)(particularly at the large scattering angles)
Summary and ConclusionSummary and Conclusion
• Large-angle differentialLarge-angle differential electron – ion scattering provides some of electron – ion scattering provides some of the the most stringentmost stringent tests of both tests of both atomic structure and collision atomic structure and collision dynamicsdynamics
• State-of-the-art DDCS calculationsState-of-the-art DDCS calculations (R-matrix) for (R-matrix) for freefree electron electron scattering from He-like and H-like ions are in scattering from He-like and H-like ions are in excellent agreementexcellent agreement with with
quasi-freequasi-free electron experiments involving ion-H electron experiments involving ion-H22 collisions over a wide collisions over a wide
energy region and many resonancesenergy region and many resonances
FutureFuture
• Improve apparatus – add Improve apparatus – add first stage and double differential first stage and double differential targettarget
• Use Use Li vaporLi vapor target that has narrower Compton profile – (Laser- target that has narrower Compton profile – (Laser-excited) Rydberg Li target?excited) Rydberg Li target?
• Expand studies to include:Expand studies to include:many electron targetsmany electron targets
higher Z ions or L shellshigher Z ions or L shells• Incorporate zero-degree electron spectrometer system in a Incorporate zero-degree electron spectrometer system in a
storage ring??!!storage ring??!!
Comparison of Compton ProfilesComparison of Compton Profiles
-650
-600
-550
-500
-450
-400
-350
-300
-250
-200
-150
-100
1s3l
1snl
RES
2l2l'nl"
2l3l'nl"
1s2lnl'
RES
B2+ B3+ B4+
(1s2)1S
(2s22p)2P
(1s2s)1S
(1s2p)3P(1s2p)1P
2l2l'
(2s2p2)2D
2l3l'
(1s22p)2P
1s
(1s22s)2S
(1s2s)3S
Bin
din
g E
ne
rgy
(eV
)
Li(2
s)
48
eV
Ee-=
19
4 e
VE
e-=
19
4 e
V
-650
-600
-550
-500
-450
-400
-350
-300
-250
-200
-150
-100
1s3l
1snl
RES
2l2l'nl"
2l3l'nl"
1s2lnl'
RES
B2+ B3+ B4+
(1s2)1S
(2s22p)2P
(1s2s)1S
(1s2p)3P(1s2p)1P
2l2l'
(2s2p2)2D
2l3l'
(1s22p)2P
1s
(1s22s)2S
(1s2s)3S
Bin
din
g E
ne
rgy
(eV
)
11
2 e
V
Ee-=
18
4 e
VE
e-=
18
4 e
V
HH22 target targetLiLi vapor target vapor target
H2 target
184 186 188 190 192 194 196 198 200 202 2040
1
2
3
4
5
6
7
8
Data R-matrix
3.92 MeV B4+ + H2
2p2
1S2s2p 1
P
2p2
1D
2s2p 3
P
2s2
1S
DD
CS
(
10 -
20 c
m2 /e
V s
r) )
Electron energy (eV)
He target
184 186 188 190 192 194 196 198 200 202 2040
1
2
3
4
5
6
7
8
Data R-matrix
3.92MeV B4++ He
DD
CS
(x1
0 -20 c
m2 /e
V s
r)
Electron Energy (eV)
Ar target
184 186 188 190 192 194 196 198 200 202 2040
2
4
6
8
10
12
14
16
2s2
1S 2s2
p 3 P
3.92 MeV B4+ + Ar2p2 1D +
2s2p 1P Data R-matrix (3s+3p) R-matrix (3s) R-matrix (3p)
DD
CS
(x1
0 -20 c
m2 /e
V s
r)
Electron Energy (eV)
The End
Many thanks to all my colleagues and friends for making my sabbatical such
a fun and exciting experience!
Summary and conclusionsSummary and conclusions
• 1800 Elastic e--Ion Scattering measurementsFirst differential observation of RES for He-like ionsFirst isoelectronic sequence study of triply-excited state
• R-matrix calculationsOverall good agreement with the measurementsESM seems to be a very good approximation
• Quasi-free e- scattering provides unique data:Not impaired by broad Compton profile!!!No problem with convolution of Compton profile!!!
Method
1s2 1S → 1s2p2 2D [RTE]
1s2s 3S →1s2s2p 4P [Capture]
Determination of the Determination of the metastable 1s2s metastable 1s2s 33S fractionS fraction
E.P. Benis et al, PRA 65, 064701 (2002)
Two successive measurements at the same production energy
)()()()(
)()()(
41
22
42
21
22
214
1 PYDYPYDY
DYDYPYf
148 150 152 154 156 158 160 162 164 166 1685
10
15
20
Gas Stripped
1s2
p2 2D
1s2
s2p 4 P
4 MeV B3+ + H2
Electron energy (eV)
Norm
aliz
ed E
lect
ron Y
ield
148 150 152 154 156 158 160 162 164 166 1685
10
15
20
Foil Stripped
1s2
p2 2D
1s2
s2p 4 P
4 MeV B3+ + H2
Electron energy (eV)
Norm
aliz
ed E
lect
ron Y
ield
1s2s 1s2s 33S S Metastable fractionMetastable fraction
1 2 4 6 8 100.1
1
10
100
Production of Metastable Fraction
25.8
Gas stripped beam Foil stripped beam Foil post-stripped beam
8.56.13.83.3 7.06.0
5.34.43.5
19.2
15.712.8
9.97.9
7.1
6.1
5.3
4.4
3.5
Stripping Energy (MeV)
B3+
[(1
s2s)
3 S]
F
ract
ion
(%
)
0
1
2
3
4
5
(1s2
p2 )2 D
(1s2
s2p
)2 P+
(1s2
s2p
)2 P_
(1s2
s2p
)4 P
(1s2
s2 )2 S
3.8MeV B3+(1s2 ) + H2
4.11MeV B3+(1s2, 1s2s) + H2
DD
CS
(x
10 -
20 c
m2 /e
V s
r)
150 155 160 165 170 175 180
0
1
2
3
4
Auger Electron Energy (eV)
Foilstripping
Gasstripping
e- scattering on ion
i
f
LS
kili
k fl f
Energy conservation: LS-coupling: total L=S=ML=MS==0
22
1fAuger k
jjLjMLjSjMSj>
e-
Ion
Ion+e-
Ion
i
i f
f
Absolute doubly differential cross section determination
TElnN
N
dd
d
I
e2
Determine the overall efficiency:
Use BEe/elastic non-resonant scattering peak
B4+(1s) + H2B3+(1s2 1S, 1s2s 3S) + H2
Determine the metastable fraction:
Use capture to RTE lines ratio
Elastic scattering of quasi-free electrons on B3+ ions
0
2
4
6
8
10
12
(2s2
p2 ) 2 D
(2s2
p2 ) 2 D
3.80 MeV B3+(1s2) + H2
4.11 MeV B3+(1s2, 1s2s) + H2
DD
CS
(x
10 -
21 c
m2 /e
V s
r)
180 185 190 195 200 205 210
0
2
4
6
8
10
Auger Electron Energy (eV)
E.P. Benis et al, in XXI ICPEAC, Sendai, Japan, p. 505 (1999)
1 2 3 4 5 6 7 80
1
2
3
4
Data IA - RTEA
(x 0.61)
SD
CS
(1
0-20 c
m2 /s
r)
Projectile Kinetic Energy (MeV)
M. Zamkov et al. Phys. Rev A 65, 032705 (2002)
Triply Excited States !2s2p2 2D
1s2p 3P
1s2s 3SRTEA
Elastic scattering of quasi-free electrons on BElastic scattering of quasi-free electrons on B3+3+ ionsionsTriply Excited States
270 275 280 285 290 295 300 305
0
2
4
6
8
10
12
14
2s2p2 2D --> 1s2p3P
2s2p2 2D --> 1s2s3S
6.6 MeV C4+[10% 1s2s 3S] + H2
D
DC
S (
10 -
21 c
m2 /e
V s
r)
Electron Energy (eV)
360 365 370 375 380 385 390 395 400 405
0
1
2
3
4
5
6
7
2s2p2 2D --> 1s2p3P
2s2p2 2D --> 1s2s3S
10.1 MeV N5+[25% 1s2s 3S] + H2
DC
CS
(1
0 -2
1 cm
2 /eV
sr)
Electron Energy (eV)
460 465 470 475 480 485 490 495 500 505 510 515 520
0
1
2
3
4
2s2p2 2D --> 1s2p3P
2s2p2 2D --> 1s2s3S
14.4 MeV O6+[20% 1s2s 3S] + H2
DD
CS
(1
0 -21 c
m2 /e
V s
r)
Electron Energy (eV)
590 595 600 605 610 615 620 625 630 635 640
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2s2p2 2D --> 1s2p 3P
2s2p2 2D --> 1s2s 3S
20.2 MeV F7+[30% 1s2s 3S] + H2
DD
CS
(1
0 -2
1 cm
2 /eV
sr)
Electron Energy (eV)
150 160 170 180 190 200 210
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
4P 2D
2s2
p 3 P
5.71 MeV B3+ + H2
Auger Electron Energy (eV)
f =25%
B3+ (1s2s 3S) → B3+ (2s2p 3P) → B4+ (1s) + eA
f =5%
150 160 170 180 190 200 210
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
2s2p 3P
2D
4PDD
CS
(x
10 -
20 c
m2 /e
V s
r)
5.88 MeV B3+ + H2
Auger Electron Energy (eV)
Elastic scattering of quasi-free electrons on ionsElastic scattering of quasi-free electrons on ions((more open channelsmore open channels))
Non-Resonant Transfer Excitation (NTE)
Uncorrelated Transfer Excitation (UTE)
T P
V
T P
V
Scattering of free electrons on HCI
Ion
e-
Scattering of quasi-free electrons on HCI
Atom
Ion
e-
V
v
Compton ProfilesCompton Profiles
zp z
x
y
p
zyxzz dpdpdppdppJ ])([)(2
-5 -4 -3 -2 -1 0 1 2 3 4 50.0
0.2
0.4
0.6
0.8
1.0
1.2
x 0.05
Compton Profiles
H (n=1) H2
He Ne H(n=10)
J(p
z') [a
.u.]
target electron momentum - pz' [a.u.]
zdp
zz dppJ )(
zz dppJ )(
(p)|2
= probability to find e- with component pz
Highest Sensitivity at large-angle scattering
d/d: 70 eV e- + Li+
1 1S 2 3PDW: Distorted WaveUDW:Unitarized DWCC5: 5-state close couplingCC11: 11-state close coupling
Largest differences between
theories at 1800!!
Griffin & Pinzola PRA90
70 eV e- + Li+: 1 1S 2 3P
Resolution dependence study
150 155 160 165 170 1750
1
2
3
4
5
6
4.0 MeV B3+ + H2
d2 /dd
(10 -
20 c
m2 /e
V s
r)
Electron Energy (eV)
FWHM(eV) 0.56 0.28 0.14
Electron scattering processesProcess Ion-atom e- -Ion e- -Atom
Elastic BEe limited yes
BEe diffraction Glory
-- Ramsauer-Townsend
yes
Resonant Elastic
RTEA ? R2TE RT2E?
? READI 3-body reco?
--
Resonant inelastic
RTEA* ? RTEX
REDA DR
--
Radiative Capture
REC RR --
Excitation e-e E limited yes
Ionization e-e I yes yes
Super elastic Yes 1s2s 3S observed yes
SummarySummary
• simplification of ion-atom collisions by separating target-electron interactions from target-nucleus interactions.
• unifying view-point for treating electron scattering in ion-atom, e-ion and Compton.
The impulse approximation provides:
0 1000 2000 3000 4000
10-22
10-21
10-20
10-19
10-18
00
inelastic scattering
Bin
ary
En
cou
nte
r
(
v e =
2V p)
1800
elastic scattering
1800
3l3
l' 2
s
3ln
l'(n>
3)
2
s
cu
sp
v e =
Vp
3l3
l' 2
s
2p2
1
s
30.04 MeV F8+
+ H2
00 electron spectra
DD
CS
(cm
2 /eV
sr)
LAB Electron Energy (eV)
Differential Differential Electron-ion scattering measurementsElectron-ion scattering measurements
• QUB-UCL (Srigengan, Williams, Newell, =250-950 Na+ PRA96) (Greenwood et al, =1200-1700 Ar+ PRL95)• CEA-AIM (Bélenger et al. =320-1480 Ar8+ , Xe3-6+ JPB96
Huber et al. =300-900 Xe6+,8+, Ba2+ PRL94)
Elastic differential
Excitation differential• JILA-ORNL-UCL (Guo et al. > 900 3s3p Ar7+ PRA’93)• CEA-AIM (Huber et al. =130-250 3s3p Ar7+ PRL’91)• CalTech (Williams et al. =40-170 sp Mg+, Zn+, Cd+ JPB’86)
Recent review:Electron-Ion scattering, I. Williams, Rep. Prog. Phys. 62 (1999) 1431
Kinematic Broadening
E
00E
00θ
50/EE
0175.01
E
sin )E(-)E(E
0
0
0
0
20
rad
F. Fremont et al 1997
0V
0V
22
1)E( m
The zero-degree Auger Projectile Spectroscopy setup
sr4
108.1
%0.1
Sum of Rutherford and Short Sum of Rutherford and Short Range amplitudesRange amplitudes
RangeShortRutherfordfi fff
Griffin & PinzolaPRA42 (1990) 248
Differential Differential ee---ion-ion scattering cross section scattering cross section
Griffin & Pinzola PRA42 (1990) 248
18018000 differential scattering differential scattering S S →→ S cross sections S cross sections
Efficiency Determination Normalization to the bare ion BEe peak
2000 2200 2400 2600 2800 30000.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
Data
Rutherford (Bare B5+)
13 MeV B5+ + H2
Laboratory Electron Energy (eV)
DD
CS
(x
10-2
1 cm
2 /eV
sr)
3 4 5 6 7 8 9 10 11 12 13 141.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
ESM Exp. q=4 Exp. q=3 Exp. q=2
Bq+ + H2
En
ha
nce
me
nt
Fa
cto
r
Projectile Kinetic Energy (MeV)2000 2200 2400 2600 2800 30000.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
Data
Rutherford (Bare B5+) R-matrix (T. Gorczyca)
13 MeV B3+ + H2
Laboratory Electron Energy (eV)
DD
CS
(x
10-2
1 cm
2 /eV
sr)
Normalize to the Non-bare BEe peak!
Impulse Approximation: Valid down to VP/v t = 3.5
4 5 6 7 8 9 102
3
4
5
6
7
8
9
10
Toth et al This work Theory
2p2 1D
Re
son
an
t E
xcita
tion
Str
en
gth
RE
S (1
0 -18 c
m2 e
V)
Atomic Number Z
R-matrix: excellent agreement with measurements
Resonant Excitation Strength for 2p2 1D
Results:
Resonant Transfer & Excitation
T.J.M. Zouros, in Recombination of Atomic Ions, NATO Advanced Study Institute Series B: Physics, Vol. 296, pp. 271-300 (1992)
2o
RTEA )12(ξ~dΩ
)0(θdσ d
LAG.Toth et al, Physica Scripta, T92, 272-274, 2001
450 460 470 480 490 500
3
4
5
6
7
8 13.79 MeV O7+
experiment
theory
DD
CS
[1
0-21 c
m2
/(e
V s
r)]
CM Electron energy (eV)
250 260 270 280 290 3006
8
10
12
14
16
18
6.75 MeV C5+
experiment
theory
DD
CS
[1
0-21 c
m2
/(e
V s
r)]
CM electron energy (eV)
350 360 370 380 390
5
6
7
8
9
10
11
12
10.49 MeV N6+
experiment
theory
DD
CS
[1
0-21 c
m2 /(
eV
sr)
]
CM electron energy (eV)
570 580 590 600 610
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.021.72 MeV F
8+
experiment
theory
DD
CS
[1
0-21 c
m2 /(
eV
sr)
]
CM electron energy (eV)
6.75 MeV C 5+ 10.5 MeV N 6+
13.8 MeV O7+ 21.7 MeV F 8+
2p2 1D
Recombination of He-like ionsRecombination of He-like ions
Kilgus et al PRA 1993