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