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Molecular structure Two-center continuum wavefunction for the ejected electron. Not oriented target nor particular rovibrational initial state in experiments Vibrational nor Rotational states resolved. Introduction. Ionization of molecules compared to atoms. Experiment. Theory. - PowerPoint PPT Presentation
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18 July 2002, Metz (France)
Omar FOJON (CONICET-UNR) Argentina
1
• Molecular structure• Two-center continuum
wavefunction for the ejected electron
• Not oriented target nor particular rovibrational initial state in experiments
• Vibrational nor Rotational states resolved
Introduction
Ionization of molecules compared to atoms
Theory Experiment
18 July 2002, Metz (France)
Omar FOJON (CONICET-UNR) Argentina
2
• DWVA (Zurales et al, 1988)• DWO (Monzani et al, 1999)• Influence of vibrational states, electronic vertical
transitions (Weck et al, 2000)
• e+/H2+ (Fojón et al, 1996)• Effective Center Models for ion impact (Rivarola et al,
1991-2002)
Theoretical work on H2 TDCS
18 July 2002, Metz (France)
Omar FOJON (CONICET-UNR) Argentina
3
• Absolute Triple Differential Cross Sections (TDCS) at very high impact energy in coplanar asymmetric geometry (Chérid et al, 1989)
• Relative TDCS at high impact energy (Jung et al, 1975 in coplanar asymmetric geometry
Experimental work on H2 (TDCS)
18 July 2002, Metz (France)
Omar FOJON (CONICET-UNR) Argentina
4
1 22 22g ge H e H
• Modelization– Electronic vertical transitions – Fixed molecular orientation during the collision– Neglect of exchange effects
The (e,2e) process of interest is
-Intermediate and high impact energies
-Asymmetric coplanar geometries
18 July 2002, Metz (France)
Omar FOJON (CONICET-UNR) Argentina
5
Cross Sections
• Fivefold differential cross section for coplanar asymmetric geometries
– Averaging over all molecular orientations, triple differential cross sections are obtained
5
24(5)02 ( )ee s
fie s s i
k kdt
d d d dE k
3
2430
12 ( )
4ee sfi
e s s i
k kdd t
d d dE k
18 July 2002, Metz (France)
Omar FOJON (CONICET-UNR) Argentina
6
T-Matrix Amplitude• The prior version of the T-matrix element reads
1 2
1 1 A Bi
P P A B
Z ZV
r r R R
1 2 1 2( ) 2 ( , , ; ) ( , , ; )efi f i it R r r V R r r
.
1 2 1 23/ 2( , , ; ) ( , ; )2
iik R
i i
eR r r r r
18 July 2002, Metz (France)
Omar FOJON (CONICET-UNR) Argentina
7
Initial bound wavefunctions
1 2( , ; ) 1 2i ir r N
1 2 2 1jA jB jA jBr r r rj e e e e Berencz Wavefunction
* * * *1 2 1 2
1 2( , ; ) A B B Br r r ri HLr r N e e e e
Heitler-London by Wang
0 1 2 00.002712 0.0711 1.1202 1.4354N
*01.166 1.406 . .a u
18 July 2002, Metz (France)
Omar FOJON (CONICET-UNR) Argentina
8
Final wavefunction
2 22 0( ; ) A Br r
f fr N e e
Final Bound wavefunction
01.3918 1.406 . . ( )a u vertical transitions
.
1 2 13/ 2( , , ; ) ( ; )2
sik R
f f C
eR r r r r
C r Continuum wavefunction TEC, TCC, BBK
approximations
18 July 2002, Metz (France)
Omar FOJON (CONICET-UNR) Argentina
9
Two Effective Center (TEC) Model
ks
ke
HH
ee
e
• Ionization near nucleus• Complete screening by passive electron• One continuum
r1
18 July 2002, Metz (France)
Omar FOJON (CONICET-UNR) Argentina
10
TEC final wavefunction
13/ 2 .
1 1 1, , 2 , ,eik rC e C j e e j jk r k r e C k r Z
*1exp( )jr
C j is chosen
appears in the t-matrix element
with j a or b
If
Weck, Fojón, Hanssen, Joulakian, and Rivarola, PRA 63 (2001) 042709
/ 21 1, , 1 / / ;1; ( . )z kC k r Z e iZ k F iZ k i kr k r
18 July 2002, Metz (France)
Omar FOJON (CONICET-UNR) Argentina
11
Two-Center Continuum (TCC) Model
ks
ke
HH
e
e
• H2+ targets
• Two-continuum wave function
Joulakian, Hanssen, Motassim and Rivarola PRA 54 (1996) 1473 for H2+
r1
18 July 2002, Metz (France)
Omar FOJON (CONICET-UNR) Argentina
12
TCC wavefunction for H2
13/ 2 .
1 1 1, 2 , , , ,eik rC e e A sc e B sck r e C k r Z C k r Z
/ 21 1, , 1 / / ;1; ( . )z kC k r Z e iZ k F iZ k i kr k r
TCC for H2 molecules
2 1scZ Asymptotic Charge 1
Weck, Fojón, Hanssen, Joulakian, and Rivarola, PRA 63 (2001) 042709
Weck, Fojón, Joulakian, Stia, Hanssen and Rivarola, PRA 66 (2002) in press
18 July 2002, Metz (France)
Omar FOJON (CONICET-UNR) Argentina
13
• Boundary conditions satisfied
• Passive electron included
• Only one continuum: easy to handle
• Boundary conditions not satisfied (correction 2Zsc=1)
• Passive electron plays no role (correction 2Zsc=1)
• Two continua
TEC vs. TCC
TEC TCC
18 July 2002, Metz (France)
Omar FOJON (CONICET-UNR) Argentina
14
0 50 100 150 200 250 300 3500
1
2
3
4 Exp. from Chérid et al (1989) CWLA from Zurales et al (1988) TCC C-TCC TEC
s= 1 deg
3DC
S (
a.u.
)
e (deg)
18 July 2002, Metz (France)
Omar FOJON (CONICET-UNR) Argentina
15
• TEC treatment
• BBK correlated continuum wavefunction in the final channel
Molecular BBK Model
ks
ke
HH
e
e
e
18 July 2002, Metz (France)
Omar FOJON (CONICET-UNR) Argentina
16
13/ 2 .
1 1 1 1, 2 , , , , , ,eik rC e e j e s j s P P ePk r e C k r C k R C k r
ee
Z
k
ss
Z
k
1
1
2ePPk
Molecular BBK Final Continuum Wf.
17
Direct and Indirect terms
ks
ke
HH
e
e
e
, ,, ( )
, ,e dir indfi j l l j
j l j l
t t t j l a b
* *2 11 2 2. .
, 1 11
1 1, , j je l lr rik r r rdir iK R
j l C j j pp j
t e r R r e e e e er R
r1pR1
Direct Term
18
Direct and Indirect terms
ks
ke
HH
e
e
e
, ,, ( )
, ,e dir indfi j l l j
j l j l
t t t j l a b
* *2 11 2 2. .
, 1 12
1 1, , j je l lr rik r r rind iK R
j l C j j pp l
t e r R r e e e e er R
r2p
R2Indirect Term
18 July 2002, Metz (France)
Omar FOJON (CONICET-UNR) Argentina
19
MBBK Cross Sections• Neglecting indirect terms and averaging over
all molecular orientations
ek K
3 2253 *
0
0
4 2 , ; ,
sin( )1
e se
e s e i
k kdN I K k
d d dE k
i sK k k
20
210 240 270 300 3300
1
290 180 270
1
2
390 180 270
0
1
2
3
4
(c) s= 3°
Ejection angle e (deg)
(b) s= 1.5°
TD
CS
(a.u
.)
Ei= 4087 eV
Ee= 20 eV (a)
s= 1°
MBBK TEC Chérid M et al (1989) 2 x BBK
21
0.00
0.09
0.18
0.270.00
0.09
0.18
0.27
210 240 270 300 3300.00
0.09
0.18
(b) s=8.9°
Ejection angle e (deg)
TDCS
(a.u
.)
(a) s=8.2°E
i=4168eV
Ee=100eV
MBBK TEC Chérid et al (1989) 2x BBK (H)
(c) s=9.6°
22
0 90 180 270 3600
3
6
0
4
8
12
16
20
(b) s=8°
T
DC
S (
a.u
.)
Ejection angle e (deg)
(a) s=4°E
i=250eV
Ee=4.5eV
MBBK TEC Jung et al (1975) 2xBBK(H) DWVA
230 90 180 270 360
0
1
2
3
0
2
4
6
(c) s=12°
Ejection angle e (deg)
MBBK TEC Jung et al (1975) Monzani et al (1999) 2 x BBK (H) (b)
s=8°
Ei=250eV
Ee=9eV
TD
CS
(a
.u.)
0
3
6
9
12(a)
s=4°
240 90 180 270 360
0
2
4
0
3
6
9
12E
i= 100 eV
Ee= 4.5 eV
(b) s=15°
Ejection angle e (deg)
(a) s=7°
TD
CS
(a
.u.)
MBBK TEC Jung et al (1975) 2 x BBK (H)
18 July 2002, Metz (France)
Omar FOJON (CONICET-UNR) Argentina
25
• MBBK: Good agreement between experiments at intermediate and high impact energy
• TEC and TCC: describe well experiments at high impact energy
• Inclusion of e-e repulsion crucial to describe the binary and recoil peak region
• Extension of TEC treatment to other diatomic molecules such as N2
Conclusions and Perspectives