Introduction Ionization of molecules compared to atoms Experiment

Theoretical work on H 2 TDCS • DWVA (Zurales et al, 1988) • DWO

Experimental work on H 2 (TDCS) • Absolute Triple Differential Cross Sections (TDCS) at

The (e, 2 e) process of interest is -Intermediate and high impact energies -Asymmetric

Cross Sections • Fivefold differential cross section for coplanar asymmetric geometries – Averaging over

T-Matrix Amplitude • The prior version of the T-matrix element reads 18 July 2002,

Initial bound wavefunctions Berencz Wavefunction Heitler-London by Wang 18 July 2002, Metz (France) Omar

Final wavefunction Final Bound wavefunction Continuum wavefunction 18 July 2002, Metz (France) Omar FOJON

Two Effective Center (TEC) Model • Ionization near nucleus • Complete screening by passive

TEC final wavefunction Weck, Fojón, Hanssen, Joulakian, and Rivarola, PRA 63 (2001) 042709 appears

Two-Center Continuum (TCC) Model Joulakian, Hanssen, Motassim and Rivarola PRA 54 (1996) 1473 for

TCC wavefunction for H 2 Weck, Fojón, Hanssen, Joulakian, and Rivarola, PRA 63 (2001)

TEC vs. TCC TEC TCC • Boundary conditions satisfied • Passive electron included •

18 July 2002, Metz (France) Omar FOJON (CONICET-UNR) Argentina 14

Molecular BBK Model • TEC treatment • BBK correlated continuum wavefunction in the final

Molecular BBK Final Continuum Wf. 18 July 2002, Metz (France) Omar FOJON (CONICET-UNR) Argentina

Direct and Indirect terms ks e Direct Term r 1 p R 1 e

Direct and Indirect terms ks e R 2 Indirect Term e e r 2

MBBK Cross Sections • Neglecting indirect terms and averaging over all molecular orientations 18

Conclusions and Perspectives • MBBK: Good agreement between experiments at intermediate and high impact

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Introduction Ionization of molecules compared to atoms Experiment Theory • Molecular structure • Two-center continuum wavefunction for the ejected electron 18 July 2002, Metz (France) • Not oriented target nor particular rovibrational initial state in experiments • Vibrational nor Rotational states resolved Omar FOJON (CONICET-UNR) Argentina 1

Theoretical work on H 2 TDCS • DWVA (Zurales et al, 1988) • DWO (Monzani et al, 1999) • Influence of vibrational states, electronic vertical transitions (Weck et al, 2000) • e+/H 2+ (Fojón et al, 1996) • Effective Center Models for ion impact (Rivarola et al, 1991 -2002) 18 July 2002, Metz (France) Omar FOJON (CONICET-UNR) Argentina 2

Experimental work on H 2 (TDCS) • 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 18 July 2002, Metz (France) Omar FOJON (CONICET-UNR) Argentina 3

The (e, 2 e) process of interest is -Intermediate and high impact energies -Asymmetric coplanar geometries • Modelization – Electronic vertical transitions – Fixed molecular orientation during the collision – Neglect of exchange effects 18 July 2002, Metz (France) Omar FOJON (CONICET-UNR) Argentina 4

Cross Sections • Fivefold differential cross section for coplanar asymmetric geometries – Averaging over all molecular orientations, triple differential cross sections are obtained 18 July 2002, Metz (France) Omar FOJON (CONICET-UNR) Argentina 5

T-Matrix Amplitude • The prior version of the T-matrix element reads 18 July 2002, Metz (France) Omar FOJON (CONICET-UNR) Argentina 6

Initial bound wavefunctions Berencz Wavefunction Heitler-London by Wang 18 July 2002, Metz (France) Omar FOJON (CONICET-UNR) Argentina 7

Final wavefunction Final Bound wavefunction Continuum wavefunction 18 July 2002, Metz (France) Omar FOJON (CONICET-UNR) Argentina TEC, TCC, BBK approximations 8

Two Effective Center (TEC) Model • Ionization near nucleus • Complete screening by passive electron • One continuum ks e e r 1 ke e H 18 July 2002, Metz (France) Omar FOJON (CONICET-UNR) Argentina H 9

TEC final wavefunction Weck, Fojón, Hanssen, Joulakian, and Rivarola, PRA 63 (2001) 042709 appears in the t-matrix element If with 18 July 2002, Metz (France) Omar FOJON (CONICET-UNR) Argentina is chosen 10

Two-Center Continuum (TCC) Model Joulakian, Hanssen, Motassim and Rivarola PRA 54 (1996) 1473 for H 2+ • H 2+ targets • Two-continuum wave function ks e e ke r 1 H 18 July 2002, Metz (France) Omar FOJON (CONICET-UNR) Argentina H 11

TCC wavefunction for H 2 Weck, Fojón, Hanssen, Joulakian, and Rivarola, PRA 63 (2001) 042709 TCC for H 2 molecules Asymptotic Charge 1 Weck, Fojón, Joulakian, Stia, Hanssen and Rivarola, PRA 66 (2002) in press 18 July 2002, Metz (France) Omar FOJON (CONICET-UNR) Argentina 12

TEC vs. TCC TEC TCC • Boundary conditions satisfied • Passive electron included • Only one continuum: easy to handle 18 July 2002, Metz (France) • Boundary conditions not satisfied (correction 2 Zsc=1) • Passive electron plays no role (correction 2 Zsc=1) • Two continua Omar FOJON (CONICET-UNR) Argentina 13

18 July 2002, Metz (France) Omar FOJON (CONICET-UNR) Argentina 14

Molecular BBK Model • TEC treatment • BBK correlated continuum wavefunction in the final channel ks e e ke e H 18 July 2002, Metz (France) Omar FOJON (CONICET-UNR) Argentina H 15

Molecular BBK Final Continuum Wf. 18 July 2002, Metz (France) Omar FOJON (CONICET-UNR) Argentina 16

Direct and Indirect terms ks e Direct Term r 1 p R 1 e H e ke H 17

Direct and Indirect terms ks e R 2 Indirect Term e e r 2 p H ke H 18

MBBK Cross Sections • Neglecting indirect terms and averaging over all molecular orientations 18 July 2002, Metz (France) Omar FOJON (CONICET-UNR) Argentina 19

Conclusions and Perspectives • 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 N 2 18 July 2002, Metz (France) Omar FOJON (CONICET-UNR) Argentina 25