18 July 2002, Metz (France) Omar FOJON (CONICET-UNR) Argentina 1 Molecular structure Two-center continuum wavefunction for the ejected electron Not oriented.

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Presentation transcript:

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+/H 2+ (Fojón et al, 1996) Effective Center Models for ion impact (Rivarola et al, ) Theoretical work on H 2 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 H 2 (TDCS)

18 July 2002, Metz (France) Omar FOJON (CONICET-UNR) Argentina 4 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

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

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

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

18 July 2002, Metz (France) Omar FOJON (CONICET-UNR) Argentina 9 Two Effective Center (TEC) Model ksks keke HH e e e Ionization near nucleus Complete screening by passive electron One continuum r1r1

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

18 July 2002, Metz (France) Omar FOJON (CONICET-UNR) Argentina 11 Two-Center Continuum (TCC) Model ksks keke HH e e H 2 + targets Two-continuum wave function Joulakian, Hanssen, Motassim and Rivarola PRA 54 (1996) 1473 for H2+ r1r1

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

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

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

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

17 Direct and Indirect terms ksks keke HH e e e r 1p R1R1 Direct Term

18 Direct and Indirect terms ksks keke HH e e e r 2p R2R2 Indirect Term

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

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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 N 2 Conclusions and Perspectives