Wave Packet Evolution Scheme to Ionization of Atoms and Molecules by Fast Electrons¹

Article type: Research Article

Authors: Serov, Vladislav V.^a | Derbov, Vladimir L.^{a; 2} | Joulakian, Boghos B.^{b; 3} | Rostovtsev, Vitaly^c | Vinitsky, Sergue I.^{d; 4}

Affiliations: [a] Theoretical and Nuclear Physics, Saratov State University, 83 Astrakhanskaya, Saratov 410026, Russia | [b] Institut de Physique, Laboratoire de Physique Moléculaire et des Collisions, Université de Metz, Technopôle 2000, 1 Rue Arargo, 57078 Metz Cedex 3, France | [c] Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna 141980 Moscow Region, Russia | [d] Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Moscow Region, Russia

Correspondence: [4] The address for manuscript correspondence: Sergue I. Vinitsky, BLTP, JINR, Dubna, Moscow region, 141980, Russia. E-mail: [email protected]. Fax: +7 09621 65084. Phone: +7 09621 63348.

Note: [1] Partially supported by RFBR (Grants No-00-01-00617, No-00-02-16337).

Note: [2] E-mail: [email protected].

Note: [3] E-mail: [email protected].

Abstract: A numerical method of the partial coordinate splitting for solving the 3+1 dimensional Schrödinger equation is proposed. The method is applied to the calculation of the multi-fold differential cross section of the ionization of the hydrogen atom and the hydrogen molecular ion by a fast electron impact. We propose a direct approach, which involves the reduction of the initial 6D Schrodinger equation to a 3D evolution problem followed by the modeling of the wave packet dynamics, thus avoiding the use of functions of the continuous spectrum of the ejected electron. The results obtained, after verification of the procedure in the case of atomic hydrogen, reveal interesting mechanisms in the case of small scattering angles.

Keywords: Ionization by fast electron impact, molecule, numerical method, time-dependent Schrödinger equation

DOI: 10.3233/JCM-2002-21-235

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 2, no. 1-2, pp. 253-259, 2002