Wave Functions of Continuous Spectrum of the Coulomb Two-center Problem¹

Article type: Research Article

Authors: Pavlov, Dmitry V.^a | Puzynin, Igor V.^a | Joulakian, Boghos B.^b | Vinitsky, Sergue I.^{c; 2}

Affiliations: [a] Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna 141980, Moscow Region, 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] Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Moscow Region, Russia

Correspondence: [2] The address for manuscript correspondence: Sergue I. Vinitsky, BLTP, JINR, Dubna, Moscow region, 141980, Russia. Fax: +7 09621 65084. Tel.: +7 09621 63348. E-mail: vinitsky@thsun1.jinr.ru.

Note: [1] Supported by Grant Nos. 00-02-16337, 00-01-00617 and 00-02-81023-Bel2000a from RFBR.

Abstract: The effective algorithm of the calculation of the wave functions of the continuous spectrum of the Coulomb two-center problem is proposed. The problem is solved by applying the finite-difference scheme of 4th-order and the continuous analog of the Newton method. The wave functions of the continuous spectrum of the electron of a positive hydrogen molecular ion together with the phase shifts are calculated and the corresponding pictures are presented. The absolute accuracy of the calculated phase shift is of the order of 10−6 for the electron momentum k ≥ 1 and the order of 10−4 for k ~ 0.1. The typical matrix elements of operators of the third component of the momentum and kinetic energy of an electron between the states of the continuous and discrete spectrum are also calculated.

Keywords: Coulomb two-center problem, continuous spectrum, continuous spectrum wave-functions, phase shifts, matrix elements

DOI: 10.3233/JCM-2002-21-236

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 2, no. 1-2, pp. 261-269, 2002