Eur. Phys. J. D (2013) 67: 258
https://doi.org/10.1140/epjd/e2013-40441-6

Regular Article

Relativistic calculations of the U^91 +(1s)–U⁹²⁺ collision using the finite basis set of cubic Hermite splines on a lattice in coordinate space

¹ St. Petersburg State University of Information Technologies, Mechanics and Optics, Kronverk av. 49, 197101 St. Petersburg, Russia
² Department of Physics, St. Petersburg State University, Ulianovskaya 1, Petrodvorets, 198504 St. Petersburg, Russia
³ Institut für Theoretische Physik, Technische Universität Dresden, Mommsenstraße 13, 01062 Dresden, Germany
⁴ GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstrasse 1, 64291 Darmstadt, Germany
⁵ Helmholtz-Institute Jena, 07743 Jena, Germany
⁶ Institut für Optik und Quantenelektronik, Friedrich-Schiller-Universität, 07743 Jena, Germany

^a e-mail: ilia.alexm@gmail.com

Received: 23 July 2013
Received in final form: 14 October 2013
Published online: 12 December 2013

Abstract

A new method for solving the time-dependent two-center Dirac equation is developed. The approach is based on the using of the finite basis of cubic Hermite splines on a three-dimensional lattice in the coordinate space. The relativistic calculations of the excitation and charge-transfer probabilities in the low-energy U^91 +(1s)–U⁹²⁺ collisions in two and three dimensional approaches are performed. The obtained results are compared with our previous calculations employing the Dirac-Sturm basis sets [I.I. Tupitsyn et al., Phys. Rev. A 82, 042701 (2010)]. The role of the negative-energy Dirac spectrum is investigated within the monopole approximation.