Eur. Phys. J. D 11, 25-29 (2000)
https://doi.org/10.1007/s100530070101

Non-partial-wave Coulomb-Born theory for the excitation of many-electron atomic ions II: Numerical description and application

¹ Department of Chemistry, The Ohio State University, Columbus, OH 43210, USA and Institute for Computational Science and Engineering, Ocean University of Qingdao, Shandong 266003, P.R. China
² Department of Physics, Toyama University, Toyama 930, Japan
³ Laboratory of Atoms and Radiations, Liaoning University, Shenyang 110036, P.R. China

Received: 6 April 1999
Published online: 15 July 2000

Abstract

A non-partial-wave Coulomb-Born theory is recently formulated to treat the excitation of many-electron atomic ions for impact by an arbitrary charged particle [Y.B. Duan et al., Phys. Rev. A 56, 2431 (1997)]. The multiple expansion of the transition matrix element is decomposed into the target form factor and the projectile form factor. These are the matrix elements of the tensor operators between quantum states so that any complicated wave function for the target ion can be employed. In this formal theory, an infinitesimally small positive quantity ε is introduced artificially to guarantee the convergence of integrals. As a supplementary part of the theory, we discuss how to choose the value of ε. It is found that the ε should be taken as functions of the momentum transfer and multipolarity λ. Illustrations are carried out by calculating the cross-sections for some typical transitions – of hydrogen-like ions for impact by electron, positron, and proton, respectively. The resulting cross-sections are in good agreement with ones produced by using a method available for ion targets with Slater-type orbitals [N.C. Deb, N.C. Sil, Phys. Rev. A 28, 2806 (1993)]. Comparisons demonstrate that the Coulomb-Born theory with non-partial wave analysis provides a powerful method to treat the excitation of many-electron atomic ions impact by an arbitrary charged particle.