A perturbative treatment for the bound states of the Hellmann potential


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Ikhdair S. M. , Sever R.

JOURNAL OF MOLECULAR STRUCTURE-THEOCHEM, vol.809, pp.103-113, 2007 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 809
  • Publication Date: 2007
  • Doi Number: 10.1016/j.theochem.2007.01.019
  • Journal Name: JOURNAL OF MOLECULAR STRUCTURE-THEOCHEM
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.103-113
  • Keywords: Hellmann potential, perturbation theory, LARGE-N-EXPANSION, B-C MESON, ENERGY-LEVELS, PSEUDOPOTENTIAL METHOD, SCHRODINGER-EQUATION, APPROXIMATION METHOD, DECAY CONSTANT, COULOMB, SPECTROSCOPY, EXCITONS

Abstract

A new approximation formalism is applied to study the bound states of the Hellmann potential, which represents the superposition of the attractive Coulomb potential -a/r and the Yukawa potential bexp(-delta r)/r of arbitrary strength h and screening parameter delta. Although the analytic expressions for the energy eigenvalues E(n,l) yield quite accurate results for a wide range of n, f in the limit of very weak screening, the results become gradually worse as the strength b and the screening coefficient 6 increase. This is because that the expansion parameter is not sufficiently small enough to guarantee the convergence of the expansion series for the energy levels. (C) 2007 Elsevier B.V. All rights reserved.