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Analytic T matrices for Coulomb plus rational separable potentials

J. Math. Phys. 16, 1441 (1975); doi:10.1063/1.522691

Issue Date: July 1975

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H. van Haeringen and R. van Wageningen
Natuurkundig Laboratorium der Vrije Universiteit, Amsterdam, The Netherlands
The l=0 partial wave projected Coulomb off-shell T matrix Tc,l=0 in momentum representation is obtained in closed form. Problems existing in the literature concerning the half- and on-shell behavior of Tc and Tc,l are discussed and clarified by means of explicit formulas. The remaining derivations in this paper are based on Tc,l=0. We consider the class of N-term separable potentials where the form factors are rational functions of p2 (in momentum representation). We prove that the l=0 T matrix corresponding to the Coulomb potential plus any such so-called rational separable potential has a very simple form, namely, it can be written in terms of rational functions and the (simple) hypergeometric function with parameters (1, igamma; 1+igamma), where gamma is the well-known Coulomb parameter. Explicit analytic formulas are derived for a number of simple members of the class, the Yamaguchi potential being one of them. In this particular case the expressions of Zachary and of Bajzer are reproduced who used a method based on the O4 symmetry. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.
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KEYWORDS and PACS

Keywords
PACS
  • 03.65.Nk
    Classical and quantum physics; mechanics and fields Quantum mechanics Scattering theory, nonrelativistic
  • 24.10.-i
    Nuclear reactions and scattering, general Nuclear reaction and scattering models and methods
  • YEAR: 1975

PUBLICATION DATA

ISSN:
0022-2488 (print)   1089-7658 (online)
Publisher:
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REFERENCES (51)
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