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Hadrons and Nuclei


Eur. Phys. J. A 11, 175-183 (2001)

s-wave bound and scattering state wave functions for a velocity-dependent Kisslinger potential

M. Al Jaghoub

Hashemite University, P.O. Box 150459, Zarka 13115, Jordan

mij@hu.edu.jo

(Received: 3 March 2001 / Revised version: 8 June 2001 Communicated by V. Vento)

Abstract
A relation linking the normalized s-wave scattering and the corresponding bound state wave functions at bound state poles is derived. This is done in the case of a non-local, velocity-dependent Kisslinger potential. Using formal scattering theory, we present two analytical proofs of the validity of the theorem. The first tackles the non-local potential directly, while the other transforms the potential to an equivalent local but energy-dependent one. The theorem is tested both analytically and numerically by solving the Schrödinger equation exactly for the scattering and bound state wave functions when the Kisslinger potential has the form of a square well. A first order approximation to the deviation from the theorem away from bound state poles is obtained analytically. Furthermore, a proof of the analyticity of the Jost solutions in the presence of a non-local potential term is also given.

PACS
03.65.Nk - Scattering theory.
24.90.+d - Other topics in nuclear reactions: general.

© Società Italiana di Fisica, Springer-Verlag 2001