Eur. Phys. J. A 11, 175-183 (2001)
s-wave bound and scattering state wave functions for a velocity-dependent Kisslinger potential
M. Al JaghoubHashemite 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.
03.65.Nk - Scattering theory.
24.90.+d - Other topics in nuclear reactions: general.
© Società Italiana di Fisica, Springer-Verlag 2001
