Eur. Phys. J. A 13, 349-354 (2002)
Bound and scattering wave functions for a velocity-dependent Kisslinger potential for l > 0
M. I JaghoubHashemite University, P.O. Box 150459, Zarka 13115, Jordan mij@hu.edu.jo
(Received: 17 October 2001 / Revised version: 4 January 2002 Communicated by V. Vento )
Abstract
Using formal scattering theory, the scattering wave functions are
extrapolated to negative energies corresponding to bound-state
poles. It is shown that the ratio of the normalized scattering and
the corresponding bound-state wave functions, at a bound-state
pole, is uniquely determined by the bound-state binding energy.
This simple relation is proved analytically for an arbitrary
angular momentum quantum number
l
> 0 , in the presence of a velocity-dependent Kisslinger
potential. The extrapolation relation is tested analytically by
solving the Schrödinger equation in the
p-wave case exactly
for the scattering and the corresponding bound-state wave functions
when the Kisslinger potential has the form of a square well. A
numerical resolution of the Schrödinger equation in the
p-wave case and of a square-well Kisslinger potential is carried
out to investigate the range of validity of the extrapolated
connection. It is found that the derived relation is satisfied
best at low energies and short distances.
03.65.Nk - Scattering theory.
24.90.+d - Other topics in nuclear reactions: general (restricted to new topics in section 24).
© Società Italiana di Fisica, Springer-Verlag 2002
