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Hadrons and Nuclei

Eur. Phys. J. A 13, 349-354 (2002)

Bound and scattering wave functions for a velocity-dependent Kisslinger potential for l > 0

M. I Jaghoub

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


(Received: 17 October 2001 / Revised version: 4 January 2002 Communicated by V. Vento )

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