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Distributions of the S-matrix poles in Woods-Saxon and cut-off Woods-Saxon potentials | | P. Salamon
; Á. Baran
; T. Vertse
; | | Date: |
20 Nov 2015 | | Abstract: | The positions of the $l=0$ $S$-matrix poles are calculated
in generalized Woods-Saxon (GWS) potential and in cut-off generalized
Woods-Saxon (CGWS) potential. The solutions of the radial equations are
calculated numerically for the CGWS potential and analytically for GWS using
the formalism of Gy. Bencze cite{[Be66]}. We calculate CGWS and GWS cases at
small non-zero values of the diffuseness in order to approach the square well
potential and to be able to separate effects of the radius parameter and the
cut-off radius parameter. In the case of the GWS potential the wave functions
are reflected at the nuclear radius therefore the distances of the resonant
poles depend on the radius parameter of the potential. In CGWS potential the
wave function can be reflected at larger distance where the potential is cut to
zero and the derivative of the potential does not exist. The positions of most
of the resonant poles do depend strongly on the cut-off radius of the
potential, which is an unphysical parameter. Only the positions of the few
narrow resonances in potentials with barrier are not sensitive to the cut-off
distance. For the broad resonances the effect of the cut-off can not be
corrected by using a suggested analytical form of the first order perturbation
correction. | | Source: | arXiv, 1511.6565 | | Services: | Forum | Review | PDF | Favorites | |
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