  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.
