Damping the tail of the Woods-Saxon potential

Cutting of the tail of the Woods Saxon (WS) potential influences the distribution of the poles of the S-matrix considerably. A new attempt is made here to correct the tail of the cut-off WS potential in order to bring the positions of the poles closer to the WS potential without cut. New types of strictly finite range potentials are introduced in which the tail of the WS and the generalized Woods-Saxon (GWS) potentials are modified to damp them at their ends. This damping affects the energies of the bound and narrow resonant states weakly. The resonant pole positions in the new potentials were affected more significantly and the new pole positions became closer to that of the GWS potential without, cut. However, the cut-off effect, cannot be diminished completely. The new potentials belong to the C-infinity function class.