Matching polynomial tails to the cut-off Woods–Saxon potential

Cutting off the tail of the Woods–Saxon (WS) and generalized WS (GWS) potentials changes the distribution of the poles of the S-matrix considerably. Here, we modify the tail of the cut-off WS (CWS) and cut-off generalized WS (CGWS) potentials by attaching Hermite polynomial tails to them beyond the cut. The tails reach the zero value more or less smoothly at the finite ranges of the potential. Reflections of the resonant wave functions can take place at different distances. The starting points of the pole trajectories have been reproduced not only for the real values and the moduli of the starting points, but also for the imaginary parts.