Remarks on the Woods-Saxon potential

More recently, comprehensive applications of approximate analytical solutions of the Woods-Saxon (WS) potential in closed form for the five-dimensional Bohr Hamiltonian have appeared lid. capak, D. Petrellis, B. Conul! and D. Bonatsos, J. Phys. G42, 95102 (2015)] and its comparison to the data for many different nuclei has clearly revealed the domains for the success and failure in case of using such potential forms to analyze the data related to the nuclear structure within the frame of the collective model. Gaining confidence from this work, the exact solvability of the WS type potentials in lower dimensions for the bound states having zero angular momentum is carefully reviewed to finalize an ongoing discussion in the related literature which clearly shows that such kind of potentials have no analytical solutions even for l = 0 case.