Effects on the energy eigenvalues of the diffuseness parameter of the Woods-Saxon potential in heavy-ion fusion

The interactions between nuclei are commonly described using a potential which consists of the well-known repulsive Coulomb and the attractive nuclear potential which is usually taken to be of Woods-Saxon form. For the elastic scattering problems, the value of the diffuseness parameter of Woods-Saxon potential extracted by fitting precise fusion cross sections is considerably larger than the value of ≅ 0.63 fm usually accepted as a typical value. Having obtained exact solutions of the Schroedinger equation with a standard form of the deformed single-particle Woods-Saxon potential by referring Nikiforov-Uvarov method, energy eigenvalues for different values of this parameter are calculated numerically and effects on the bound states of the energy spectrum of it are discussed in heavy-ion fusion. In addition, the energy eigenvalues of the Woods-Saxon potential are investigated within the framework of complex quantum mechanics formulation. (author)