Parameterization of Woods-Saxon potential in view of Particle-vibration coupling for 208Pb

In this study, the particle-vibration coupling for nuclei around 208Pb was taken into account. Then, Hamiltonian matrix in the basis of particle vibration eigenvectors was constructed and after matrix Diagonalization, fitting with experimental states was performed. Therefore, a set of pure single particle states was obtained which also called modified experimental levels. The results show that the neutron and proton energy gap were considerably increased to 0.81 MeV and 0.39 MeV in modified spectrum, respectively. The shell model parameters of phenomenological Woods-Saxon (WS) potential was then adjusted to reproduce these modified experimental states. The results showed that, WS potential with the help of new parameters predict the experimental states more precisely.&nbsp