Recent developments in the Wigner - Kirkwood mass formula

The recently proposed microscopic - macroscopic model for nuclear masses, based on the shell corrections obtained by using the semi - classical Wigner - Kirkwood (WK) ℏ expansion of one body quantal partition function, has been extended to the even - even deformed nuclei. The nuclear potential is assumed to be deformed Woods - Saxon with spin - orbit contribution. The Coulomb potential is obtained by folding charge densities. The resulting partition function is expanded upto the fourth order in ℏ to obtain averaged energies. The shell corrections thus obtained along with pairing energies determined within the framework of the Lipkin - Nogami scheme constitute microscopic part of the model. The macroscopic part is obtained from a liquid drop formula, with nine adjustable parameters. These parameters are fitted by considering a large set of 561 even - even nuclei with Z ≥ 8 and N ≥ 8. The fit yields rms deviation of merely 610 keV from the corresponding experimental masses. A few applications of the mass formula are presented and discussed in this paper.