Microscopic-macroscopic approach for binding energies with the Wigner-Kirkwood method

Abstract

The semiclassical Wigner-Kirkwood $\ensuremath{\hbar}$ expansion method is used to calculate shell corrections for spherical and deformed nuclei. The expansion is carried out up to fourth order in $\ensuremath{\hbar}$. A systematic study of Wigner-Kirkwood averaged energies is presented as a function of the deformation degrees of freedom. The shell corrections, along with the pairing energies obtained by using the Lipkin-Nogami scheme, are used in the microscopic-macroscopic approach to calculate binding energies. The macroscopic part is obtained from a liquid drop formula with six adjustable parameters. Considering a set of 367 spherical nuclei, the liquid drop parameters are adjusted to reproduce the experimental binding energies, which yields a root mean square (rms) deviation of 630 keV. It is shown that the proposed approach is indeed promising for the prediction of nuclear masses.