Wigner-kirkwood method for microscopic-macroscopic calculation of binding energies

We propose to use the semi-classical Wigner-Kirkwood ℏ expansion to calculate shell corrections for spherical and deformed nuclei. The expansion is carried out up to fourth order in Latin small letter ℏ. 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 rms deviation of 630 keV. © 2010 World Scientific Publishing Company.