Liquid drop model with different neutron versus proton deformations

The nuclear binding energies for 28 nuclei including several isotopic chains with masses ranging from $A=64\mathrm{}$ to $A=226\mathrm{}$ were evaluated using the Skyrme effective nucleon-nucleon interaction and the extended Thomas-Fermi approximation. The neutron and proton density distributions are assumed in the form of Fermi functions, the parameters of which are determined so as to minimize the total binding energy of any given nucleus. The present study is restricted to quadrupole shapes, but the neutron and proton density distributions are free to have different deformations. A simple expression for the variation of the nuclear energy with the neutron-proton deformation difference is derived.