Neutron and proton distribution in nuclei

We calculate the energy gap for deformed nuclei using the gap equation which appears in the Migdal theory of finite Fermi systems with pair correlations. To obtain good agreement with experiment for nuclei with neutron excess, it is necessary to choose differently the forms of the density dependent residual interaction for the protons and neutrons because of the difference between their density distributions. The distributions we get are in good agreement with experiment as well as with other theoretical predictions. We also show which approximations are required to reduce the general gap equation to the special Migdal equation.