Derivation of a proximity interaction between nuclei from the Hartree-Fock functional with Skyrme interactions

The potential between heavy or medium heavy spherical nuclei is derived on the basis of the proximity approximation and the assumption of undisturbed spherical density distributions. The HF-theory with Skyrme forces is used to write the energy as a functional of the density. The resulting potential consists of an isoscalar and a (much smaller) isospin-dependent part. Depending on the choice of the Skyrme parameters calculated interaction between heavy ions are close to the double folding potential or to the proximity potential. Our interaction can be factorized with a very good approximation into scaling factors and universal functions of the proximity distance in units of the surface thickness.