Diffuse surface nuclear and Coulomb potential energies for heavy-ion reactions

The nuclear and Coulomb potential energies are calculated for heavy-ion reactions using a modified form of the liquid-drop model of the nucleus. Effects of the finite range of the nuclear force, of the surface diffuseness and intrinsic deformation of spheroidal interacting ions are included explicitly. In order to evaluate the potential energies before the density distributions of the two nuclei overlap appreciably, multipole expansion formulae are derived, from which the dependence of the interaction energy upon the relative orientation of the ions can be studied in detail. After the densities begin to overlap, an adiabatic approximation for the nuclear and Coulomb energies is achieved by prescribing a continuous deformation of the density distributions, as proposed by Nix and Sierk. Special attention is paid to the choice of the radius and diffuseness parameters of the ions. Furthermore, the constants of the model are selected from a study of fusion radii and barrier heights, fission saddle-point energies, nuclear energy at the strong absorption radius, and fusion cross sections for light ion systems at energies below the Coulomb barrier. In particular, the fusion of two oblate 12C nuclei is examined and it is shown that the corresponding cross section below the Coulomb barrier depends strongly on their relative orientation. The fusion of two spherical 16O nuclei is also discussed. (Auth.)