Classical Self-Consistent Nuclear Model

Abstract

The Thomas-Fermi method in simplest form is applied to find the radial distribution of nucleons in a spherical nucleus in the absence of Coulomb forces. Saturation is obtained by hypothesizing a two-body force quadratically dependent on relative momentum. The effective one-nucleon potential energy is therefore velocity dependent. Solving the basic integral equation and imposing generally accepted values for the average and Fermi kinetic energies in the nuclear matter limit ($A\ensuremath{\rightarrow}\ensuremath{\infty}$) gives a solution exhibiting surface and saturated interior regions. Fixing one more parameter (the force range, taken to be $\frac{\ensuremath{\hbar}}{{m}_{\ensuremath{\pi}}c}$) determines all numerical features (e.g., surface thickness, interaction strength) at reasonable values.