Common nonlinearities in different approaches to nuclear physics

Abstract

It is pointed out that for 1D (3D spherically symmetric systems) the static versions of the single-particle Schrodinger equations of Hartree and Thomas-Fermi methods and of nuclear hydrodynamics are (for two- and three-body Skyrme forces) equivalent to each other having the same nonlinearities,\( \sim \psi ^3 + \psi ^5 \). At the level of two-body forces the same holds for their relation to the cubic nonlinear Schrodinger equations arising from the application of inverse methods to bound-state problems. It is speculated that this nonlinearity,\( \sim \psi ^3 \), is characteristic for nuclear physics.