The variational Hartree method is applied to a system of N bosons interacting via Skyrme-type attractive and repulsive forces. When the system condenses into its ground state, the wave function for a single boson, φ, may be described by means of the nonlinear, time-independent Schrödinger equation, ${\mathrm{\nabla }}^2$φ=${\mathrm{\epsilon }}_1$φ-A‖φ${\mathrm{\Vert }}^2$φ+B‖φ${\mathrm{\Vert }}^4$φ. In one dimension, this equation has a single, analytic, bound state solution and exhibits the property of saturation. In the physically more interesting case of three dimensions with spherical symmetry, no analytic solutions are known, so that a numerical solution must be resorted to, and this shows that saturation is again obtained. However, an analytic approximation to the three-dimensional wave function, which is very accurate for values of ${\epsilon }_1$B/$A^2$>0.1, is deduced and studied. Approximate analytic expressions for the Hartree potential energy, kinetic energy, and mean square radius of the system are thereby derived, and applications to finite nuclei and infinite nuclear matter are considered.

• Received 1 February 1988

DOI:https://doi.org/10.1103/PhysRevC.38.1911