Hartree solutions for the self-Yukawian boson sphere

Abstract

The ground state of an N-boson assembly interacting through two-body attractive Yukawa forces is analyzed in the Hartree approximation. The solution, which is not universal, can be adequately characterized by a unique parameter \ensuremath{\mu}\ifmmode \tilde{}\else \~{}\fi{} proportional to \ensuremath{\mu}${N}^{\mathrm{\ensuremath{-}}1}$, where ${\ensuremath{\mu}}^{\mathrm{\ensuremath{-}}1}$ is the range of the force. It is found that for \ensuremath{\mu}\ifmmode \tilde{}\else \~{}\fi{} larger than a critical value, there is no bound solution for the system. Our solutions are shown to rigorously fulfill the virial theorem.