Ground-State Energy and Sound Velocity of a System of Interacting Bosons

Abstract

The method of Padé approximants is used to evaluate the ground-state energy $E_0$ of a system of interacting bosons. The density ${\rho }_0$ of particles in the zero-momentum state appears as a free parameter. In particular, the method is applied to a system of hard spheres of radius $c$ and density $\rho$. The result is close to the exact value for low densities and has a singularity at a density which corresponds to close packing when ${\rho }_0=\frac{1}{4}\rho$. The calculated sound velocity as a function of $\rho$ coincides with the experimental values for liquid helium II for ${\rho }_0=\frac{1}{2}\rho$ and $c=2.16\mathrm{}$ Å.