Optimal and nearly optimal distribution functions forHe4

Abstract

The properties of the Euler-Lagrange equation obtained by minimizing the hypernetted-chain energy of a boson fluid are studied. We consider the asymptotic form of the resulting two-body distribution function, $g\left(r\right)\mathrm{}$, and show that $g\left(r\right)-1\mathrm{}$ is proportional to $r^{-4\mathrm{}}$ for short-ranged potentials. The stability condition for $g\left(r\right)\mathrm{}$ is expressed as an eigenvalue problem, and the relation to the adiabatic compressibility is established. Previous numerical results for liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ are shown to describe an energy minimum. The existence of low-lying eigenvalues for all $l$ and the nature of the related nonspherically symmetric eigenfunctions suggest the existence of additional "crystalline" solutions of the Euler-Lagrange equations.