OPTIMAL AND NEARLY OPTIMAL DISTRIBUTION FUNCTIONS FOR HE-4

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(r), and show that g(r)-1 is proportional to r-4 for short-ranged potentials. The stability condition for g(r) is expressed as an eigenvalue problem, and the relation to the adiabatic compressibility is established. Previous numerical results for liquid He4 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. © 1979 The American Physical Society."