Theory of the (Normal) Ground State of Liquid Helium Three

Abstract

A theory of the normal ground state of liquid ${\mathrm{He}}^{3}$ is constructed using matrix elements in a representation of correlated basis functions. The Rayleigh-Schr\"odinger perturbation theory is adapted to our nonorthogonal basis. Several means of classifying terms are avaiable; one of them is recognized as best suited for the study of liquid ${\mathrm{He}}^{3}$. To the second order in the classification scheme, the following ground-state properties are calculated and compared with experiment and results of the Brueckner-Gammel theory: energy per particle, equilibrium density, compressibility, velocity of sound, and paramagnetic susceptibility. The radial distribution function of liquid ${\mathrm{He}}^{3}$ at zero temperature is also calculated. A study of the L\"owdin transformation as a procedure for orthogonalizing the correlated basis shows that the correction to the Hamiltonian involves unphysical $N$ dependences; these arise out of high-order irreducible clusters and unlinked diagrams. It is verified that the unphysical terms cancel out completely in each of several lowest orders.