The Correlated Basis Function Method and its Application to Liquid 3He, Nuclear Matter and Neutron Matter

Abstract

Abstract The method of correlated basis functions is studied and applied to the Fermi systems: liquid 3 He, nuclear matter and neutron matter. The reduced cluster integrals xijkl... and so the sub-normalization integrals Iijkl... are generalized to coinciding quantum numbers out of the set {i, j, k, I,...}. This generalization has an important consequence for the radial distribution function g (r) (and then for the liquid structure function) ; g(r) has no contributions of the order O (A-1). For 3 He the state-independent two-body correlation function g(r) is calculated from the Euler-Lagrange equation (in the limit of r → 0) for the unrenormalized two-body energy functional. For nuclear matter and neutron matter we adopt the three-parameter correlation function of Bäckman et al. Then the energy expectation values are calculated by including up to the three-body terms in the unrenormalized and renormalized version of the correlated basis functions method. The experimental ground-state energy and density of liquid s He can be well reproduced by the present method with the Lennard-Jones-(6 -12) potential. The same method is applied to the nuclear matter and neutron matter calculations with the OMY-potential. The results of the energy expectation values indicate a practical superiority of the unrenormalized cluster expansion method over the renormalized one.