A variational theory of nuclear matter

Abstract

The pair-correlation operator f ij in the variational wave function of nuclear matter is generated from a two-body Schrc̈dinger equation with boundary conditions which require the correlated wave function to heal at a distance d. The two-body cluster energy is calculated exactly, while the f ij is approximated by a sum of central, spin, isospin and tensor correlation operators to evaluate the many-body cluster contributions (MBCC). The distribution functions that represent the MBCC are expanded in powers of the non-central correlations. The zeroth order term in this expansion represents a sum of all MBCC with central correlations, and is evaluated by the Fermi hypernetted chain equations. The first order terms are identically zero, while all the second order terms are calculated. When the range of correlations d is about 2 r 0 the expansion appears to converge, and is used to obtain upper bounds to the nuclear matter energy with various potentials. The upper bounds are much lower than energies suggested by earlier calculations; for example the Reid soft core potential gives E( k F = 1.7 fm −1) < −25 MeV. More stringent upper bounds, hopefully close to the true energy, may be obtained by minimizing E( d). The minimum is expected at d ≈ 3 r 0; however at such large vales of d the three-body tensor rings in the second order terms give large negative contribution. General rules for calculating higher order terms in the expansion are given and the method seems simple enough to study the third and higher order terms.