Tensor optimized Fermi sphere method for nuclear matter—Power series correlated wave function and a cluster expansion

Abstract

A new formalism, called “tensor optimized Fermi sphere (TOFS) method”, is developed to treat the nuclear matter using a bare interaction among nucleons. In this method, the correlated nuclear matter wave function is taken to be a power series type, ΨN=[∑n=0N(1∕n!)Fn]Φ0 and an exponential type, Ψex=exp(F)Φ0, with the uncorrelated Fermi-gas wave function Φ0, where the correlation operator F can induce central, spin–isospin, tensor, etc. correlations, and Ψex corresponds to a limiting case of ΨN (N→∞). In the TOFS formalism based on Hermitian form, it is shown that the energy per particle in nuclear matter with Ψex can be expressed in terms of a linked-cluster expansion. On the basis of these results, we present the formula of the energy per particle in nuclear matter with ΨN. We call the Nth-order TOFS calculation for evaluating the energy with ΨN, where the correlation functions are optimally determined in the variation of the energy. The TOFS theory is applied for the study of symmetric nuclear matter using a central NN potential with short-range repulsion. The calculated results are fairly consistent to those of other theories such as the Brueckner–Hartree–Fock approach etc.