A new formalism of nuclear matter: tensor-optimized Fermi sphere method

Abstract

A new formalism of nuclear matter, called “tensor-optimized Fermi sphere (TOFS) method”, is developed to handle the nuclear matter using a bare interaction among nucleons. In this formalism, the correlated nuclear matter wave function is taken to be a power-series type of the correlation function F, $\varPsi _{N}=[\sum _{n=0}^{N} (1/n!)F^{n}]\varPhi _{0}$, where F can induce central, spin-isospin, tensor, spin-orbit, etc. correlation, and $\varPhi _{0}$ is the uncorrelated Fermi-gas wave function. The validity of our formalism is based on a linked-cluster expansion theorem established in the TOFS theory with Hermitian form. The connection between $\varPsi _{N}$ and an exponential type correlated nuclear matter wave function, $\varPsi _{ex}=\exp (F) \varPhi _{0}$, is emphasized to lead to the theorem. The framework of TOFS is a variational method, in which the correlation function F is determined by minimizing the energy per particle in nuclear matter with respect to the nuclear matter wave function $\varPsi _{N}$. The first application of the TOFS theory is performed to study the property of nuclear matter using the Argonne V4’ NN potential. It is found that the density dependence of the energy per particle in nuclear matter is reasonably reproduced up to the nuclear matter density $\rho \simeq 0.20$ $\hbox {fm}^{-3}$, in comparison with other methods such as the Brueckner-Hartree-Fock (BHF) approach. We discuss the explicit contributions of many-body terms in the total energy, and indicate the importance of higher-body terms.