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

TL;DR

The paper introduces the tensor optimized Fermi sphere (TOFS) method, a new formalism for nuclear matter calculations using correlated wave functions expressed as power series or exponentials, with results consistent with existing theories.

Contribution

It develops the TOFS formalism for nuclear matter, providing a new power series and exponential wave function approach with linked-cluster expansion for energy calculations.

Findings

Results agree with Brueckner-Hartree-Fock approach

Energy per particle calculated with TOFS is consistent

Correlation functions are optimized via variational method

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, $\Psi_{N}=[\sum_{n=0}^{N} {(1/n!)F^n}]\Phi_0$ and an exponential type, $\Psi_{\rm ex}=\exp(F) \Phi_0$, with the uncorrelated Fermi-gas wave function $\Phi_0$, where the correlation operator $F$ can induce central, spin-isospin, tensor, etc.~correlations, and $\Psi_{\rm ex}$ corresponds to a limiting case of $\Psi_{N}$ ($N \rightarrow \infty$). In the TOFS formalism based on Hermitian form, it is shown that the energy per particle in nuclear matter with $\Psi_{\rm ex}$ 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 $\Psi_{N}$. We call the $N$th-order TOFS calculation for evaluating the energy with $\Psi_N$, 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.