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

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.