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, ${\Psi }_N=[{\sum }_{n=0}^N(1/n!)F^n]{\Phi }_0$ and an exponential type, ${\Psi }_{\mathrm{ex}}=\exp (F){\Phi }_0$, with the uncorrelated Fermi-gas wave function ${\Phi }_0$, where the correlation operator $F$ can induce central, spin-isospin, tensor, etc.~correlations, and ${\Psi }_{\mathrm{ex}}$ corresponds to a limiting case of ${\Psi }_N$ ($N\to \infty$). In the TOFS formalism based on Hermitian form, it is shown that the energy per particle in nuclear matter with ${\Psi }_{\mathrm{ex}}$ 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.

35 pages, 2 figures: version accepted for publication in Annals of Physics

References in corpus (10)

• Quantum Monte Carlo calculation of the equation of state of neutron matter
• Quantum Monte Carlo calculations of symmetric nuclear matter
• Critical Temperature for $\alpha$-Particle Condensation within a Momentum Projected Mean Field Approach
• Tensor-optimized antisymmetrized molecular dynamics as a successive variational method in nuclear many-body system
• Many Body Approach for Quartet Condensation in Strong Coupling
• Successive variational method of the tensor-optimized antisymmetrized molecular dynamics for central interaction in finite nuclei
• Power series expansion method in tensor-optimized antisymmetrized molecular dynamics beyond the Jastrow correlation method
• Diagrammatic calculation of thermodynamical quantities in nuclear matter
• Hybridization of tensor-optimized and high-momentum antisymmetrized molecular dynamics for light nuclei with bare interaction
• Short-range correlation in high-momentum antisymmetrized molecular dynamics

Cited by in corpus (4)

• Contact representation of short range correlation in light nuclei studied by the High-Momentum Antisymmetrized Molecular Dynamics
• Variational calculation of nuclear matter in finite particle number approach using unitary correlation operator and high-momentum pair methods
• Finite particle number description of neutron matter using the unitary correlation operator and high-momentum pair methods
• Finite particle-number description of symmetric nuclear matter with spin excitations of high-momentum pairs induced by tensor force