Coupled-cluster studies of infinite nuclear matter

Abstract

Background: Coupled-cluster (CC) theory is a widely used many-body method for studying strongly correlated many-fermion systems. It allows for systematic inclusions of complicated many-body correlations beyond a mean field. Recent applications to finite nuclei have shown that first-principles approaches like CC theory can be extended to studies of medium-heavy nuclei, with excellent agreement with experiment. However, CC calculations of properties of infinite nuclear matter are rather few and date back more than 30 yr.Purpose: The aim of this work is thus to develop the relevant formalism for performing CC calculations in nuclear matter and neutron-star matter, including thereby important correlations to infinite order in the interaction and testing modern nuclear forces based on chiral effective field theory. Our formalism includes also the exact treatment of the so-called Pauli operator in a partial-wave expansion of the equation of state.Methods: Nuclear- and neutron-matter calculations are done using a coupled particle-particle and hole-hole ladder approximation. The coupled ladder equations are derived as an approximation of CC theory, leaving out particle-hole and nonlinear diagrams from the CC doubles amplitude equation. This study is a first step toward CC calculations for nuclear and neutron matter.Results: We present results for both symmetric nuclear matter and pure neutron matter employing state-of-the-art nucleon-nucleon interactions based on chiral effective field theory. We employ also the newly optimized chiral interaction [Ekstr\"om et al., Phys. Rev. Lett. 110, 192502 (2013)] to study infinite nuclear matter. The ladder approximation method and corresponding results are compared with conventional Brueckner-Hartree-Fock theory. The ladder approximation is derived and studied using both exact and angular-averaged Pauli exclusion operators, with angular-averaged input momenta for the single-particle potentials in all calculations. The inclusion of an exact treatment of the Pauli operators in a partial-wave expansion yields corrections of the order of $1.7%--2%$ of the total energy in symmetric nuclear matter. Similarly, the inclusion of both hole-hole and particle-particle ladders result in corrections of the order $0.7%--2%$ compared to the approximation with only particle-particle ladders. Including these effects, we get at most almost a $6%$ difference between our CC calculation and the standard Brueckner-Hartree-Fock approach.Conclusions: We have performed CC calculations of symmetric nuclear matter and pure neutron matter including particle-particle and hole-hole diagrams to infinite order using an exact Pauli operator and angular-averaged single-particle energies. The contributions from hole-hole diagrams and exact Pauli operators add important changes to the final energies per particle.