Low-Density Neutron Matter and the Unitary Limit

Isaac Vidaña

doi:10.3389/fphy.2021.660622

Abstract

We review the properties of neutron matter in the low-density regime. In particular, we revise its ground state energy and the superfluid neutron pairing gap and analyze their evolution from the weak to the strong coupling regime. The calculations of the energy and the pairing gap are performed, respectively, within the Brueckner–Hartree–Fock (BHF) approach of nuclear matter and the Bardeen–Cooper–Schrieffer (BCS) theory using the chiral nucleon-nucleon interaction of Entem and Machleidt at N3LO and the Argonne V18 phenomenological potential. Results for the energy are also shown for a simple Gaussian potential with a strength and range adjusted to reproduce the1S0neutron-neutron scattering length and effective range. Our results are compared with those of quantum Monte Carlo (QMC) calculations for neutron matter and cold atoms. The Tan contact parameter in neutron matter is also calculated, finding a reasonable agreement with experimental data from ultra-cold atoms only at very low densities. We find that low-density neutron matter exhibits a behavior close to that of a Fermi gas at the unitary limit, although, this limit is actually never reached. We also review the properties (energy, effective mass, and quasiparticle residue) of a spin-down neutron impurity immersed in a low-density free Fermi gas of spin-up neutrons already studied by the author in a recent work where it was shown that these properties are very close to those of an attractive Fermi polaron in the unitary limit.

Highlights

Pure neutron matter [1] is an ideal infinite nuclear system whose properties are of remarkable interest for a comprehensive understanding of neutron stars and neutron-rich nuclei
Interesting are the properties of neutron matter at low densities, since they are crucial to understanding the physics of the inner crust of neutron stars [2], where the number density varies from ∼ 10−3 to ∼ 0.08 fm−3, and matter consists of a mixture of very neutron-rich nuclei, electrons, and a superfluid neutron gas
Using the BHF approach, very recently, in reference [65] the author of the present work have analyzed the energy, effective mass and quasiparticle residue of a spindown neutron impurity in a low-density free Fermi gas of spinup neutrons, showing that these properties are in remarkable agreement with those of the attractive Fermi polaron in the unitary limit realized in ultra-cold atomic gases experiments

Summary

INTRODUCTION

Pure neutron matter [1] is an ideal infinite nuclear system whose properties are of remarkable interest for a comprehensive understanding of neutron stars and neutron-rich nuclei. Unitary Fermi gases have been experimentally realized with ultra-cold trapped alkali atoms (with 6Li and 40K being the most commonly used ones), where the effective range of the interaction is re ∼ 10−4k−F 1, and the scattering length as can be tuned from negative to positive values with the help of magnetic fields, becoming infinity at the so-called Feshbach resonance [34] These experiments provide constraints on the properties of unitary. Using the BHF approach, very recently, in reference [65] the author of the present work have analyzed the energy, effective mass and quasiparticle residue of a spindown neutron impurity in a low-density free Fermi gas of spinup neutrons, showing that these properties are in remarkable agreement with those of the attractive Fermi polaron in the unitary limit realized in ultra-cold atomic gases experiments.

GROUND STATE ENERGY

SUPERFLUID PAIRING GAP

NEUTRON POLARON

SUMMARY AND CONCLUSIONS