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arXiv:1111.0298 · Physical Review C

Phase separation in low-density neutron matter

Alexandros Gezerlis, Rishi Sharma

Published Jan 17, 2012• 12 citations
arXivHTMLPDF

Abstract

Low-density neutron matter has been studied extensively for many decades, with a view to better understanding the properties of neutron-star crusts and neutron-rich nuclei. Neutron matter is beyond experimental control, but in the past decade it has become possible to create systems of fermionic ultracold atomic gases in a regime close to low-density neutron matter. In both these contexts pairing is significant, making simple perturbative approaches impossible to apply and necessitating ab initio microscopic simulations. Atomic experiments have also probed polarized matter. In this work, we study population-imbalanced neutron matter (possibly relevant to magnetars and to density functionals of nuclei) arriving at the lowest-energy configuration to date. For small-to-intermediate relative fractions, the system turns out to be fully normal, while beyond a critical polarization we find phase coexistence between a partially polarized normal neutron gas and a balanced superfluid gas. As in cold atoms, a homogeneous polarized superfluid is close to stability but not stable with respect to phase separation. We also study the dependence of the critical polarization on the density.

DOI
10.1103/physrevc.85.015806

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Low-density neutron matter has been studied extensively for many decades, with a view to better understanding the properties of neutron-star crusts and neutron-rich nuclei. Neutron matter is beyond experimental control, but in the past decade it has become possible to create systems of fermionic ultracold atomic gases in a regime close to low-density neutron matter. In both these contexts pairing is significant, making simple perturbative approaches impossible to apply and necessitating ab initio microscopic simulations. Atomic experiments have also probed polarized matter. In this work, we study population-imbalanced neutron matter (possibly relevant to magnetars and to density functionals of nuclei) arriving at the lowest-energy configuration to date. For small-to-intermediate relative fractions, the system turns out to be fully normal, while beyond a critical polarization we find phase coexistence between a partially polarized normal neutron gas and a balanced superfluid gas. As in cold atoms, a homogeneous polarized superfluid is close to stability but not stable with respect to phase separation. We also study the dependence of the critical polarization on the density.
Low-density neutron matter is relevant to the study of neutron-rich nuclei and neutron star crusts. Unpolarized neutron matter has been studied extensively over a number of decades, while experimental guidance has recently started to emerge from the field of ultracold atomic gases. In this work, we study population-imbalanced neutron matter (possibly relevant to magnetars and to density functionals of nuclei) by applying a quantum Monte Carlo method that has proven successful in the field of cold atoms. We report on the first ab initiosimulations of superfluid low-density polarized neutron matter. For systems with small imbalances, we find a linear dependence of the energy on the polarization, the proportionality coefficient being dependent on the density. We also present results for the momentum and pair distributions of the two fermionic components.
Experiments with cold Fermi atoms can be tuned to probe strongly-interacting fluids that are very similar to the low-density neutron matter found in the crusts of neutron stars. In contrast to traditional superfluids and superconductors, matter in this regime is very strongly paired, with gaps of the order of the Fermi energy. We compute the T=0T=0T=0 equation of state and pairing gap for cold atoms and low-density neutron matter as a function of the Fermi momentum times the scattering length. Results of quantum Monte Carlo calculations show that the equations of state are very similar. The neutron matter pairing gap at low densities is found to be very large but, except at the smallest densities, significantly suppressed relative to cold atoms because of the finite effective range in the neutron-neutron interaction.
Ultracold dilute atomic gases can be considered as model systems to address some pending problem in Many-Body physics that occur in condensed matter systems, nuclear physics, and astrophysics. We have developed a general method to probe with high precision the thermodynamics of locally homogeneous ultracold Bose and Fermi gases. This method allows stringent tests of recent many-body theories. For attractive spin 1/2 fermions with tunable interaction (6Li), we will show that the gas thermodynamic properties can continuously change from those of weakly interacting Cooper pairs described by BardeenCooper-Schrieffer theory to those of strongly bound molecules undergoing Bose-Einstein condensation. First, we focus on the finite-temperature Equation of State (EoS) of the unpolarized unitary gas. Surprisingly, the low-temperature properties of the strongly interacting normal phase are well described by Fermi liquid theory and we localize the superfluid phase transition. A detailed comparison with theories including Monte-Carlo calculations has revealed some surprises and the Lee-Huang-Yang corrections for low-density bosonic and fermionic superfluids are quantitatively measured for the first time. Despite orders of magnitude difference in density and temperature, our equation of state can be used to describe low density neutron matter such as the outer shell of neutron stars.
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.
Cold gas experiments can be tuned to achieve strongly-interacting regimes such as that of low-density neutron matter found in neutron-stars' crusts. We report T=0T=0T=0 diffusion Monte Carlo results (i) for the ground state of both spin-1/2 fermions with short-range interactions and low-density neutron matter in a cylindrical container, and (ii) properties of these systems with a vortex line excitation. We calculate the equation of state for cold atoms and low-density neutron matter in the bulk systems, and we contrast it to our results in the cylindrical container. We compute the vortex line excitation energy for different interaction strengths, and we find agreement between cold gases and neutron matter for very low densities. We also calculate density profiles, which allow us to determine the density depletion at the vortex core, which depends strongly on the short-ranged interaction in cold atomic gases, but it is of $\ensuremath{\approx}25%$ for neutron matter in the density regimes studied in this work. Our results can be used to constrain neutron matter properties by using measurements from cold Fermi gases experiments.