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arXiv:2201.01308 · Condensed Matter

The 1S0 Pairing Gap in Neutron Matter

Stefano Gandolfi, Georgios Palkanoglou, Joseph Carlson, Alexandros Gezerlis, Kevin E. Schmidt

Published Feb 1, 2022• 26 citations
arXivHTMLPDF

Abstract

We report ab initio calculations of the S wave pairing gap in neutron matter calculated using realistic nuclear Hamiltonians that include two- and three-body interactions. We use a trial state, properly optimized to capture the essential pairing correlations, from which we extract ground state properties by means of auxiliary field diffusion Monte Carlo simulations. We extrapolate our results to the thermodynamic limit by studying the finite-size effects in the symmetry-restored projected Bardeen-Cooper-Schrieffer (PBCS) theory and compare our results to other ab initio studies done in the past. Our quantum Monte Carlo results for the pairing gap show a modest suppression with respect to the mean-field BCS values. These results can be connected to cold atom experiments, via the unitarity regime where fermionic superfluidity assumes a unified description, and they are important in the prediction of thermal properties and the cooling of neutron stars.

DOI
10.3390/condmat7010019

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We report ab initio calculations of the S wave pairing gap in neutron matter calculated using realistic nuclear Hamiltonians that include two- and three-body interactions. We use a trial state, properly optimized to capture the essential pairing correlations, from which we extract ground state properties by means of auxiliary field diffusion Monte Carlo simulations. We extrapolate our results to the thermodynamic limit by studying the finite-size effects in the symmetry-restored projected Bardeen-Cooper-Schrieffer (PBCS) theory and compare our results to other ab initio studies done in the past. Our quantum Monte Carlo results for the pairing gap show a modest suppression with respect to the mean-field BCS values. These results can be connected to cold atom experiments, via the unitarity regime where fermionic superfluidity assumes a unified description, and they are important in the prediction of thermal properties and the cooling 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.
Abstract We compute singlet pairing gaps and critical temperatures in pure neutron matter with different many-body approximations. Medium effects tend to reduce gaps and critical temperatures compared to the standard BCS ansatz. In the mean-field approximation, the ratio of these two quantities remains constant across a wide range of densities. This constant ratio is close to the universal prediction of BCS theory, whether three-neutron interactions are included or not. Using a more sophisticated many-body approach that incorporates the effect of short-range correlations in pairing properties, we find that the gap to critical temperature ratio in the low-density regime is substantially larger than the BCS prediction, independently of the interaction. In this region, our results are relatively close to experiments and theoretical calculations from the unitary Fermi gas. We also find evidence for a different density dependence of zero-temperature gaps and critical temperatures in neutron matter.
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.
We present theoretical and experimental evidence for a new phase of matter in neutron-rich systems that we call multimodal superfluidity. Using ab initio lattice calculations, we show that the condensate consists of coexisting s-wave pairs, p-wave pairs in entangled double pair combinations, and quartets composed of bound states of two s-wave pairs. We identify multimodal superfluidity as a general feature of single-flavor spin-1/2 fermionic systems with attractive s-wave and p-wave interactions, provided the system is stable against collapse into a dense droplet. Beyond neutrons at sub-saturation densities, we demonstrate that this phase appears in generalized attractive extended Hubbard models in one, two, and three dimensions. We elucidate the mechanism for this coexistence using self-consistent few-body Cooper models and compare with Bardeen-Cooper-Schrieffer theory. We also derive the form of the effective action and show that spin, rotational, and parity symmetries remain unbroken. Finally, we analyze experimental data to show that p-wave pair gaps and quartet gaps are present in atomic nuclei, and we discuss the consequences of this new phase for the structure and dynamics of neutron star crusts.
After a brief historical overview of superfluidity in connection with neutron matter and cold fermionic atoms, we discuss the commonalities between these two systems as well as their relevance to the physics of neutron star crusts. We then present the methodological tools we use to attack the many-body problem, comparing Quantum Monte Carlo to mean-field theory and to the analytic expectations at weak coupling. We review recent results on the equation of state and the pairing gap of cold atoms and neutron matter and contrast them with a variety of calculations by other groups. We conclude by giving a few directions of possible future inquiry.
Thermal properties of low-density neutron matter are investigated by determinantal quantum Monte Carlo lattice calculations on 3+1 dimensional cubic lattices. Nuclear effective field theory (EFT) is applied using the pionless single- and two-parameter neutron-neutron interactions, determined from the 1S0{}^{1}{S}_{0}1S0​ scattering length and effective range. The determination of the interactions and the calculations of neutron matter are carried out consistently by applying EFT power counting rules. The thermodynamic limit is taken by the method of finite-size scaling, and the continuum limit is examined in the vanishing lattice filling limit. The 1S0{}^{1}{S}_{0}1S0​ pairing gap at $T\ensuremath{\approx}0$ is computed directly from the off-diagonal long-range order of the spin pair-pair correlation function and is found to be approximately 30% smaller than BCS calculations with the conventional nucleon-nucleon potentials. The critical temperature Tc{T}_{c}Tc​ of the normal-to-superfluid phase transition and the pairing temperature scale T∗{T}^{*}T∗ are determined, and the temperature-density phase diagram is constructed. The physics of low-density neutron matter is clearly identified as being a BCS-Bose-Einstein condensation crossover.