Low-density Neutron Matter Research Articles

Strongly paired fermions: Cold atoms and 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 $T=0$ 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.

Recent Progress in Quantum Monte Carlo Calculations of Nuclear Structure and Reactions

We describe recent progress in Quantum Monte Carlo calculations of nuclear structure and reactions. Significant advances have been made recently in understanding the nuclear Hamiltonian, including realistic two- and three-nucleon interactions. We describe recent progress in solving the nuclear Hamiltonian for two important long-standing problems in nuclear theory: (1) low-energy scattering in n- 4 He and the spin-orbit splitting obtained with microscopic Hamiltonians, and (2) the pairing gap in low-density neutron matter. Accurate calculations of both quantities are fundamental in understanding nuclei from the underlying microscopic Hamiltonian.

The neutrino response of low-density neutron matter from the virial expansion

Abstract We generalize our virial approach to study spin-polarized neutron matter and the consistent neutrino response at low densities. In the long-wavelength limit, the virial expansion makes model-independent predictions for the density and spin response, based only on nucleon–nucleon scattering data. Our results for the neutrino response provide constraints for random-phase approximation or other model calculations, and we compare the virial vector and axial response to response functions used in supernova simulations. The virial expansion is suitable to describe matter near the supernova neutrinosphere, and this work extends the virial equation of state to predict neutrino interactions in neutron matter.

The virial equation of state of low-density neutron matter

We present a model-independent description of low-density neutron matter based on the virial expansion. The virial equation of state provides a benchmark for all nuclear equations of state at densities and temperatures where the interparticle separation is large compared to the thermal wavelength. We calculate the second virial coefficient directly from the nucleon-nucleon scattering phase shifts. Our results for the pressure, energy, entropy and the free energy correctly include the physics of the large neutron-neutron scattering length. We find that, as in the universal regime, thermodynamic properties of neutron matter scale over a wide range of temperatures, but with a significantly reduced interaction coefficient compared to the unitary limit.

Erratum: Mean field calculation of thermal properties of simple nucleon matter on a lattice [Phys. Rev. C 70, 014315 (2004)

Thermal properties of single species nucleon matter are investigated assuming a simple form of the nucleon-nucleon interaction. The nucleons are placed on a cubic lattice, hopping from site to site and interacting through a spin-dependent force, as in the extended, attractive Hubbard model. A mean field calculation in the Hartree-Fock Bogoliubov approximation suggests that the superfluid ground state generated by strong nucleon pairing undergoes a second-order phase transition to a normal state as the temperature increases. The calculation is shown to lead to a promising description of the thermal properties of low-density neutron matter. A possibility of a density wave phase is also examined.

Mean field calculation of thermal properties of simple nucleon matter on a lattice

Thermal properties of single species nucleon matter are investigated assuming a simple form of the nucleon-nucleon interaction. The nucleons are placed on a cubic lattice, hopping from site to site and interacting through a spin-dependent force, as in the extended, attractive Hubbard model. A mean field calculation in the Hartree-Fock-Bogoliubov approximation suggests that the superfluid ground state generated by strong nucleon pairing undergoes a second-order phase transition to a normal state as the temperature increases. The calculation is shown to lead to a promising description of the thermal properties of low-density neutron matter. A possibility of a density wave phase is also examined.

Off-shell pairing correlations from meson-exchange theory of nuclear forces

We develop a model of off-mass-shell pairing correlations in nuclear systems, which is based on the meson-exchange picture of nuclear interactions. The temporal retardations in the model are generated by the Fock-exchange diagrams. The kernel of the complex gap equation for baryons is related to the in-medium spectral function of mesons, which is evaluated nonperturbatively in the random phase approximation. The model is applied to the low-density neutron matter in neutron star crusts by separating the interaction into a long-range one-pion-exchange component and a short-range component parametrized in terms of Landau Fermi liquid parameters. The resulting Eliashberg-type coupled nonlinear integral equations are solved by an iterative procedure. We find that the self-energies extend to off-shell energies of the order of several tens of MeV. At low energies the damping of the neutron pair correlations due to the coupling to the pionic modes is small, but becomes increasingly important as the energy is increased. We discuss an improved quasiclassical approximation under which the numerical solutions are obtained.

GFMC studies of low-density neutron matter

Green's function Monte Carlo methods are used to provide benchmarks for studies of low-density neutron matter. The zero-temperature equation of state and pair correlation functions are studied for the AV8 $^\prime$ NN interaction model, and for an idealized model comprised of neutrons with a short-range interaction and an arbitrarily large (negative) scattering length. For this idealized problem the equation of state is a constant multiplied by the Fermi-gas energy, this constant is found to be nearly 1/2. Similar ratios are found for realistic NN interactions.

Spatial structure of a vortex in low density neutron matter.

We study in a fully self-consistent approach the structure of a vortex in low density superfluid neutron matter. We determine that the matter density profile of a vortex shows a significant depletion in the region of the core, a feature never reported for a vortex state in a Fermi superfluid.

Trapped atomic Fermi gases

A many-body system of fermion atoms with a model interaction characterized by the scattering length a is considered. We treat both a and the density as parameters assuming that the system can be created artificially in a trap. If a is negative the system becomes strongly correlated at densities ρ∼| a| −3, provided the scattering length is the dominant parameter of the problem. It means that we consider | a| to be much bigger than the radius of the interaction or any other relevant parameter of the system. The density ρ c1 at which the compressibility vanishes is defined by ρ c1 ∼| a| −3. Thus, a system composed of fermion atoms with the scattering length a→−∞ is completely unstable at low densities, inevitably collapsing until the repulsive core stops the density growth. As a result, any Fermi system possesses the equilibrium density and energy if the bare particle–particle interaction is sufficiently strong to make a negative and to be the dominant parameter. This behavior can be realized in a trap. Our results show that a low density neutron matter can have the equilibrium density.

Pairing with polarization effects in low-density neutron matter

We study the properties of the ${}^{1}{S}_{0}$ pairing gap in low-density neutron matter. Different corrections to the lowest-order scattering length approximation are explored, resulting in a strong suppression with respect to the BCS result.

Effective interactions and superfluid energy gaps for low density neutron matter

We use a polarization potential approach to calculate properties of neutron matter at sub-nuclear densities with particular attention to the superfluid pairing interaction. Our model divides the quasi-particle scattering amplitude at the Fermi surface into two distinct parts: a direct particle-hole irreducible piece and an induced particle-hole reducible contribution. The direct part is constructed from realistic two-nucleon potentials. Short-range correlations are taken into account phenomenologically by modifying the potentials at short distances. The induced contribution is generated as a self-consistent summation of particle-hole reducible diagrams. The resulting quasi-particle scattering amplitude is fully antisymmetric for all moment 0⩽ q⩽2 k F. Realistic bounds on the s-wave pairing gap are given and consequences for the dynamics of rotating neutron stars are briefly discussed.

Effect of polarization on superfluidity in low density neutron matter

It is shown that, contrary to an earlier estimate, the polarizability of the neutron medium tends to suppress rather than enhance the isotropic energy gap in low-density neutron-star matter.