Hot Neutron Matter Research Articles

Structure Factors for Hot Neutron Matter from AbInitio Lattice Simulations with High-Fidelity Chiral Interactions.

We present the first abinitio lattice calculations of spin and density correlations in hot neutron matter using high-fidelity interactions at next-to-next-to-next-to-leading order in chiral effective field theory. These correlations have a large impact on neutrino heating and shock revival in core-collapse supernovae and are encapsulated in functions called structure factors. Unfortunately, calculations of structure factors using high-fidelity chiral interactions were well out of reach using existing computational methods. In this Letter, we solve the problem using a computational approach called the rank-one operator (RO) method. The RO method is a general technique with broad applications to simulations of fermionic many-body systems. It solves the problem of exponential scaling of computational effort when using perturbation theory for higher-body operators and higher-order corrections. Using the RO method, we compute the vector and axial static structure factors for hot neutron matter as a function of temperature and density. The abinitio lattice results are in good agreement with virial expansion calculations at low densities but are more reliable at higher densities. Random phase approximation codes used to estimate neutrino opacity in core-collapse supernovae simulations can now be calibrated with abinitio lattice calculations.

Effect of chiral nuclear forces on the neutrino mean free path in hot neutron matter

We study the role of chiral nuclear forces on the propagation of neutrinos in hot neutron matter. In particular, we analyze the convergence of the dynamical structure factor and the neutrino mean free path with the order of the power counting of the chiral forces, as well as the role of the regulator cut-off of these forces in the determination of these quantities. Single-particle energies and chemical potentials needed to calculate the dynamical structure factor are obtained within the Brueckner--Hartree--Fock approximation extended to finite temperature. Our results show that the dynamical structure factor and the neutrino mean free path depend on the cut-off only when the chiral potential is considered at leading order (LO) and next-to leading order (NLO), becoming this dependence strongly reduced at higher orders in the chiral power counting due to the role of three-nucleon forces that start to contribute at next-to-next-to leading order (N$^2$LO) being, in particular, almost negligible at next-to-next-to-next-to leading order (N$^3$LO). The neutrino mean free path is found to converge up to densities slightly below $\sim 0.15$ fm$^{-3}$ when increasing the order of the chiral power counting, although no signal of convergence is found for densities above this value. The uncertainty associated with our order-by-order nuclear many-body calculation of the neutrino mean free path is roughly estimated from the difference between the results obtained at N$^2$LO and N$^3$LO, finding that it varies from about a few centimeters at low densities up to a bit less than $2$ meters at the largest one considered in this work, $0.3$ fm$^{-3}$.

Asymmetry of the neutrino mean free path in partially spin polarized neutron matter within the Skyrme model

The asymmetry in the neutrino mean free path for the absorption reaction $\nu + n \rightarrow e^{-} + p$, is evaluated within hot neutron matter under a strong magnetic field. We consider densities in the range $0.05 \leq \rho \leq 0.4$ fm$^{-3}$, several temperatures up to 30 MeV and magnetic field strengths from $B=0$ up to $B=10^{18}$~G. Polarized neutron matter is described within the non--relativistic Hartree--Fock model using the LNS Skyrme interaction. The neutrino mean free path has a weak dependence with the temperature and in the strong magnetic field region, it decreases for growing values of it. This contrast with the scattering reaction $\nu + n \rightarrow \nu' + n'$, where the average mean free path is almost independent of the magnetic field and has a strong dependence with the temperature. We have evaluated the asymmetry from both the absorption and scattering reactions. Our results shows that the total asymmetry depends on the magnetic field intensity, the density and the temperature. For a density of $0.16$ fm$^{-3}$ and for a magnetic field strength of B=$10^{17}$~G, the asymmetry in the mean free path is found to be, $\sim 9\%$ and $\sim 3.4\%$ for temperatures of T$=15$ and $30$ MeV, respectively. While the same set of asymmetries for B=$10^{18}$~G, is $\sim 58\%$ and $\sim 48\%$.

Asymmetry of the neutrino mean free path in hot neutron matter under strong magnetic fields

The neutrino mean free path in neutron matter under a strong magnetic field is evaluated for the inelastic scattering reaction and studied as a function of the neutron matter density in the range $0.05 \leq \rho \leq 0.4$ fm$^{-3}$ for several temperatures up to 30 MeV and magnetic field strengths B=0 G, $10^{18}$ G and $2.5\times 10^{18}$ G. Polarized neutron matter is described within the non--relativistic Brueckner--Hartree--Fock (BHF) approach using the Argonne V18 nucleon-nucleon potential supplemented with the Urbana IX three-nucleon force. Explicit expressions of the cross section per unit volume for the scattering of a neutrino with a spin up or spin down neutron are derived from the Fermi Golden rule. Our results show that the mean free path depends strongly on the angle of the incoming neutrino, leading to an asymmetry in this quantity. This asymmetry depends on the magnetic field intensity and on the density, but it is rather independent of the temperature. For a density of $0.16$ fm$^{-3}$ at a temperature T$=30$MeV, the asymmetry in the mean free path is found to be of $\sim 15\%$ for B=$10^{18}$G and $\sim 38\%$ for B=$2.5 \times 10^{18}$G.

Magnetized hot neutron matter: Lowest order constrained variational calculations

We have studied the spin polarized hot neutron matter in the presence of strong magnetic field. In this work, using the lowest order constrained variational method at finite temperature and employing AV18 nuclear potential, some thermodynamic properties of spin polarized neutron matter such as spin polarization parameter, free energy, equation of state and effective mass have been calculated. It has been shown that the strong magnetic field breaks the symmetry of the free energy, leading to a magnetized equilibrium state. We have found that the equation of state becomes stiffer by increasing both magnetic field and temperature. The magnetic field dependence of effective mass for the spin-up and spin-down neutrons has been investigated.

Hot neutron matter from a self-consistent Green's-functions approach

A systematic study of the microscopic and thermodynamical properties of pure neutron matter at finite temperature within the self-consistent Green's-function approach is performed. The model dependence of these results is analyzed by both comparing the results obtained with two different microscopic interactions, the CD Bonn and the Argonne V18 potentials, and by analyzing the results obtained with other approaches, such as the Brueckner-Hartree-Fock approximation, the variational approach, and the virial expansion.

The Bethe Homework Problem for Hot Neutron Matter in the Static Fluctuation Approximation

Nonrelativistic neutron matter is investigated in the static fluctuation approximation (SFA) within the framework of the Bethe homework problem. The idea is to introduce this new technique in the present context and compare it with other, better-known techniques. As a bonus, since the temperature enters SFA without any complexities, conceptual or otherwise, the thermodynamic properties of the system are calculated as functions of temperature.

Recent Results from Nuclear Lattice Simulations

We discuss recent progress in the study of nuclear and neutron matter by combining chiral effective field theory with non-perturbative lattice methods. We present results for hot neutron matter at temperatures 20 to 40 MeV and densities below twice nuclear matter density. This proceedings article is a summary of results from work done in collaboration with Bugra Borasoy and Thomas Schaefer1.

Nuclear Lattice Simulations with EFT

This proceedings article is a summary of results from work done in collaboration with Buḡra Borasoy and Thomas Schaefer. We study nuclear and neutron matter by combining chiral effective field theory with non-perturbative lattice methods. We present results for hot neutron matter at temperatures 20 to 40 MeV and densities below twice nuclear matter density.

Nuclear lattice simulations with chiral effective field theory

We study nuclear and neutron matter by combining chiral effective field theory with nonperturbative lattice methods. In our approach, nucleons and pions are treated as point particles on a lattice. This allows us to probe larger volumes, lower temperatures, and greater nuclear densities than in lattice QCD. The low-energy interactions of these particles are governed by chiral effective theory, and operator coefficients are determined by fitting to zero temperature few-body scattering data. The leading dependence on the lattice spacing can be understood from the renormalization group and absorbed by renormalizing operator coefficients. In this way, we have a realistic simulation of many-body nuclear phenomena with no free parameters, a systematic expansion, and a clear theoretical connection to QCD. We present results for hot neutron matter at temperatures $20--40\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$ and densities below twice the nuclear matter density.

Microscopic calculation of the neutrino mean free path inside hot neutron matter

We calculate the neutrino mean free path and the Equation of State of pure neutron matter at finite temperature within a selfconsistent scheme based on the Brueckner--Hartree--Fock approximation. We employ the nucleon-nucleon part of the recent realistic baryon-baryon interaction (model NSC97e) constructed by the Nijmegen group. The temperatures considered range from 10 to 80 MeV. We report on the calculation of the mean field, the residual interaction and the neutrino mean free path including short and long range correlations given by the Brueckner--Hartree--Fock plus Random Phase Approximation (BHF+RPA) framework. This is the first fully consistent calculation in hot neutron matter dedicated to neutrino mean free path. We compare systematically our results to those obtain with the D1P Gogny effective interaction, which is independent of the temperature. The main differences between the present calculation and those with nuclear effective interactions come from the RPA corrections to BHF (a factor of about 8) while the temperature lack of consistency accounts for a factor of about 2.

The Hot Neutron Star

In this paper the equation of state of hot neutron matter is calculated. Involving the Oppenheimer-Volkov-Tolman equation global parameters of a neutron star at finite temperature are obtained.

Neutrino propagation and spin zero sound in hot neutron matter with Skyrme interactions

We present microscopic calculations of neutrino propagation in hot neutron matter above nuclear density within the framework of the Random Phase Approximation . Calculations are performed for non- degenerate neutrinos using various Skyrme effective interactions. We find that for densities just above nuclear density, spin zero sound is present at zero temperature for all Skyrme forces considered. However it disappears rapidly with increasing temperature due to a strong Landau damping. As a result the mean-free path is given, to a good approximation, by the mean field value. Because of the renormalization of the bare mass in the mean field, the medium is more transparent as compared to the free case. We find, in contrast, that at several times nuclear density, a new type of behavior sets in due to the vicinity of a magnetic instability. It produces a strong reduction of the mean free path. The corresponding transition density however occurs in a region where inputs from more realistic calculations are necessary for the construction of a reliable Skyrme type parametrization.

Gravitational radiation from a rotating protoneutron star

This paper discusses the gravitational radiation that accompanies the formation of a rotating protoneutron star. Mainly large-scale entropy inhomogeneities develope inside the star. As a result, bubbles of hot nuclear substance are formed, and convective motions arise: bubbles of hot neutron matter float to the surface of the star, while cold matter sinks to its center. Such large-scale motions of material give rise to an inhomogeneous mass distribution inside the star. Variable asymmetry appears in the mass distribution, and this causes gravitational radiation.

Gravity waves accompanying supernova explosions

Gravitational radiation arising during the formation of a protoneutron star is studied. Here it is mainly large-scale nonuniformities that develop inside the star. The entropy and density profiles of such nonuniformities resemble the “mushroom cloud” of a nuclear explosion. A bubble of hot neutron matter floats to the surface of the star, like the “mushroom cloud” of an explosion in the earth’s atmosphere. Depending on the symmetry of the problem, from two to six bubbles can float upward at the same time. The characteristic masses of such bubbles are 0.01M⊗ and the radial velocities reach ∼0.1c. The energy radiated in the form of gravitational waves in one cycle of bubbles floating to the surface is ∼10−2M⊗c2−10−10M⊗c2. Such cycles occur repeatedly as the neutron star cools. This phase can last up to seconds. The total energy radiated in the form of gravitational radiation can reach 10−1M⊗c2.

Metastability of dense neutron matter

We formulate a theory of metastability of dense neutron matter with respect to the first-order phase transition to a pion-condensed state. The theory is based on the idea of nucleation of the pion-condensed phase in the metastable normal matter through the appearance of spontaneously growing drops of the new phase. Different paths leading from the false to the true ground state of dense neutron matter are considered. Also, both quantum fluctuations — that dominate at the low temperatures typical of neutron stars-and thermal fluctuations — that dominate during the gravitational collapse of massive stars — are considered. The calculations performed for realistic models of cold neutron matter yield an interval of metastability (on the time scale of the age of the universe) which is as large as half of that between the baryon density ρ N where the metastability starts and ρ c where the potential barrier (without surface effects) between the true and the false ground state vanishes. Possible astrophysical implications of this finding for neutron stars are discussed. In the case of the pion condensation in hot neutron matter ( T ~ 5 MeV) the region of metastability (on the time scale of the gravitational collapse of a massive star) is much narrower than in cold neutron matter. Consequently additional energy release and entropy generation from the first-order phase transition in hot supercompressed matter are found to be negligible. The theory outlined here can be used for the description of other phase transitions in dense nuclear matter, such as the transition to the quark phase for instance.