Energy Of Neutron Matter Research Articles

Analyzing the Fierz rearrangement freedom for local chiral two-nucleon potentials

Chiral effective field theory is a framework to derive systematic nuclear interactions. It is based on the symmetries of quantum chromodynamics and includes long-range pion physics explicitly, while shorter-range physics is expanded in a general operator basis. The number of low-energy couplings at a particular order in the expansion can be reduced by exploiting the fact that nucleons are fermions and therefore obey the Pauli exclusion principle. The antisymmetry permits the selection of a subset of the allowed contact operators at a given order. When local regulators are used for these short-range interactions, however, this "Fierz rearrangement freedom" is violated. In this paper, we investigate the impact of this violation at leading order (LO) in the chiral expansion. We construct LO and next-to-leading order (NLO) potentials for all possible LO-operator pairs and study their reproduction of phase shifts, the ${}^4$He ground-state energy, and the neutron-matter energy at different densities. We demonstrate that the Fierz rearrangement freedom is partially restored at NLO where subleading contact interactions enter. We also discuss implications for local chiral three-nucleon interactions.

Symmetry Parameter Constraints from a Lower Bound on Neutron-matter Energy

Abstract We propose the existence of a lower bound on the energy of pure neutron matter (PNM) on the basis of unitary-gas considerations. We discuss its justification from experimental studies of cold atoms as well as from theoretical studies of neutron matter. We demonstrate that this bound results in limits to the density-dependent symmetry energy, which is the difference between the energies of symmetric nuclear matter and PNM. In particular, this bound leads to a lower limit to the volume symmetry energy parameter S 0. In addition, for assumed values of S 0 above this minimum, this bound implies both upper and lower limits to the symmetry energy slope parameter L ,which describes the lowest-order density dependence of the symmetry energy. A lower bound on neutron-matter incompressibility is also obtained. These bounds are found to be consistent with both recent calculations of the energies of PNM and constraints from nuclear experiments. Our results are significant because several equations of state that are currently used in astrophysical simulations of supernovae and neutron star mergers, as well as in nuclear physics simulations of heavy-ion collisions, have symmetry energy parameters that violate these bounds. Furthermore, below the nuclear saturation density, the bound on neutron-matter energies leads to a lower limit to the density-dependent symmetry energy, which leads to upper limits to the nuclear surface symmetry parameter and the neutron-star crust–core boundary. We also obtain a lower limit to the neutron-skin thicknesses of neutron-rich nuclei. Above the nuclear saturation density, the bound on neutron-matter energies also leads to an upper limit to the symmetry energy, with implications for neutron-star cooling via the direct Urca process.

Static Response of Neutron Matter.

We generalize the problem of strongly interacting neutron matter by adding a periodic external modulation. This allows us to study from first principles a neutron system that is extended and inhomogeneous, with connections to the physics of both neutron-star crusts and neutron-rich nuclei. We carry out fully nonperturbative microscopic quantum MonteCarlo calculations of the energy of neutron matter at different densities, as well as different strengths and periodicities of the external potential. In order to remove systematic errors, we examine finite-size effects and the impact of the wave function ansatz. We also make contact with energy-density functional theories of nuclei and disentangle isovector gradient contributions from bulk properties. Finally, we calculate the static density-density linear response function of neutron matter and compare it with the response of other physical systems.

Single-Particle Spectrum of Pure Neutron Matter

We have calculated the self-consistent auxiliary potential effects on the binding energy of neutron matter using the Brueckner–Hartree–Fock approach by adopting the Argonne V18 and CD-Bonn potentials. The binding energy with the four different choices for the self-consistent auxiliary potential is discussed. Also, the binding energy of neutron matter has been computed within the framework of the self-consistent Green’s function approach. We also compare the binding energies obtained in this study with those obtained by various microscopic approaches. It is found that the use of the continuous choice tends to give binding energies about 2–4 MeV larger than the gap choice at kF = 1.8 fm−1. In the case of symmetric nuclear matter this difference is larger.

Neutron matter from chiral effective field theory interactions

The neutron-matter equation of state constrains the properties of many physical systems over a wide density range and can be studied systematically using chiral effective field theory (EFT). In chiral EFT, all many-body forces among neutrons are predicted to next-to-next-to-next-to-leading order (N3LO). We present details and additional results of the first complete N3LO calculation of the neutron-matter energy, which includes the subleading three-nucleon as well as the leading four-nucleon forces, and provides theoretical uncertainties. In addition, we discuss the impact of our results for astrophysics: for the supernova equation of state, the symmetry energy and its density derivative, and for the structure of neutron stars. Finally, we give a first estimate for the size of the N3LO many-body contributions to the energy of symmetric nuclear matter, which shows that their inclusion will be important in nuclear structure calculations.

Quantum Monte Carlo Calculations with Chiral Effective Field Theory Interactions

We present the first quantum MonteCarlo (QMC) calculations with chiral effective field theory (EFT) interactions. To achieve this, we remove all sources of nonlocality, which hamper the inclusion in QMC calculations, in nuclear forces to next-to-next-to-leading order. We perform auxiliary-field diffusion MonteCarlo (AFDMC) calculations for the neutron matter energy up to saturation density based on local leading-order, next-to-leading order, and next-to-next-to-leading order nucleon-nucleon interactions. Our results exhibit a systematic order-by-order convergence in chiral EFT and provide nonperturbative benchmarks with theoretical uncertainties. For the softer interactions, perturbative calculations are in excellent agreement with the AFDMC results. This work paves the way for QMC calculations with systematic chiral EFT interactions for nuclei and nuclear matter, for testing the perturbativeness of different orders, and allows for matching to lattice QCD results by varying the pion mass.

Neutron Matter at Next-to-Next-to-Next-to-Leading Order in Chiral Effective Field Theory

Neutron matter presents a unique system for chiral effective field theory because all many-body forces among neutrons are predicted to next-to-next-to-next-to-leading order (N(3)LO). We present the first complete N(3)LO calculation of the neutron matter energy. This includes the subleading three-nucleon forces for the first time and all leading four-nucleon forces. We find relatively large contributions from N(3)LO three-nucleon forces. Our results provide constraints for neutron-rich matter in astrophysics with controlled theoretical uncertainties.

Maximum mass and radius of neutron stars, and the nuclear symmetry energy

We calculate the equation of state of neutron matter with realistic two- and three-nucleon interactions using quantum Monte Carlo techniques and illustrate that the short-range three-neutron interaction determines the correlation between neutron matter energy at nuclear saturation density and higher densities relevant to neutron stars. Our model also makes an experimentally testable prediction for the correlation between the nuclear symmetry energy and its density dependence---determined solely by the strength of the short-range terms in the three-neutron force. The same force provides a significant constraint on the maximum mass and radius of neutron stars.

Chiral three-nucleon forces and neutron matter

We calculate the properties of neutron matter and highlight the physics of chiral three-nucleon forces. For neutrons, only the long-range 2 pi-exchange interactions of the leading chiral three-nucleon forces contribute, and we derive density-dependent two-body interactions by summing the third particle over occupied states in the Fermi sea. Our results for the energy suggest that neutron matter is perturbative at nuclear densities. We study in detail the theoretical uncertainties of the neutron matter energy, provide constraints for the symmetry energy and its density dependence, and explore the impact of chiral three-nucleon forces on the S-wave superfluid pairing gap.

Spin–orbit and tensor interactions in homogeneous matter of nucleons: accuracy of modern many-body theories

We study the energy per particle of symmetric nuclear matter and pure neutron matter using realistic nucleon–nucleon potentials having noncentral tensor and spin–orbit components, up to three times the empirical nuclear matter saturation density, ρ0=0.16 fm−3. The calculations are carried out within the frameworks of the Brueckner–Bethe–Goldstone (BBG) and correlated basis functions (CBF) formalisms, in order to ascertain the accuracy of the methods. The two hole-line approximation, with the continuous choice for the single particle auxiliary potential, is adopted for the BBG approach, whereas the variational Fermi hypernetted chain/single operator chain theory, corrected at the second order perturbative expansion level, is used in the CBF one. The energies are then compared with the available quantum and variational Monte Carlo results in neutron matter and with the BBG, up to the three hole-line diagrams. For neutron matter and potentials without spin–orbit components all methods, but perturbative CBF, are in reasonable agreement up to ρ∼3ρ0. After the inclusion of the LS interactions, we still find agreement around ρ0, whereas it is spoiled at larger densities. The spin–orbit potential lowers the energy of neutron matter at ρ0 by ∼3–4 MeV per nucleon. In symmetric nuclear matter, the BBG and the variational results are in agreement up to ∼1.5ρ0. Beyond this density, and in contrast with neutron matter, we find good agreement only for the potential having spin–orbit components.

Neutron stars and quantum billiards

Homogeneous neutron matter at subnuclear densities becomes unstable towards the formation of inhomogeneities. Depending on the average value of the neutron density one can observe the appearance of either bubbles, rods, tubes or plates embeded in a neutron gas. We estimate the quantum corrections to the ground state energy (which could be termed either shell correction or Casimir energy) of such phases of neutron matter. The calculations are performed by evaluating the contribution of the shortest periodic orbits in the Gutzwiller trace formula for the density of states. The magnitude of the quantum corrections to the ground state energy of neutron matter are of the same order as the energy differences between various phases.

Density dependence of charge symmetry breaking

We study the Okamoto-Nolen-Schiffer (ONS) anomaly in the binding energy of mirror nuclei at high density by adding a single neutron or proton to a quark gluon plasma. In this high-density limit we find an anomaly equal to two-thirds of the Coulomb exchange energy of a proton. This effect is dominated by quark electromagnetic interactions---rather than by the up-down quark mass difference. At normal density we calculate the Coulomb energy of neutron matter using a string-flip quark model. We find a nonzero Coulomb energy because of the neutron's charged constituents. This effect could make a significant contribution to the ONS anomaly.

Effect of bulk constants on the binding energy of neutron matter and beta stability of a neutron star.

We have studied pure neutron matter using a derivative scalar coupling (DSC) model and different nonlinear models. It is found that small bound energy of pure neutron matter at equilibrium density is due to the high value of effective nucleon mass ${\mathit{m}}_{\mathit{n}}^{\mathrm{*}}$ in this model. Other nonlinear models having large ${\mathit{m}}_{\mathit{n}}^{\mathrm{*}}$(${\mathrm{\ensuremath{\rho}}}_{0}$) also yield bound neutron matter. It is also shown that the role of symmetry energy is very significant in the study of neutron matter and the beta stability of neutron matter. \textcopyright{} 1996 The American Physical Society.

Comparison of the relativistic mean-field theory and the Skyrme Hartree-Fock theory for properties of nuclei and nuclear matter

We make comparisons of the relativistic mean-field theory with the non-linear parameter set NL1 and the Skyrme Hartree-Fock theory with the parameter sets SIII and Ska for the properties of nuclei and nuclear matter. We find that both the SIII and Ska parameter sets give similar results for the nuclear binding energies and the nuclear radii of various proton-closed isotopes. The relativistic mean-field theory with the parameter set NL1 describes successfully the nuclear binding energy and the nuclear charge radii simultaneously in the entire mass region. The neutron radii obtained by the parameter set NL1 are larger than those of the SIII and Ska interactions. The Skyrme forces SIII and Ska provide the energy of neutron matter to be less than that of nuclear matter at high density.

Solid cores in neutron stars?

The possibility of a liquid-to-solid phase transition in neutron stars is investigated. The ground-state energy of neutron matter is calculated by means of Pandharipande's variational LOCV method, and the ground-state energy of a neutron solid is calculated by a similar method. Both bcc and fcc structures and two possible spin configurations (parallel spins and “mixed” spins) are considered. The possibility of a phase transition from normal neutron matter into a neutron solid is then considered, but no phase transition is found to occur for the specific two-body potential assumed and the chosen spin configuration. The liquid is in general energetically favourable to the solid, and we get very poor localization of the neutrons in the lattice at energy minimum for the solid. The bcc structure, however, is found to be energetically favourable to the fcc structure.

Ground-state energy of neutron gas in Jastrow theory with a soft-core potential

The energy of neutron matter is calculated within the framework of the FIY cluster expansion including the contribution from three-body clusters.

The effect of the Δ(1236) in the two-nucleon problem and in neutron matter

A two nucleon interaction for the 1S 0 state is constructed by replacing the σ-meson in an OBEP by an inelastic process involving the Δ(1236). The values of the two free parameters introduced to fit δ( 1 s 0) are justified by more fundamental approaches. The binding energy of neutron matter is calculated, and it is shown there is a considerable repulsive contribution not present for an equivalent σ-meson interaction.

Superfluid condensation energy of neutron matter

The detailed energetics of pure neutron matter, an ideal form of neutron-star matter, are investigated at low density. The energy shift associated with the normal-to-superfluid-state transition induced by S-wave pairing is estimated by a variational method, with trial superfluid-state and reference normal-state wave functions incorporating strong short-range correlations. The neutron system remains unbound, and indeed there is no indication of a relative minimum of the ground state energy of the (assumed uniform) system as a function of density. However, the transition energy is not entirely negligible compared to the other characteristic energies of the problem - it may be somewhat greater than one-tenth the normal-state energy at densities typical of the inner crust of a neutron star.