This paper presents a detailed assessment of the ability of the 240 Skyrme interaction parameter sets in the literature to satisfy a series of criteria derived from macroscopic properties of nuclear matter in the vicinity of nuclear saturation density at zero temperature and their density dependence, derived by the liquid-drop model, in experiments with giant resonances and heavy-ion collisions. The objective is to identify those parametrizations which best satisfy the current understanding of the physics of nuclear matter over a wide range of applications. Out of the 240 models, only 16 are shown to satisfy all these constraints. Additional, more microscopic, constraints on the density dependence of the neutron and proton effective mass β-equilibrium matter, Landau parameters of symmetric and pure neutron nuclear matter, and observational data on high- and low-mass cold neutron stars further reduce this number to 5, a very small group of recommended Skyrme parametrizations to be used in future applications of the Skyrme interaction of nuclear-matter-related observables. Full information on partial fulfillment of individual constraints by all Skyrme models considered is given. The results are discussed in terms of the physical interpretation of the Skyrme interaction and the validity of its use in mean-field models. Future work on application of the Skyrme forces, selected on the basis of variables of nuclear matter, in the Hartree-Fock calculation of properties of finite nuclei, is outlined.

Skyrme interaction and nuclear matter constraints

Self-consistent Green's function method for nuclei and nuclear matter

The theory governing the strong nuclear force—quantum chromodynamics—predicts that at sufficiently high energy densities, hadronic nuclear matter undergoes a deconfinement transition to a new phase of quarks and gluons1. Although this has been observed in ultrarelativistic heavy-ion collisions2,3, it is currently an open question whether quark matter exists inside neutron stars4. By combining astrophysical observations and theoretical ab initio calculations in a model-independent way, we find that the inferred properties of matter in the cores of neutron stars with mass corresponding to 1.4 solar masses (M⊙) are compatible with nuclear model calculations. However, the matter in the interior of maximally massive stable neutron stars exhibits characteristics of the deconfined phase, which we interpret as evidence for the presence of quark-matter cores. For the heaviest reliably observed neutron stars5,6 with mass M ≈ 2M⊙, the presence of quark matter is found to be linked to the behaviour of the speed of sound cs in strongly interacting matter. If the conformal bound $${c}_{\rm{s}}^{2}\le 1/3$$
 (ref. 7) is not strongly violated, massive neutron stars are predicted to have sizable quark-matter cores. This finding has important implications for the phenomenology of neutron stars and affects the dynamics of neutron star mergers with at least one sufficiently massive participant. The cores of neutron stars could be made of hadronic matter or quark matter. By combining first-principles calculations with observational data, evidence for the presence of quark matter in neutron star cores is found.

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Evidence for quark-matter cores in massive neutron stars

We present the first quantum Monte Carlo (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 Monte Carlo (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.

/pdf/quantum-monte-carlo-calculations-with-chiral-effective-field-3o7fnxtven.pdf

Quantum Monte Carlo calculations with chiral effective field theory interactions

Observations of thermal radiation from neutron stars can potentially provide information about the states of supranuclear matter in the interiors of these stars with the aid of the theory of neutron-star thermal evolution. We review the basics of this theory for isolated neutron stars with strong magnetic fields, including most relevant thermodynamic and kinetic properties in the stellar core, crust, and blanketing envelopes.

/pdf/neutron-stars-cooling-and-transport-1equgwjsa8.pdf

Neutron Stars—Cooling and Transport

We calculated the equation of state of neutron matter at zero temperature by means of the auxiliary field diffusion Monte Carlo (AFDMC) method combined with a fixed-phase approximation. The calculation of the energy was carried out by simulating up to 114 neutrons in a periodic box. Special attention was given to reducing finite-size effects at the energy evaluation by adding to the interaction the effect due to the truncation of the simulation box, and by performing several simulations using different numbers of neutrons. The finite-size effects due to kinetic energy were also checked by employing the twist-averaged boundary conditions. We considered a realistic nuclear Hamiltonian containing modern two- and three-body interactions of the Argonne and Urbana family. The equation of state can be used to compare and calibrate other many-body calculations and to predict properties of neutron stars.

Quantum Monte Carlo calculation of the equation of state of neutron matter

We present a quantum Monte Carlo study of the zero-temperature equation of state of neutron matter and the computation of the {sup 1}S{sub 0} pairing gap in the low-density regime with {rho}<0.04 fm{sup -3}. The system is described by a nonrelativistic nuclear Hamiltonian including both two- and three-nucleon interactions of the Argonne and Urbana type. This model interaction provides very accurate results in the calculation of the binding energy of light nuclei. A suppression of the gap with respect to the pure BCS theory is found, but sensibly weaker than in other works that attempt to include polarization effects in an approximate way.

Equation of state of superfluid neutron matter and the calculation of the 1S0 pairing gap.

We report results of the equation of state of neutron matter in the low-density regime, where the Fermi wave vector ranges from $0.4\ensuremath{\leqslant}{k}_{F}\ensuremath{\leqslant}1.0 \phantom{\rule{0.3em}{0ex}}{\mathrm{fm}}^{\ensuremath{-}1}$. Neutron matter in this regime is superfluid because of the strong and attractive interaction in the ${}^{1}{S}_{0}$ channel. The properties of this superfluid matter are calculated starting from a realistic Hamiltonian that contains modern two- and three-body interactions. The ground state energy and the ${}^{1}{S}_{0}$ superfluid energy gap are calculated using the auxiliary field diffusion Monte Carlo method. We study the structure of the ground state by looking at pair distribution functions as well as the Cooper-pair wave function used in the calculations.

Equation of state of low-density neutron matter, and the 1 S 0 pairing gap

We review the double asymptotic scaling phenomenon for the structure functions of the deepinelastic scattering process. We present an analytical parameterization of the contributions from the twist-two operators of the Wilson operator product expansion and power suppressed terms. Higher twist corrections to F
 2 at small x are studied for the case of a flat initial condition for the twist-two QCD evolution in the next-to-leading order approximation. Higher twist terms are estimated using two different approaches: one motivated by BFKL and the other motivated by the renormalon formalism. The results of the latter approach are in very good agreement with deep inelastic scattering data from HERA.

/pdf/small-x-behavior-of-parton-distributions-a-study-of-higher-3tm21asdis.pdf

Small x behavior of parton distributions: a study of higher twist effects

We study the heavy-quark contributions to the proton structure function F2(x,Q2) at next-to-leading order using compact formulas at small values of Bjorken's x variable. The formulas provide a good agreement with the modern HERA data for F2c(x,Q2).

A. Yu. Illarionov

Papers

Quantum Monte Carlo calculation of the equation of state of neutron matter

Equation of state of superfluid neutron matter and the calculation of the 1S0 pairing gap.

Equation of state of low-density neutron matter, and the 1 S 0 pairing gap

Small x behavior of parton distributions: a study of higher twist effects

F2c at low x