Higher-order symmetry energy and neutron star core-crust transition with Gogny forces

We study the symmetry energy and the core-crust transition in neutron stars using the finite-range Gogny nuclear interaction and examine the deduced crustal thickness and crustal moment of inertia. We start by analyzing the second-, fourth- and sixth-order coefficients of the Taylor expansion of the energy per particle in powers of the isospin asymmetry for Gogny forces. These coefficients provide information about the departure of the symmetry energy from the widely used parabolic law. The neutron star core-crust transition is evaluated by looking at the onset of thermodynamical instability of the liquid core. The calculation is performed with the exact (i.e., without Taylor expansion) Gogny EoS for the core, and also with its Taylor expansion in order to assess the influence of isospin expansions on locating the inner edge of neutron star crusts. It is found that the properties of the core-crust transition derived from the exact EoS differ from the predictions of the Taylor expansion even when the expansion is carried through sixth order in the isospin asymmetry. Gogny forces, using the exact EoS, predict the ranges $0.094 \text{ fm}^{-3} \lesssim \rho_t \lesssim 0.118\text{ fm}^{-3}$ for the transition density and $0.339 \text{ MeV fm}^{-3} \lesssim P_t \lesssim 0.665 \text{ MeV fm}^{-3}$ for the transition pressure. The transition densities show an anticorrelation with the slope parameter $L$ of the symmetry energy. The transition pressures are not found to correlate with $L$. Neutron stars obtained with Gogny forces have maximum masses below $1.74M_\odot$ and relatively small moments of inertia. The crustal mass and moment of inertia are evaluated and comparisons are made with the constraints from observed glitches in pulsars.Comment: 24 pages, 15 figures, discussions and bibliography updated, to appear in Physical Review

New Gogny interaction suitable for astrophysical applications

The D1 family of parametrizations of the Gogny interaction commonly suffers from a rather soft neutron matter equation of state that leads to maximal masses of neutron stars well below the observational value of two solar masses. We propose a reparametrization scheme that preserves the good properties of the Gogny force but allows one to tune the density dependence of the symmetry energy, which, in turn, modifies the predictions for the maximum stellar mass. The scheme works well for D1M, and leads to a new parameter set, dubbed D1M⁎. In the neutron-star domain, D1M⁎predicts a maximal mass of two solar masses and global properties of the star in harmony with those obtained with the SLy4 Skyrme interaction. By means of a set of selected calculations in finite nuclei, we check that D1M⁎performs comparably well to D1M in several aspects of nuclear structure in nucleiThe work of LMR was supported by Spanish Ministry of Economy and Competitiveness (MINECO) Grants No.FPA2015-65929-P and FIS2015-63770-P. C.G., M.C., and X.V. were partially sup-ported by Grant FIS2014-54672-P from MINECO and FEDER, Grant 2014SGR-401 from Generalitat de Catalunya, and Project MDM-2014-0369 of ICCUB (Unidad de Excelencia María de Maeztu) from MINECO. C.G. also acknowledges Grant BES-2015-074210 from MINEC

Finite-size instabilities in finite-range forces

It has been recently shown that some Gogny finite-range interactions suffer from finite-size instabilities in coordinate-space calculations [Eur. Phys. J. A 55, 150 (2019)10.1140/epja/i2019-12838-7]. We confirm this finding by using the Hartree-Fock (HF) method in the quasilocal approximation to finite-range forces. The use of the quasilocal approximation substantially simplifies the calculations as compared with those including the exact exchange contribution to the energy and HF fields. The quantity most affected by the finite-size instabilities in the coordinate-space calculations is the spatial density at the origin that wildly oscillates as the HF iterative process proceeds. In addition to the recent D1M∗ parametrization of the Gogny force, we find that the D1M parametrization also shows this deficiency in several nuclei. We find that the harmonic-oscillator basis with its ultraviolet cutoff provides converged results in a wide and realistic range of basis sizes. This result serves as a justification of the numerous calculations with D1M and D1M∗ in finite nuclei that show no trace of instabilit