symmetry S S Article Unified Equation of State for Neutron Stars Based on the Gogny Interaction Xavier Viñas 1,* , Claudia Gonzalez-Boquera 1 , Mario Centelles 1 , Chiranjib Mondal 2 and Luis M. Robledo 3,4   Citation: Viñas, X.; Gonzalez- Boquera, C.; Centelles, M.; Mondal, C.; Robledo, L.M. Unified Equation of State for Neutron Stars Based on the Gogny Interaction. Symmetry 2021, 13, 1613. https://doi.org/10.3390/ sym13091613 Academic Editor: Charalampos Moustakidis Received: 26 July 2021 Accepted: 18 August 2021 Published: 2 September 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos (ICCUB), Facultat de Física, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain; claugb@fqa.ub.edu (C.G.-B.); mario@fqa.ub.edu (M.C.) 2 Laboratoire de Physique Corpusculaire Caen, 6 Boulevard Marchal Juin, CEDEX, 14000 Caen, France; mondal@lpccaen.in2p3.fr 3 Departamento de Física Teórica and CIAFF, Universidad Autónoma de Madrid, 28049 Madrid, Spain; luis.robledo@uam.es 4 Center for Computational Simulation, Universidad Politécnica de Madrid, Campus de Montegancedo, Boadilla del Monte, 28660 Madrid, Spain * Correspondence: xavier@fqa.ub.edu Abstract: The effective Gogny interactions of the D1 family were established by D. Gogny more than forty years ago with the aim to describe simultaneously the mean field and the pairing field corresponding to the nuclear interaction. The most popular Gogny parametrizations, namely D1S, D1N and D1M, describe accurately the ground-state properties of spherical and deformed finite nuclei all across the mass table obtained with Hartree–Fock–Bogoliubov (HFB) calculations. However, these forces produce a rather soft equation of state (EoS) in neutron matter, which leads to predict maximum masses of neutron stars well below the observed value of two solar masses. To remove this limitation, we built new Gogny parametrizations by modifying the density dependence of the symmetry energy predicted by the force in such a way that they can be applied to the neutron star domain and can also reproduce the properties of finite nuclei as good as their predecessors. These new parametrizations allow us to obtain stiffer EoS’s based on the Gogny interactions, which predict maximum masses of neutron stars around two solar masses. Moreover, other global properties of the star, such as the moment of inertia and the tidal deformability, are in harmony with those obtained with other well tested EoSs based on the SLy4 Skyrme force or the Barcelona–Catania–Paris–Madrid (BCPM) energy density functional. Properties of the core-crust transition predicted by these Gogny EoSs are also analyzed. Using these new Gogny forces, the EoS in the inner crust is obtained with the Wigner–Seitz approximation in the Variational Wigner–Kirkwood approach along with the Strutinsky integral method, which allows one to estimate in a perturbative way the proton shell and pairing corrections. For the outer crust, the EoS is determined basically by the nuclear masses, which are taken from the experiments, wherever they are available, or by HFB calculations performed with these new forces if the experimental masses are not known. Keywords: unified equation of state; Gogny interaction; neutron star; symmetry energy; tidal deformability; moment of inertia 1. Introduction The standard Gogny interactions of the D1 family [1] consist of a finite-range part, which is modeled by two Gaussian form-factors including all the possible spin and isospin exchange terms, a zero-range density dependent term, which simulates the effect of the three-body forces, and a spin-orbit force, which is also of zero-range as in the case of Skyrme forces. Large-scale Hartree–Fock–Bogoliubov (HFB) calculations performed in a harmonic oscillator basis with the D1S parametrization [2,3] reveal that there is a systematic Symmetry 2021, 13, 1613. https://doi.org/10.3390/sym13091613 https://www.mdpi.com/journal/symmetry