An accurate determination of the core-crust transition is necessary in the modelling of neutron stars for astrophysical purposes. The transition is intimately related to the isospin dependence of the nuclear force at low baryon densities

To study the symmetry energy and the core-crust transition in neutron stars using the finite-range Gogny nuclear interaction and to examine the deduced crustal thickness and crustal moment of inertia. Methods: The second-, fourth- and sixth-order coefficients of the Taylor expansion of the energy per particle in powers of the isospin asymmetry are analyzed 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 Gogny EoS (i.e., the Gogny EoS with the full isospin dependence) for the β-equilibrated matter of the core, and also with the Taylor expansion of the Gogny EoS in order to assess the influence of isospin expansions on locating the inner edge of neutron star crusts.

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 fm−3 . ρt . 0.118 fm−3 for the transition density and 0.339 MeV fm−3 . Pt . 0.665 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 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.

The finite-range exchange contribution of the nuclear force, and its associated non-trivial isospin dependence, is key in determining the core-crust transition properties. Finite-order isospin expansions do not reproduce the core-crust transition results of the exact EoS. The predictions of the Gogny D1M force for the stellar crust are overall in broad agreement with those obtained using the Skyrme-Lyon EoS.