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

Purpose 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 \beta -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 .

Results 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 1.74 M _ { \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 .

Conclusions 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 .