The detailed knowledge of the inner crust properties of neutron stars might be important to explain different phenomena such as pulsar glitches or the possibility of an $r$-process site in neutron star mergers. It has been shown in the literature that quantal effects like shell correction or pairing may play a relevant role to determine the composition of the inner crust of the neutron star. In this paper we construct the equation of state of the inner crust using the finite-range Gogny interactions, where the mean field and the pairing field are calculated with same interaction. We have used the semiclassical variational Wigner-Kirkwood method along with shell and pairing corrections calculated with the Strutinsky integral method and the BCS approximation, respectively. Our results are compared with those of some popular models from the literature. We report a unified equation of state of the inner crust and core computed with the D1M* Gogny force, which was specifically fabricated for astrophysical calculations.

• Received 6 March 2020
• Accepted 22 June 2020
• Corrected 22 October 2020

DOI:https://doi.org/10.1103/PhysRevC.102.015802