Symmetry Energy in the Inner Crust Region of Neutron Stars: A Study Around the Neutron Drip Density Point using the Compressed Liquid Drop Model

Abstract

The properties of neutron star’s inner crust have been investigated using the Compressible Liquid Drop Model, particularly around the neutron drip density region, which is the boundary between the outer and inner crust. Symmetry energy in the equations of state SLy4 and BSk3 was calculated to determine the density data between the outer and inner crusts. The properties of the inner crust can be understood through parameters such as the change in the number of nucleons in the atomic nucleus, the asymmetry parameter in surface energy, and volume energy. It was shown that the choice of the symmetry energy expansion coefficient (L) of order-1 results in a distinct energy range of 9-11 MeV within the neutron drip region. This contrasts significantly with the energy symmetry observed around saturation density, which reaches (30 ± 4) MeV in the reference models used. Furthermore, it was found that symmetry energy affects the neutron composition in the inner crust. As the density increases, neutron numbers rise, while proton counts exhibit relative stability within the range of 40 to 50 for each atomic nucleus. Importantly, we observe a marked decrease in proton fraction at the onset of the neutron drip region, where ???? ≅10 MeV, suggesting electron capture processes transforming protons into neutrons. This phenomenon contributes to the presence of neutron and free neutron gas layers within the inner crust.