Structure of neutron matter and neutron-interactions in a Supernova (SN) are investigated by the theoretical model approach. For that purpose, we calculate the neutron skin thicknesses, neutron-proton interactions, density distributions, central depletions in nuclei using Skyrme Hartree-Fock (SHF) model. The neutron skin thickness (NST) properties are obtained by bulk and surface contributions, based on two-parameter Fermi (2pF) distributions, as a function of the relative neutron excess I = (N- Z)/A. For the central depletion in the nucleus, the depletion fraction (DF) of nuclei is calculated by bubble parameters b and b '. To demonstrate the accuracy of the mass model in the theoretical model, calculated binding energies are compared with the theoretical and experimental data in the literature, namely the relativistic mean-field theory (RMFT), atomic mass evaluation (AME), and finite-range droplet model (FRDM). The fluctuations in the mass model are shown for average neutron-proton interactions delta, V1n- 1p and the residual neutron-proton interaction delta np for both odd-A and even-A nuclei. Additionally, the single-particle energy levels and charge form factors for some nuclei are presented for the contribution experimental processes. The based on the theoretical and experimental data, the importance and relevance of results of the calculated results are discussed.