Neutron Structure Properties of Titanium in a Supernova

Abstract

We calculated important neutron matter properties of ${}^{44}$Ti in the envelope of supernova SN 1987A and its isotopic chain ($12\leqslant N\leqslant 82$) using the Skyrme–Hartree–Fock approach such as the residual and average neutron–proton interactions, neutron skin thickness, bubble structure, single-particle energy level, charge form factor as well as some fundamental nuclear structure properties. For the skin properties, the surface and bulk contributions to neutron skin thickness are obtained based on two-parameter Fermi distributions. Hence, the two-parameter Fermi distributions are obtained by proton and neutron density distributions. To demonstrate the central depletion in the nuclei, the bubble parameters $b$ and $b^{\prime}$ are calculated for each nucleus as functions of neutron number $N$ and the relative neutron excess $I=(N-Z)/A$. The accuracy and importance of the calculated results are explained and discussed in terms of quantum Coulomb repulsion, quantum shell and mechanical effects, $nn$-interactions, orbital angular l of orbitals, and principal quantum number $n$.