Hartree-Fock Calculations of 12C Nucleus at Equilibrium and Under Static Compression

Abstract

The ground state features of the semi-doubly magic ¹²C nucleus (i.e. binding energy, nuclear radius, radial density distribution, and single particle energies) are estimated using ab initio calculations at equilibrium and under high static compression. Nijmegen and Reid soft-core (RSC) potentials are used as input nucleon-nucleon interactions. Within the framework of the constrained spherical Hartree-Fock approximations, we do the calculations in no-core shell-model space, which consists of six major oscillator shells (i.e. 21 single particle orbitals). The sensitivity of the ground state features of the ¹²C nucleus to the degree of compression and the sensitivity of the equation of state to the two potentials are investigated. We also discovered that the nuclear binding energy calculated using the Nijmegen potential is higher than that calculated using the RSC potential. When utilizing the Nijmegen potential, the curve reaches zero binding energy faster than when using the RSC potential. Besides, in the case of Nijmegen, the spectrum of single-particle energies increases more quickly than in the case of RSC potential under compression. The space between single-particle energy shells is also visible in the energy spectrum. At high compression, the radial density distribution becomes higher than that in the interior zone when the RSC potential is applied