Ground state properties of $^{4}He$ and $^{12}C$ nuclei at equilibrium and at large static compression at zero temperature using Nijmegen and Reid Soft Core nucleon-nucleon interactions

Abstract: In this paper, we investigate the ground state properties ($i.e$ binding energy, nuclear radius, radial density distribution and single particle energies) for $^{4}He$ and $^{12}C$ nuclei at equilibrium and at large static compression at zero temperature by using two realistic different potentials namely, Nijmegen and Reid Soft Core (RSC)potentials. We carry out the calculations in No-Core Shell Model space consisting of six major oscillator shells within the framework of the Constrained Spherical Hartree- Fock (CSHF) approximations. We find out that, the computed equilibrium root mean square radii and the Hartree Fock energies for 4He and 12C with those two different potentials are very close to the experimental values of the nuclear radii and nuclear binding energies for the same nuclei.