  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.
