Properties of ⁴He Nucleus in the Mean Field Approximation with Compression

Abstract

Constrained spherical Hartree–Fock approximations are used to investigate nuclear system of closed shell $^{4}{\hbox {He}}$ nucleus. Two potentials were used: Reid soft core (RSC) and Nijmegen potentials. Moreover, the dependence of the nuclear properties was studied for the degree of compression. It was seen that it is possible to compress the nucleus into a smaller volume. This means that nuclear equation of state becomes softer for the compressed nucleus. Also, the nucleus becomes more bounded using RSC than Nijmegen potential. The $E_{{\mathrm{HF}}}$ increases steeply toward zero binding energy under compression for both potentials. In the case of using Nijmegen potential, the curve increases to zero binding energy more than RSC potential. In addition to that the spectrum of single particle increases more rapidly for Nijmegen than for RSC potential under compression. For the compressed nucleus, the energy spectrum also clearly shows the gaps between single-particle energy shells. In addition, it is preserved the ordering of the energy spectrum levels and the gaps among them. Finally, except in the interior region, the radial density distribution remains constant, while it is larger with RSC than with Nijmegen potential. At large compression, it becomes larger than that in the interior region when RSC potential is used.