Le champ self-consistant et l'étude des états fondamentaux des noyaux légers à couches complétes

Abstract

In the present work an approximate Hartree-Fock self-consistent-field calculation is carried out for the ground state of light closed shell nuclei 4He, 16O and 40Ca. Starting with an assumed nucleon-nucleon interaction v( r i− r j) , we derive the effective Hartree-Fock fields w( r i ) and the single-particle energies. A central two-body exchange force is chosen and a hard core, introdiced in a phenomenological way, is treated by the Moszkowski-Scott separation method. The individual particle trial wave functions, which are combinations of harmonic oscillator wave functions, are determined by a variational principle. For certain interactions containing a hard core, the binding energies, the rms radii and the charge distributions are well explained for 16O and 40Ca. Furthermore, the single-particle spectrum which is calculated for 16O is close to the experimental one. The Hartree-Fock fields for 1S and 1P nucleons are given and the average shape agrees with the results that one would obtain from the scattering of nucleons by nuclei.