Structure of the O16 nucleus

Abstract

An approximate Hartree-Fock self-consistent-field calculation is carried out for the ground state of the O 16 nucleus. The two-body interaction used has a finite hard core as well as tensor and Serber exchange interaction. Our zeroth-order wave function gives an improved ground state energy of −116.3 MeV as compared to −87.8 MeV obtained with harmonic oscillator wave functions in zeroth order in a previous calculation using the same Hamiltonian. The calculated value of the r.m.s. radius is 2.07 fm. Coulomb forces are neglected in zero order and contribute 18.2 MeV when treated as a first order perturbation. A projection operator technique is used to construct 1,1 S wave functions from the various excited configurations which interact with the ground state. The configuration interaction calculation yields −13.6 MeV as the correlation energy, giving a total binding energy nearly identical with that obtained in an earlier calculation which used harmonic oscillator wave functions in zeroth order. Thus the net correlation energy is found to be very much smaller than would appear from the simple shell model. The tensor force does not contribute to the energy of the 1,1 S ground state configuration, and the configuration interaction effects due to the tensor force are found to be quite small (≈−0.2 MeV). The fact that total correlation energy including tensor force is small indicates that L − S coupling is a good approximation for the ground state of closed shell nuclei like O 16 . The 3, 1 P states arising from the configurations p −1 d and p −1 2s in L − S coupling are calculated. These states are associated with dipole resonance in O 16 . The calculation shows that most of the dipole sum is obtained from our two 3, 1 P states. The methods of calculation described in this paper are quite general and can be applied easily to either open or closed shell nuclei, if the two-body interaction has no worse than an integrable singularity (integrable hard core).