Properties of Finite Nuclei

Abstract

The application of the reaction-matrix theory to the calculation of binding energies and other properties of finite nuclei is investigated. We consider ${\mathrm{O}}^{16}$ and ${\mathrm{Ca}}^{40}$. The single-particle wave functions are obtained from a self-consistent shell-model potential defined so as to minimize the total energy of the nucleus. The attractive part of the reaction matrix is derived from the long-range part of a central spin-independent potential acting in $S$ states only. We treat the nonlocality of this reaction matrix in the effective-mass approximation and the nonlocal shell-model potential is then also obtained in the similar form. For the repulsive part of the reaction matrix we compare the local-density approximation of Brueckner and co-workers with a more detailed one. We find that the local-density approximation gives an underestimate of the binding by 2-2.5 MeV/nucleon. The center-of-mass correction increases the calculated binding further with 0.8 and 0.2 MeV/nucleon in ${\mathrm{O}}^{16}$ and ${\mathrm{Ca}}^{40}$, respectively. We investigate the possibility of replacing the nonlocal shell-model potential by certain local potentials. We try the harmonic oscillator and the Gaussian potentials, minimizing the energy with respect to the one parameter for the first, and the two parameters for the second. The binding differs by not more than 0.2 MeV/nucleon between these local potentials and the nonlocal self-consistent potential. In fact the local potentials often give more binding, owing to approximations necessary in the self-consistent potential in some cases.