Realistic Potentials and Shell Model. I

Using the recent theory developed by Shakin et al. for nuclear-structure calculations, energy-level calculations are made for realistic potentials such as the Yale potential and the nonlocal Tabakin potential. As examples, ${\mathrm{Zr}}^{90}$ and ${\mathrm{Ti}}^{50}$ are considered. The results for the spectra of these nuclei are compared with those of other authors and the experimental data. The agreement with the ${\mathrm{Ti}}^{50}$ spectrum is good. In the case of ${\mathrm{Zr}}^{90}$ the agreement is improved if we admit a configuration dependence for the effective interaction arising from the possibility of having different size parameters for the $g_{\frac{9}{2}}$ and $p_{\frac{1}{2}}$ orbits. The Yale potential yields better agreement with the experimental data than does the Tabakin potential. It is shown that the matrix elements of the Coulomb force between two protons in these nuclei do not affect the relative splittings of the energy levels by an appreciable amount. These matrix elements have a tendency to vary systematically with the total angular momentum for a given configuration.