Level Structure ofSc43and Odd-Mass Ca Isotopes with Reaction Matrix Elements

Employing ${\mathrm{Ca}}^{40}$ as the core, the odd-parity states of ${\mathrm{Sc}}^{43}$ and ${\mathrm{Ca}}^{43}$ are calculated within the shell-model framework using the reaction matrix elements of the Hamada-Johnston nucleon-nucleon potential as calculated by Kuo and Brown. The three extracore particles are considered to occupy the $0f-1p$ orbitals. The effect of including the additional $0g_{\frac{9}{2}}$ orbital is also investigated. The odd-mass calcium isotopes (${\mathrm{Ca}}^{43}$, ${\mathrm{Ca}}^{45}$, and ${\mathrm{Ca}}^{47}$) are then described by the modified Tamm-Dancoff approximation (MTDA) method and the results are compared with the shell-model calculations of Federman and Talmi and of Engeland and Osnes that had been carried out in a much more restricted configuration space. The MTDA calculations are also performed with the reaction matrix elements of the Tabakin interaction for comparison with the Hamada-Johnston results.