Structure of Nuclei with Neutron Excess—Ca47andK47

A shell-model calculation of the low-lying states of ${\mathrm{Ca}}^{47}$ and ${\mathrm{K}}^{47}$ was performed employing interaction matrix elements derived from the Hamada-Johnston potential. The configurations of ${\mathrm{Ca}}^{47}$ and ${\mathrm{K}}^{47}$ were limited to one-hole states and two-hole, one-particle states relative to a ${\mathrm{Ca}}^{48}$ core. The change in the single-particle energies in going from ${\mathrm{Ca}}^{40}$ to ${\mathrm{Ca}}^{48}$ is discussed. These changes were calculated by a first-order perturbation method using the Hamada-Johnston matrix elements. Of interest in ${\mathrm{K}}^{47}$ is the fact that the ground state has spin and parity ${\mathrm{½}}^{+}$, whereas the corresponding value is ${\frac{3}{2}}^{+}$ for the other potassium isotopes. The positive-parity states of ${\mathrm{Ca}}^{47}$ lie at surprisingly low excitation energy, and their structure is of particular interest. The spectrum of the negative-parity states of ${\mathrm{Ca}}^{47}$ was also calculated, as well as spectroscopic factors for single-nucleon transfer reactions. Good agreement with experiment was obtained for the negative-parity states, but the results for the positive-parity states were not entirely satisfactory.