Shell-Model Study of the Calcium Isotopes (A=42−48) Using a Pairing-Plus-Surface-Tensor Interaction

The calcium isotopes ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$ through ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ are described within the framework of the conventional shell model using a phenomenological effective two-body interaction. The residual interaction consists of usual $j-j$ pairing plus a surface-tensor force. ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ is assumed to be an inert core. Besides all possible configurations arising from $1f_{\frac{7}{2}}$ and $2p_{\frac{3}{2}}$ orbits, configurations of the form ${\left(1\mathrm{}{f}_{\frac{7}{2}}\right)}^{n1\mathrm{}}{\left(1\mathrm{}{f}_{\frac{5}{2}}\right)}^{n2\mathrm{}}$ where $n_1+n_2=n$ (the number of extracore neutrons) and $n_2=1, 2$, are also considered in the basis vector spaces. The calculated ground-state energies as well as the excited energy levels are in good agreement with the experimental values. Reproduction of single-neutron spectroscopic factors for stripping and pickup reactions is also good.