Shell-model calculations on odd-parity levels of nuclei in the range 33S−41Ca

Abstract

The shell model is used to investigate quantitatively some odd-parity levels of nuclei in the range 33S−41Ca. An inert 32S core is assumed with a residual two-particle interaction of the outer nucleons. Only one nucleon is considered to be in the 1f7/2 shell, while the others are in the 1d3/2 shell. The interaction matrix elements are reduced to linear expressions in 14 parameters (i.e. 12 two-particle interactions and two binding energies to the core).

The numerical results are presented as they are obtained from fitting the 14 parameters to 60 nuclear level energies. From the values of these parameters the energies and spins of about 240 levels are derived. Though the root mean square deviation of the calculated energies from the experimental energies is about 0.5 MeV, most of the level orders are calculated correctly. In addition, the energies of some 0+ levels are calculated from configurations containing two particles in the 1f7/2 shell. These level energies appear to have a larger spread around the experimental energies.

An expansion of the matrix elements of the effective interaction of one nucleon in the 1d3/2 and one in the 1f7/2 shell in terms of interactions moments shows that the mean two-body interaction for the T = 0 case is attractive, with a significant quadrupole splitting; this agrees with a weak spin dependence of the effective nuclear forces. The mean two-body interaction for the T = 1 case is slightly repulsive, the octupole splitting being the most significant one.