Rotational Bands and Pairing Interaction in the Shell Model

Sammanfattning: One of the goals pursued in the present research was to understand the nuclear phenomena (such as rotational bands, their backbending and termination, deformation, pairing correlations, etc.) using different views provided by different nuclear models. The employed models complement each other: spherical shell model provided the laboratory frame description, the intrinsic frame description was provided by the deformed shell model, while the rotor model allowed to relate both reference frames. The research was concentrated on the properties of light nuclei, especially of the N=Z nuclei which are of particular interest since the neutrons and protons are occupying the same j-shells, and thus neutron-proton pairing correlations play an important role. The role of the T=0 (neutron-proton) and T=1 (neutron-neutron, proton-proton or neutron-proton) pairing interactions in the shell model to the properties of the rotational bands was discussed. In particular, it was shown that the J=0 T=1 two-particle pairing interaction is important even at relatively high spin. It may affect the way the rotational band terminates. If the termination involves alignment of one proton pair and one neutron pair each giving 2 units of angular momentum, the last transition to the band-terminating state costs additional energy as compared to a rotational reference. This situation most readily occurs in N=Z nuclei having half-filled j-shell. Three such bands in ²²Na, ⁴⁸Cr and ⁹⁰Rh, were investigated in a greater detail. The band energies as well as calculated pairing energies (originating from T=0 and T=1 pairing interactions) have similar spin dependence. It was also discussed that the pairing interactions do not have large influence to the quadrupole properties of a state, if this state is well-separated in energy from other states. The structure of rotational bands in ⁶²Ga was discussed. This N=Z odd-odd nucleus has T=1 ground state, that is considered to be an outcome of the competition between T=0 and T=1 pairings. And indeed, the calculated pairing energies indicate that the J=0 T=1 state gains more pairing energy than the lowest T=0 states do. The rotational bands are investigated using the spherical shell model and the deformed shell model. It is shown that the backbend of the observed T=0 band may be explained in terms of a crossing of the two bands having different structure. Only one T=1 state was observed in this nucleus: its ground state. However, the isobaric analog states observed in ⁶²Zn could be used as a reference for the calculated T=1 states. The yrast band in ⁴⁸Cr was investigated paying attention to the nuclear shape. The performed calculations confirmed that the nucleus becomes triaxial for higher spins after the backbending at spin 10. In addition, the rotation occurs around the intermediate axis. Such rotation is forbidden in the classical rotor model. A recently observed excited band in ³⁶Ar has similar properties as the yrast band in ⁴⁸Cr. Both the spherical and deformed shell models suggested that this band has four particles excited from the sd-shell to the pf-shell.