Application of the unified model with Coriolis coupling to 22Na, 26Al and 30P

Abstract

The collective rotational model of Bohr, Mottelson and Nilsson is applied to the doubly odd sd shell nuclei 22Na, 26Al and 30P. The odd neutron and odd proton are placed in Nilsson orbitals generated by the axially symmetric deformed core. The Hamiltonian is composed of the collective rotational energy, including the Coriolis terms; the single-particle Nilsson energies; and a residual interaction between the last odd neutron and proton. The effective matrix elements calculated by Kuo and Brown from the Hamada-Johnston nucleon-nucleon potential are used for the residual interaction between the last two nucleons. Nuclear energy levels and wave functions are calculated by diagonalizing this Hamiltonian on a basis consisting of the rotational bands built on single-particle states obtained by placing the odd neutron and odd proton in all available sd shell Nilsson single-particle and single-hole orbitals. The deformation parameter β is determined for each nucleus by fitting the experimental energy spectrum. The other model parameters are assigned the same value for all the nuclei treated, except for the coefficient {ce:inline-formula}D{/ce:inline-formula} of the {ce:inline-formula}l·l{/ce:inline-formula} term in the Nilsson Hamiltonian, which must be varied to produce a satisfactory spectrum for 30P. Magnetic moments, electric quadrupole moments, and Ml and E2 transition rates and mixing ratios are calculated. The calculated results are compared with experimental data. Agreement between the theoretical and experimental energy spectra is satisfactory for all three nuclei for states below 2 MeV, but there are discrepancies for states above 2 MeV in 22Na. For the electromagnetic properties, agreement is satisfactory for transitions from states below 2 MeV in 22Na and 30P, but there are discrepancies for states above 2 MeV in 30P and for low-lying states in 26Al.