Coriolis-Coupling Model Prediction of Moments and Transition Rates for Deformed Odd Nuclei in the1f72Shell

Abstract

The magnetic dipole and electric quadrupole moments and reduced transition probabilities have been computed for the Coriolis-coupling model using the wave functions obtained in an earlier paper. These wave functions were obtained from a linear combination of the ten rotational bands based on the ten available single-particle and core excited states in the $1f\ensuremath{-}2p$ shell, and the corresponding eigenvalues were consistent with the observed level spectra of the odd nuclei in the $1{f}_{\frac{7}{2}}$ shell. The moments and transition rates predicted here are also in good agreement with experiment. Thus, the observed magnetic moments can no longer be considered as evidence supporting the validity of solely the spherical shell model for these nuclei. Contributions to the magnetic moment from single-particle terms and from cross terms between the bands are found to be important and have been included. The observed inhibition of the $M1$ transitions (which are allowed in the collective model) is a consequence of the strong band mixing which results in strong cancellation between the contributions from the direct and the cross terms. The good agreement between the predicted and observed values of the quadrupole moments and $B(E2)$ values has been achieved using the free proton charge of unity and neutron charge of zero. The contribution to the quadrupole moment from the single-particle term is found to be important, and on occasion constitutes as much as 50% of the total quadrupole moment. Furthermore, the collective spectroscopic quadrupole moment, with proper inclusion of the contribution from different bands, in some cases has a different sign from the intrinsic quadrupole moment. Proper inclusion of the contributions to the quadrupole moment from different bands and of the single-particle term leads to the important result that odd nuclei may yet have a very small quadrupole moment despite having large deformations.