Spin dependence of intrinsic and transition quadrupole moments

The relation connecting an angular momentum dependence of the γ-transition energies with the reduced transition probabilities B[E2;(I+2)_gr→I_gr] in the ground-state rotational band is derived based on the Bohr Hamiltonian. The relation is applicable to both β-rigid and β-soft both being γ-rigid nuclei. Based on this result the approximate expression is obtained for the intrinsic quadrupole moment and, therefore, for the spectroscopic quadrupole moment in terms of the reduced E2 transition probabilities. It is shown that an angular momentum dependence of the intrinsic quadrupole moment can be well approximated by a linear function of I. The results obtained are direct consequences of the Bohr Hamiltonian with the Davidson potential.