Deformation parameters and transition probabilities for shears bands in Pb isotopes

Abstract

Tilt angles, deformation parameters, angular momenta, and reduced magnetic dipole and electric quadrupole transition probabilities are calculated within the framework of the tilted-axis cranking model for shears bands in the neutron-deficient Pb isotopes $^{193}\mathrm{Pb}$ to $^{202}\mathrm{Pb}$. The self-consistently calculated quadrupole-deformation parameters for the various configurations lie around ${\ensuremath{\varepsilon}}_{2}=\ensuremath{-}0.1$, and the triaxiality is small. The tilt angle, i.e., the angle between the angular momentum and the nuclear symmetry axis, remains almost constant within each band, showing only a small increase toward higher angular momenta. The angular momentum increases mainly due to the shears effect, which is a step-by-step alignment of high-$j$ proton and neutron orbitals into the direction of the total angular momentum. Calculated and experimental $M1$ transition rates are in good agreement. They decrease with increasing spin within the bands as expected for the shears effect. The calculated $B(E2)$ values show only a weak spin dependence. However, the experimental $B(E2)$ values have large errors, and more accurate data are needed to decide between the present model and a recently suggested geometrical approach.