Semiclassical description of the shears mechanism and the role of effective interactions

By deriving the angle between the proton and neutron spin vectors $j_{\pi }$ and $j_{\nu }$ in the shears bands in ${}^{198,199}\mathrm{Pb},$ we present a semiclassical analysis of the $B\left(M1\mathrm{}\right)\mathrm{}$ and $B\left(E2\mathrm{}\right)\mathrm{}$ transition probabilities as a function of the shears angle. This provides a semiempirical confirmation of the shears mechanism proposed by Frauendorf using the tilted-axis-cranking model. In addition, we propose that the rotational-like behavior observed for these bands may arise from a residual proton-neutron interaction.