The effects of deformation on isovector electromagnetic and weak transition strengths

The summed strength for transitions from the ground state of ¹²C via the operators st, ℓt, rY¹t, r[Y¹s]^λt and r[Y¹ℓ]^λt are calculated using the ΔN = 0 rotational model. If we choose the z-component of the isospin operator t_z, the above operators are relevant to electromagnetic transitions; if we choose t₊, they are relevant to weak transitions such as neutrino capture. In going from the spherical limit to the asymptotic (oblate) limit the strength for the operator st decreases steadily to zero; the strength for the operator ℓt (scissors mode) increases by a factor of three. For the last three operators, isovector dipole, spin dipole and orbital dipole (including the twist mode), it is shown that the summed strength is independent of deformation. The main difference in the behavior is that for the first two operators we have in-shell transitions whereas for the last three operators the transitions are out of shell.