M3 transition to the scissors mode in the two-rotor model and random-phase approximation.

The M3 transition to the K/sup /pi// = 1/sup +/ band describing the scissors mode is evaluated in schematic random-phase approximation for heavy deformed nuclei. The equivalence between this microscopic description of the mode and the one given within the classical two-rotor model is stressed. It is shown how such a schematic approach improves quantitatively the description of the mode with respect to the rigid two-rotor model and, in particular, provides more reliable values of the M1 and M3 strengths. A rough estimate of the importance of the spin versus the orbital contribution to the mentioned strengths is also made by carrying out the same schematic calculation in the neutron-proton formalism and using a Nilsson basis for /sup 164/Dy chosen as representative of all nuclei in the rare-earth region. The spin contribution is found to be non-negligible but still quite small in both cases. The total M3 strength is smaller than the one predicted in the rigid two-rotor model and other approaches, but still observable. The possibility of actually observing such a transition in relation to the fragmentation of the strength is finally discussed.