Scissors Modes:The first overtone

Scissors modes were predicted in the framework of the Two-Rotor Model. This model has an intrinsic harmonic spectrum, so that the level above the Scissors Mode, the first overtone, has excitation energy twice that of the Scissors Mode. Since the latter is of the order of 3 MeV in the rare earth region, the energy of the overtone is below threshold for nucleon emission, and its width should remain small enough for the overtone to be observable. We find that $B(E2)\uparrow_{overtone} = {3 /over 64 \theta_0^{2}}B(E2)\uparrow_{scissors}$, where $\theta_0$ is the zero-point oscillation amplitude, which in the rare earth region is of order $10^{-1}$.