Scissors Modes: The elusive breathing overtone

Abstract

The Two-Rotor Model predicts two levels above the Scissors Modes with degenerate intrinsic energy. They have $J^{\pi }=0^{+},2^{+}$ and are referred to as overtones. Their energy is below threshold for nucleon emission, which should make them observable. The $J^{\pi }=0^{+}$ overtone, that has the structure of an isovector breathing mode, has vanishing $E0$ amplitude so that cannot be directly excited, but it could be reached in the decay of the $J=2^{+}$ overtone. We discuss such a process and evaluate the $B(E2)$ strength, which, however, turns out to be very small.

Comments: 4 pages, no figure