Scissors Modes: The elusive breathing overtone

The Two-Rotor Model predicts two levels above the Scissors Modes with degenerate intrinsic energy. They have $J^π= 0^+,2^+$ and are referred to as overtones. Their energy is below threshold for nucleon emission, which should make them observable. The $J^π=0^+$ 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.

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