Scissors Modes: The elusive breathing overtone

TL;DR

This paper investigates the theoretical prediction of breathing overtone modes in the Two-Rotor Model, focusing on their properties, excitation mechanisms, and the challenges in observing these elusive nuclear excitations.

Contribution

It introduces the concept of breathing overtones above Scissors Modes, analyzes their structure and decay pathways, and evaluates their excitation strengths within the Two-Rotor Model.

Findings

The $J^{}^+$ overtone has a breathing mode structure with small $B(E2)$ strength.

The $J=2^+$ overtone can decay into the $J^{}^+$ overtone.

The $J^{}^+$ overtone cannot be directly excited due to vanishing $E0$ amplitude.

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.