Scissors Modes:The first overtone

TL;DR

This paper predicts the existence of a first overtone of the scissors mode in nuclei, with specific energy and transition strength, based on the Two-Rotor Model, suggesting it could be experimentally observable in rare earth nuclei.

Contribution

It introduces the prediction of the first overtone of the scissors mode and derives its excitation energy and transition probability within the Two-Rotor Model framework.

Findings

First overtone has twice the energy of the scissors mode.

Transition probability of overtone is proportional to the inverse square of zero-point oscillation amplitude.

Overtone energy is below nucleon emission threshold, making it potentially observable.

Abstract

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}$.