Semi-classical and boson descriptions of scissors states

TL;DR

The paper investigates scissors-like magnetic dipole states in nuclei using a two-rotor model for protons and neutrons. It develops both a semi-classical description via the time-dependent variational principle with SU(2) coherent states and a Dyson boson expansion to access wobbling modes and chiral twin bands, applying the framework to $^{156}$Gd. Wobbling frequencies from both methods yield consistent ground- and one-phonon-band energies, and the calculated M1 transition strengths reveal notable differences between the semi-classical and Dyson approaches due to renormalization effects. The results indicate that the two-rotor system can exhibit both wobbling and chiral motion with a shears-like character, and predict chiral partner bands arising from symmetry breaking, motivating experimental exploration of low-energy scissors-like states.

Abstract

A two interacting rotors Hamiltonian is alternatively treated semi-classically and by a Dyson boson expansion method. The linearized equations of motion lead to dispersion equation for the wobbling frequency. One defined a ground band with energies consisting in a rotational part and one half of the vibrational wobbling energy. Adding to each state energy the corresponding wobbling quanta one obtains the first excited band. Phonon amplitudes are used to calculate the reduced probability for the inter-band M1 transitions. The states exhibit a shears character. One points out a chiral symmetry which is broken by the interaction term, leading to a pair of twin chiral bands. Applications are made for $^{156}$Gd. One outlines the ability of the two rotor model to account for the wobbling and chiral motion in nuclei. Although the chosen trial function has not a definite total angular momentum, for two particular ansatz of the pairs $I_p,I_n$ the average value of the total angular momentum approximates, to a certain accuracy, the partial angular momentum $I_p$ In this context, the rotational bands defined throughout this present paper could be labeled by the total I.

Figures (6)

• Figure 1: Color online. Contour plots for four angular momenta pairs, $(I_p,I_n)$, and the energy function (3.20)
• Figure 2: Color online. Semi-classical and boson wobbling frequencies($\omega_s^{I_p1}$ and $\omega_b^{I_p1}$), the first band energies( $E_{s,1}^{I_p1}$ and $E_{b,1}^{I_p1}$) and energies in the one phonon excited band ($E_{s2}^{I_p1}$ and $E_{b2}^{I_p1}$)
• Figure 3: Color online. The minimum value for the semi-classical energy function given by Eq.(3.20), considered for $I_p=I_n=I$, is plotted in units of [V/2].
• Figure 4: Color online. Wobbling frequencies given by the semi-classical and boson expansion method, respectively are presented in the left panel. Energies for the yrast and the first one phonon excited bands corresponding to a semi-classical approach are shown in the right panel.
• Figure 5: Color online. Energy spacing in the ground and excited band.