Predictions of conventional and microscopic triaxial cranking models for light nuclei

TL;DR

This paper introduces a microscopic triaxial cranking model (MSCRM3) that dynamically accounts for angular velocity effects, revealing three-dimensional rotational phenomena in light nuclei that conventional models miss.

Contribution

The paper develops and compares a new microscopic triaxial cranking model (MSCRM3) with the conventional model, highlighting its ability to predict complex rotational features in light nuclei.

Findings

MSCRM3 predicts reduced energy-level spacing in 20Ne.

MSCRM3 captures three-dimensional rotation phenomena.

Conventional models are effectively uniaxial and miss these phenomena.

Abstract

The conventional cranking model for uniaxial rotation is frequently used to study rotational features in deformed nuclei. However, the model uses a constant angular velocity. To investigate the effect of a dynamic angular velocity, a quantal microscopic time-reversal and D2 invariant cranking model for triaxial rotation (MSCRM3) including residual correction terms is derived from a unitary transformation of the nuclear Schrodinger equation and using Hartree-Fock approach. Except for the angular velocity and residual terms, MSCRM3 and the conventional cranking model for triaxial rotation (CCRM3) Schrodinger equations are identical in form, and are solved iteratively in a similar manner. The article identifies the differences in the rotational features predicted by CCRM3 and MSCRM3 for 20Ne, 24Mg, and 28Si using a self-consistent deformed harmonic-oscillator potential. The rotational features studied are: rotational relaxation of the intrinsic system, stability of the rotational states, various rotation modes, nuclear shapes, their transitions, and band termination. MSCRM3 predicts the observed reduced energy-level spacing in 20Ne between J=6 and 8 and attributes its occurrence to quenching of a wobbly rotation. The remaining discrepancy between the observed and MSCRM3-predicted excitation energies for 20Ne is removed by including the spin-orbit interaction and the residuals of the square of the angular momentum and interaction. CCRM3 does not predict the three dimensional phenomena predicted by MSCRM3 (such as the reduced energy-level spacing in 20Ne and the rotational-band termination at J=12 in prolate 28Si and triaxial 24Mg, etc. arising from the angular velocity). We, therefore, conclude that CCRM3 is effectively a uniaxial rotation model. Therefore, using CCRM3 or its uniaxial version, one would miss capturing three-dimensional rotation phenomena.