Description of anti-magnetic rotation in nuclei within the generalized variable moment of inertia model

Abstract

The Generalized Variable-Moment-of-Inertia (GVMI) model, based on a nonlinear phenomenological rotational energy expression, is applied to investigate the negative-parity \(\Delta I=2\) Antimagnetic Rotation (AMR) bands in \(^{105}\textrm{Cd}\) and \(^{101}\textrm{Pd}\) nuclei. The model provides a satisfactory description of the observed excitation energies and reproduces the corresponding trend of the rotational frequency \(\hbar \omega \). The semiclassical geometrical interpretation of the angular-momentum composition of the band is based on the gradual alignment of the relevant angular momentum vectors of proton-holes toward the neutron angular-momentum vector. This phenomenological description is consistent with the characteristic closing of the twin shears in AMR. The resulting evolution of the shears geometry is further used to examine the observed decrease of the electric quadrupole transition probabilities B(E2) with increasing spin. Thus, the GVMI approach offers a simple and transparent phenomenological framework for correlating the rotational energies, rotational frequencies, angular-momentum geometry, and B(E2) systematics of the band. Complementary microscopic insight is also provided by Cranked Shell Model (CSM) calculations, which include pairing correlations, for both \(^{105}\textrm{Cd}\) and \(^{101}\textrm{Pd}\) spectra with appropriate configurations before and after the backbending. The CSM results are found to be consistent with the observed rotational behavior associated with the AMR band. The comparison between the phenomenological GVMI analysis and the CSM results indicates that the simple GVMI parametrization captures important empirical features of the observed band while providing a complementary geometrical interpretation of its angular-momentum evolution. The present study therefore does not aim to replace microscopic descriptions of AMR, but demonstrates the usefulness of the GVMI model as a phenomenological tool for obtaining first-order structural information on such rotational bands.