A microscopic cranking model for uni-axial rotation with vanishing collective angular momentum

TL;DR

This paper extends a microscopic cranking model to describe nuclear rotation with near-zero collective angular momentum, revealing new insights into the transition to conventional models and predicting nuclear properties with notable accuracy.

Contribution

The paper generalizes the microscopic cranking model to include the limit of vanishing collective angular momentum, connecting it to the conventional cranking model and analyzing its implications.

Findings

Predicted excitation energy and quadrupole moment closely match empirical data.

The model predicts a higher terminal angular momentum (10) than observed (8).

The model's limitations include neglecting pairing correlations and quasi-particle effects.

Abstract

The rigid-irrotational flow transformation in the previous microscopic cranking model (MCRM) for nuclear collective rotation about a single axis and its coupling to intrinsic motion is generalized. This generalization allow us to consider the limit of vanishingly small collective angular velocity and hence collective angular momentum while the collective moment of inertia remains finite. In this limit, the collective flow become large and oppose one another collaborating the vanishing of the collective angular momentum. In this limit, the MCRM equation for the angular-momentum constraint on the intrinsic wavefunction becomes identical to that of the conventional cranking model (CCRM). In this limit, the MCRM Schrodinger equation also becomes identical to that of the CCRM with an added irrotational-flow kinetic energy component. In this limit, the time-reversal invariance of the MCRM Schrodinger equation is destroyed. The two MCRM equations (with no free parameters) are solved for the ground-state rotational band in the nucleus for a simple deformed harmonic oscillator potential. The predicted excitation energy and quadrupole moment are close to those observed empirically, with the differences seemingly attributable to the absence, in the model, of pairing correlations at low angular momenta and Coriolis-force induced quasi-particle rotation alignment at higher angular momenta. The ground-state terminal (cut-off) angular momentum is predicted to be 10 instead of 8 observed empirically and predicted by the CCRM. It is assumed that pairing correlations would reduce the cut-off angular momentum.