Reexamine the nuclear chiral geometry from the orientation of the angular momentum

TL;DR

This paper reexamines nuclear chiral geometry, clarifying previous paradoxes by analyzing angular momentum orientations and showing chiral interpretation is valid only at higher spins when angular momenta are comparable.

Contribution

It provides a revised understanding of nuclear chiral geometry by clarifying the conditions under which chiral rotation interpretation is valid, based on angular momentum analysis.

Findings

The paradox arises from small rotor angular momentum near the bandhead.

Chiral geometry interpretation is valid only at certain higher spins.

Effective angle approach is appropriate when angular momenta are comparable.

Abstract

The paradox on the previous interpretation for the nuclear chiral geometry based on the effective angle has been clarified by reexamining the system with the particle-hole configuration $\pi (1h_{11/2})^1 \otimes \nu(1h_{11/2})^{-1}$ and rotor with deformation parameter $\gamma=30^\circ$. It is found that the paradox is caused by the fact that the angular momentum of the rotor is much smaller than those of the proton and the neutron near the bandhead. Hence, it does not support a chiral rotation interpretation near the bandhead. The nuclear chiral geometry based on the effective angle makes sense only when the angular momentum of the rotor becomes comparable with those of the proton and the neutron at the certain spin region.