First order Coriolis-coupling for rotational spectrum of a tetrahedrally-deformed core plus one-particle system

TL;DR

This paper investigates the rotational spectra of tetrahedral nuclear configurations with a single valence nucleon, revealing characteristic splitting patterns and introducing generalized decoupling parameters to interpret these structures.

Contribution

It provides a detailed analysis of Coriolis-coupling effects in tetrahedral nuclei, offering analytical solutions and new insights into their rotational spectra and degeneracy patterns.

Findings

Spectral splitting into two sequences for certain orbitals

Persistence of double-sequence structures in complex spectra

Analytical interpretation using first-order Coriolis-coupling solutions

Abstract

The possible existence of shape-coexisting nuclear configurations with tetrahedral symmetry is receiving an increasing attention due to unprecedented nuclear structure properties, in particular in terms of the exotic 4-fold nucleonic level degeneracies and the expected long lifetimes which may become a new decisive argument in the exotic nuclei research programs. The present article addresses the rotational structure properties of the tetrahedrally-symmetric even-even core configurations coupled with a single valence nucleon. We focus on the properties of the associated Coriolis-coupling Hamiltonian proposing the solutions based on the explicit construction of the bases of the irreducible representations of the tetrahedral point-group on the one-hand side and the microscopic angular-momentum and parity projection nuclear mean-field approach on the other. It is shown that for one-particle occupying an orbital belonging to the $E_{1/2}$ or $E_{5/2}$ irreducible representation, the rotational spectrum splits into two sequences, the structures analogous to those of the $K=1/2$ rotational bands in the axially symmetric nuclei. Although the spectrum is generally more complicated for one-particle occupying a 4-fold degenerate orbital belonging to the $G_{3/2}$ representation, an appearance of the correlated double-sequence structures persists. The spectra of the doubly-magic tetrahedral core plus one-particle systems can be well interpreted using the analytical solutions of the first order Coriolis-coupling Hamiltonian. We introduce the notion of the generalized decoupling parameters, which determine the size of the energy-splitting between the double-sequence structures.