Microscopic study of tetrahedrally symmetric nuclei by an angular-momentum and parity projection method

TL;DR

This paper investigates the rotational excitations of nuclei with hypothetical tetrahedral symmetry using a microscopic projection method, revealing characteristic energy patterns and deformation-dependent transitions.

Contribution

It introduces a microscopic approach to study tetrahedral symmetric nuclei and compares deformation-induced energy transitions with quadrupole cases.

Findings

Excitation patterns match group-theory predictions for tetrahedral symmetry.

Transition from linear to rigid-rotor energy dependence with increasing deformation.

Comparison of tetrahedral and quadrupole deformation energy transitions.

Abstract

We study the properties of the nuclear rotational excitations with hypothetical tetrahedral symmetry by employing the microscopic mean-field and residual-interaction Hamiltonians with angular-momentum and parity projection method; we focus on the deformed nuclei with tetrahedral doubly-closed shell configurations. We find that for pure tetrahedral deformation the obtained excitation patterns satisfy the characteristic features predicted by group-representation theory applied to the tetrahedral symmetry group. We find that a gradual transition from the approximately linear to the characteristic rigid-rotor, parabolic energy-vs.-spin dependence occurs as a function of the tetrahedral deformation parameter. The form of this transition is compared with the similar well-known transition in the case of quadrupole deformation.