Tetrahedral symmetry in Zr nuclei: Calculations of low-energy excitations with Gogny interaction

TL;DR

This paper investigates low-energy excitations in Zirconium isotopes with tetrahedral symmetry using Gogny interactions, confirming theoretical predictions and highlighting the importance of angular momentum projection in nuclear structure calculations.

Contribution

The study provides a detailed computational analysis of tetrahedral symmetry in Zr nuclei, employing Gogny interactions and projection techniques to confirm group theory predictions.

Findings

Spectra follow expected tetrahedral symmetry patterns

Angular momentum projection significantly lowers energy levels

Correlation energies are large for tetrahedral and octupole deformations

Abstract

We report on the results of the calculations of the low energy excitation patterns for three Zirconium isotopes, viz. $^{80}$Zr$_{40}$, $^{96}$Zr$_{56}$ and $^{110}$Zr$_{70}$, reported by other authors to be doubly-magic tetrahedral nuclei (with tetrahedral magic numbers $Z$=40 and $N$=40, 56 and 70). We employ the realistic Gogny effective interactions using three variants of their parametrisation and the particle-number, parity and the angular-momentum projection techniques. We confirm quantitatively that the resulting spectra directly follow the pattern expected from the group theory considerations for the tetrahedral symmetric quantum objects. We also find out that, for all the nuclei studied, the correlation energy obtained after the angular momentum projection is very large for the tetrahedral deformation as well as other octupole deformations. The lowering of the energies of the resulting configurations is considerable, i.e. by about 10 MeV or even more, once again confirming the significance of the angular-momentum projections techniques in the mean-field nuclear structure calculations.