Efficient Method for Quantum Number Projection and Its Application to Tetrahedral Nuclear States

TL;DR

This paper introduces an efficient quantum number projection method applicable to general mean-field states with broken symmetries, enabling microscopic calculations of tetrahedral nuclear states and their energy spectra.

Contribution

The authors developed a novel, efficient quantum number projection technique for general mean-field states, facilitating the first microscopic calculations of tetrahedral nuclear energy spectra.

Findings

Successfully calculated low-lying rotational spectra for tetrahedral deformation in Zr isotopes.

Identified characteristic features of molecular tetrahedral rotors in the spectra.

Observed transitional spectra between vibrational and rotational states at moderate deformation.

Abstract

We have developed an efficient method for quantum number projection from most general HFB type mean-field states, where all the symmetries like axial symmetry, number conservation, parity and time-reversal invariance are broken. Applying the method, we have microscopically calculated, for the first time, the energy spectra based on the exotic tetrahedral deformation in $^{108,110}$Zr. The nice low-lying rotational spectra, which have all characteristic features of the molecular tetrahedral rotor, are obtained for large tetrahedral deformation, $\alpha_{32} \gtsim 0.25$, while the spectra are of transitional nature between vibrational and rotational with rather high excitation energies for $\alpha_{32}\approx 0.1-0.2$