Toward extremes of angular momentum: Application of the Pfaffian algorithm in realistic calculations

TL;DR

This paper introduces the Pfaffian algorithm to efficiently compute matrix elements in high-spin nuclear states, enabling the inclusion of complex multi-quasiparticle configurations in realistic calculations.

Contribution

The paper applies the Pfaffian algorithm to expand the Projected Shell Model to include 6-quasiparticle states, facilitating studies of high-spin phenomena in nuclei.

Findings

6-qp states dominate the yrast band beyond spin 34ħ in 166Hf

The third back-bending in moment of inertia is explained by 6-qp configurations

Analysis of multi-qp high-K isomers in 176Hf provided insights into nuclear structure

Abstract

In a calculation of rotated matrix elements with angular momentum projection, the generalized Wick's theorem may encounter a practical problem of combinatorial complexity when the configurations have more than four quasi-particles (qps). The problem can be solved by employing the Pfaffian algorithm generally applicable to calculations of matrix elements for Hartree-Fock-Bogoliubov states with any number of qps. This breakthrough in many-body techniques enables studies of high-spin states in a shell-model framework. As the first application of the Pfaffian algorithm, the configuration space of the Projected Shell Model is expanded to include 6-qp states for both positive and negative parities. Taking $^{166}$Hf as an example, we show that 6-qp states become the main configuration of the yrast band beyond spin $I \approx 34\hbar$, which explains the observed third back-bending in moment of inertia. Structures of multi-qp high-$K$ isomers in $^{176}$Hf are analyzed as another example.