Microscopic nuclear structure study of $^{229}$Th by Projected Shell Model

TL;DR

This paper uses the projected shell model to analyze the nuclear structure of $^{229}$Th, accurately describing low-energy levels and transition probabilities, which enhances understanding of its isomeric state for applications like nuclear clocks.

Contribution

The study applies a state-of-the-art microscopic projected shell model to $^{229}$Th, providing detailed insights into its low-energy nuclear structure and transition properties.

Findings

Accurately describes low-energy levels of $^{229}$Th

Provides a $B(M1)$ value consistent with recent measurements

Suggests small multipole mixing in the second-excited state transition

Abstract

$^{229}$Th, a crucial candidate for nuclear clocks and many other applications, is a typical heavy nucleus with an extremely low-energy isomeric state $^{229m}$Th. A detailed study of the nuclear structure of $^{229}$Th is performed here by the microscopic model of state-of-the-art projected shell model. Our calculation describes well low-energy levels of $^{229}$Th, and provides a reduced transition probability $B(M1)$ of $0.0240$ W.u. for the isomeric transition which agrees well with the radiative lifetime of $^{229m}$Th measured recently. Our result supports a small multipole mixing for the cross-band transition of the second-excited state of $^{229}$Th, suggesting that further investigations on the inconsistencies in the decay of the second-excited state should be necessary. The physics behind these properties is revealed by the analysis of the nuclear wave functions. Our findings provide a deep insight into $^{229}$Th from the microscopic nuclear structure point of view, and offer the chance for further studies for nuclear clocks and relevant topics by microscopic nuclear structure theory.