Microscopic nuclear structure study of 229Th by projected shell model

${}^{229}$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 $B\left(M1\right)$ 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.