Shell-model method for Gamow-Teller transitions in heavy deformed odd-mass nuclei

A shell-model method for calculating Gamow-Teller (GT) transition rates in heavy deformed odd-mass nuclei is presented. The method is developed within the framework of the projected shell model. To implement the computation requirement when many multi-quasiparticle configurations are included in the basis, a numerical advancement based on the Pfaffian formula is introduced. With this new many-body technique, it becomes feasible to perform state-by-state calculations for the GT nuclear matrix elements of $\beta$-decay and electron-capture processes, including those at high excitation energies in heavy nuclei which are usually deformed. The first results, ${\beta }^{-}$ decays of the well-deformed $A=153$ neutron-rich nuclei, are shown as the example. The known $log\left(ft\right)$ data corresponding to the $B({\mathrm{GT}}^{-}$) decay rates of the ground state of ${}^{153}\mathrm{Nd}$ to the low-lying states of ${}^{153}\mathrm{Pm}$ are well described. It is further shown that the $B$(GT) distributions can have a strong dependence on the detailed microscopic structure of relevant states of both the parent and daughter nuclei.

Figure 1

The calculated GT strength distribution for ${\beta }^{\pm }$ transition from the first $1/2^{-}$ state of ${}^{83}\mathrm{Zr}$ respectively to all $1/2^{-},3/2^{-}$ states of (a) ${}^{83}\mathrm{Nb}$ and (b) ${}^{83}\mathrm{Y}$, as a function of excitation energies.

Figure 2

Same as Fig. 1, but in logarithmic scale.

Figure 3

(a) Calculated energies and (b) transition energies of the yrast band and (c) calculated energies and (d) transition energies of the band based on the $5/2$ isomer for ${}^{153}\mathrm{Nd}$, as compared with the data taken from Refs. [61, 62].

Figure 4

Calculated energy levels of ${}^{153}\mathrm{Pm}$, as compared with the data taken from Ref. [61].

Figure 5

Calculated GT strength distribution from the $3/2^{-}$ ground state and the $5/2^{+}$ isomeric state of ${}^{153}\mathrm{Nd}$ to the excited states of ${}^{153}\mathrm{Pm}$.

Figure 6

Same as Fig. 5, but in logarithmic scale.

Figure 7

Calculated GT strength distribution from two $3/2^{-}$ states of ${}^{153}\mathrm{Nd}$ at about 3.5 MeV to the excited states of ${}^{153}\mathrm{Pm}$.