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

A method for calculation of Gamow-Teller transition rates is developed by using the concept of the Projected Shell Model (PSM). The shell model basis is constructed by superimposing angular-momentum-projected multiquasiparticle configurations, and nuclear wave functions are obtained by diagonalizing the two-body interactions in these projected states. Calculation of transition matrix elements in the PSM framework is discussed in detail, and the effects caused by the Gamow-Teller residual forces and by configuration-mixing are studied. With this method, it may become possible to perform a state-by-state calculation for β-decay and electron-capture rates in heavy, deformed nuclei at finite temperatures. Our first example indicates that, while experimentally known Gamow-Teller transition rates from the ground state of the parent nucleus are reproduced, stronger transitions from some low-lying excited states are predicted to occur, which may considerably enhance the total decay rates once these nuclei are exposed to hot stellar environments.

Figure 1

Calculated energy levels of the ground band in ${}^{164}\mathrm{Ho}$ (upper panel) and ${}^{164}\mathrm{Dy}$ (lower panel) are compared with data. The ground state of the odd-odd ${}^{164}\mathrm{Ho}$ nucleus has $I^{\pi }=1^{+}$.

Figure 2

Calculated $B$($E$2) values of the ground band in ${}^{164}\mathrm{Dy}$ are compared with data.

Figure 3

Distribution of the $B$(GT${}^{+}$) strength.

Figure 4

Distribution of the $B$(GT${}^{-}$) strength.

Figure 5

Distribution of the $B$(GT${}^{-}$) strength. The numbers are the same as those of Fig. 4, but plotted in the scale as Fig. 3.

Figure 6

$B$(GT) values calculated for the five different cases. Available data are shown in stars. The $B$(GT) data are converted from the experimental Log $\mathit{ft}$ values [34] through Eq. (29).

Figure 7

Possible transition paths from the ground band of ${}^{164}\mathrm{Ho}$ to that of ${}^{164}\mathrm{Dy}$. Experimentally known energies for these states are also displayed.

Figure 8

Calculated $B$(GT) (upper panel) and Log $\mathit{ft}$ values (lower panel) for the ${}^{164}\mathrm{Ho}$ → ${}^{164}\mathrm{Dy}$ electron-capture process. Available data are shown in stars. Data are taken from Ref. [34].