α decay of high-spin isomers in $N=84$ isotones

The superfluid tunneling model is applied to the calculation of half-lives of the observed $\alpha$ decays in $N=84$ isotones. Results of our calculations are compared to experimental data on the ground-state $\alpha$ decays along the isotonic chain from ${}^{144}\mathrm{Nd}$ to ${}^{159}\mathrm{Re}$. Good agreement is found. The $\alpha$ decays of the known high-spin isomers in ${}^{155}\mathrm{Lu}, {}^{156}\mathrm{Hf}, {}^{157}\mathrm{Ta}$, and ${}^{158}\mathrm{W}$ are also well reproduced, once a reduction in the pairing strength is taken into account. This includes reproduction of the main features of the recently observed fine structure from ${}^{155}\mathrm{Lu}(25/2^{-})$ and ${}^{156}\mathrm{Hf}\left(8^{+}\right)$. Predictions for the $\alpha$-decay fine structure of ${}^{157}\mathrm{Ta}(25/2^{-})$ and ${}^{158}\mathrm{W}\left(8^{+}\right)$ high-spin isomers are presented.

Figure 1

Decimal logarithm of $\alpha$-decay half-lives (in seconds) for the strongest decay branch from the ground state of each of the $N=84$ isotones. The filled circles are the experimental data (second column of Table 1) and the red crosses are the results from the STM calculations using the pairing gaps $\mathrm{\Delta }={\mathrm{\Delta }}_{\mathrm{VJH}}$ (fourth column of Table 1).

Figure 2

Decimal logarithms of the ratios between the experimental and theoretical $\alpha$-decay half-lives for the strongest decay branch from the ground state of each of the $N=84$ isotones. The open circles use the STM calculations with the standard pair gap parametrization $\mathrm{\Delta }={\mathrm{\Delta }}_{\mathrm{BM}}$, while the red crosses use the STM calculations with the pairing gaps calculated using $\mathrm{\Delta }={\mathrm{\Delta }}_{\mathrm{VJH}}$, as discussed in the text. The blue squares are values calculated using the Royer formulas [7]. The dashed horizontal lines indicate values of ±0.477, corresponding to a factor-3 difference between experimental and theoretical $\alpha$-decay half-lives.

Figure 3

Decimal logarithm of the $\alpha$-decay half-lives (in seconds) for the $L=8$ transition from the high-spin isomers in ${}^{155}\mathrm{Lu}, {}^{156}\mathrm{Hf}, {}^{157}\mathrm{Ta}$, and ${}^{158}\mathrm{W}$. The black filled circles are the experimental data while the red crosses (red open squares) are the results from the STM calculations using the pairing gaps $\mathrm{\Delta }={\mathrm{\Delta }}_{\mathrm{VJH}}$ ($\mathrm{\Delta }=0.6\times {\mathrm{\Delta }}_{\mathrm{VJH}}$).

Figure 4

The $\alpha$-decay branches from the isomers ${}^{155}\mathrm{Lu}(25/2^{-})$ (data points to the left of the plot) and ${}^{156}\mathrm{Hf}\left(8^{+}\right)$ (data points to the right), given as a percentage of the total $\alpha$ decay from those states, $b_{\alpha }$. The horizontal axis is marked by the spin parity, $J^{\pi }$, of the state in the daughter nucleus to which the $\alpha$ line decays. The black filled circles are the experimental data while the red open squares are the results from the STM calculations using the pairing gaps $\mathrm{\Delta }=0.6\times {\mathrm{\Delta }}_{\mathrm{VJH}}$.