Enhancement of $\alpha$-particle formation near ${}^{100}\mathrm{Sn}$

The superfluid tunneling model is applied to the calculation of ground-state–to–ground-state α decay in the even-even neutron-deficient Te-Ba nuclei. We show that there is a larger α-particle formation probability in nuclei of this region above ${}^{100}\mathrm{Sn}$ when compared to analogous nuclei above ${}^{208}\mathrm{Pb}$. This is consistent with the expected systematic variation of the pair gap $\mathrm{\Delta }$ as a function of mass number. The recent experimental data on the α decay of the $N=Z$ nuclei ${}^{104}\mathrm{Te}$ and ${}^{108}\mathrm{Xe}$ are shown to leave open the possibility of enhanced α-particle formation involving nucleon correlations beyond the standard treatment of like-nucleon pairing, which is the mechanism suggested as underlying “superallowed” α decay.

Figure 1

Plots of the variation of the α-particle formation probabilities $P$ along (a) the $N=58$ isotonic chain, and along (b) the Te isotopic chain (open circles). The values of $P$ are taken from Table 1. The rise in $P$ as one approaches the $N=Z$ line is clearly seen. The red crosses are values of $P$ for the analogous nuclei above ${}^{208}\mathrm{Pb}$, by which we mean the same type and number of nucleons beyond the closed shells, namely in (a) the $\mathrm{N}=134$ isotones ${}^{222}\mathrm{Ra}$, ${}^{220}\mathrm{Rn}$, and ${}^{218}\mathrm{Po}$, and in (b) the Po isotopic chain ${}^{214}\mathrm{Po}$, ${}^{216}\mathrm{Po}$, and ${}^{218}\mathrm{Po}$.

Figure 2

An exclusion plot showing limits for the pair gaps, $\mathrm{\Delta }\left({}^{104}\mathrm{Te}\right)$ and $\mathrm{\Delta }\left({}^{108}\mathrm{Xe}\right)$, which are extracted using the STM in order to reproduce possible values of the half lives of ${}^{104}\mathrm{Te}$ and ${}^{108}\mathrm{Xe}$. The filled circles with horizontal error bars are the values for $\mathrm{\Delta }\left({}^{108}\mathrm{Xe}\right)$ extracted from the STM in order to reproduce the half life of $T_{1/2}={58}_{-23}^{+106}\mu \mathrm{s}$, while the extracted value of $\mathrm{\Delta }\left({}^{104}\mathrm{Te}\right)$ corresponds to a half life of $T_{1/2}=18$ ns, and is therefore a lower limit. Different possible values of the ${}^{108}\mathrm{Xe}$ α-decay energy, $E_{\alpha }({}^{108}\mathrm{Xe})$, are indicated to the left, with an additional constraint on the sum energy being assumed; the filled circles assume $\sum E_{\alpha }=9.3\mathrm{MeV}$, while the solid curve indicates the range of possible $\mathrm{\Delta }\left({}^{108}\mathrm{Xe}\right)$ values assuming $\sum E_{\alpha }=9.4\mathrm{MeV}$. The additional constraint requiring that $\mathrm{\Delta }\left({}^{108}\mathrm{Xe}\right)>\mathrm{\Delta }\left({}^{104}\mathrm{Te}\right)$ and the special limiting case treating the problem as a pure pairing force in a single-$j$ shell, such that $\mathrm{\Delta }\left({}^{108}\mathrm{Xe}\right)=1.32\times \mathrm{\Delta }\left({}^{104}\mathrm{Te}\right)$, are indicated with the dashed lines. The resulting region of allowed values of $\mathrm{\Delta }\left({}^{104}\mathrm{Te}\right)$ and $\mathrm{\Delta }\left({}^{108}\mathrm{Xe}\right)$ is indicated by the shaded hash marks. The region extends to higher values beyond the edges of the plot.