$\alpha$ decay of high-K isomers in ${}^{270}\mathrm{Ds}$ and ${}^{266}\mathrm{Hs}$ in a superfluid tunneling model

We use the superfluid tunneling model (STM) to calculate the half-lives of ground-state $\alpha$ decays of even-even superheavy nuclei (SHN) with $Z\ge 100$. The experimental data are reproduced to accuracies comparable to other contemporary models of $\alpha$ decay of SHN. We apply the STM to the case of the $\alpha$ decaying high-K isomers identified in the decay chains of ${}^{270}\mathrm{Ds}$. By accounting for the $\alpha$-decay Q values, $Q_{\alpha }$, the angular momentum difference between initial and final states, L, and a reduction in the pairing gap, Δ, we are able to reproduce the observed $\alpha$ decay of the isomers, including the unusual competition between $L\approx 10$ and $L\approx 0\alpha$ branches seen for the K isomer in ${}^{270}\mathrm{Ds}(Z=110)$.

Figure 1

Decimal logarithm of $\alpha$-decay half-lives (in seconds) of even-even isotopes with $Z\ge 100$ as a function of nuclear mass number A. The experimental data are marked with (blue) crosses (errors are typically less than the size of the symbol—see comment in caption of Table 1). The results of the calculations from the superfluid tunneling model are shown as filled (red) circles. The data points for each isotope chain, indicated with the corresponding element symbol, are joined by solid lines to guide the eye.

Figure 2

Decimal logarithms of the ratios between the experimental and theoretical half-lives using the data in Table 1. The solid (red) circles, the solid (blue) triangles, and the open (black) squares represent $\mathrm{lo}{\mathrm{g}}_{10}\left(T_{1/2,\mathrm{expt}}/T_{1/2,\mathrm{theo}}\right)$, where $T_{1/2,\mathrm{theo}}$ is calculated using the superfluid tunneling model, the Viola-Seaborg formula [7] with the parametrization of [8], and the Royer formula of [9], respectively.

Figure 3

Schematic of the decay scenario for ${}^{270}\mathrm{Ds}$ based on the preliminary data published in [13]. The half-lives of ground and isomeric states and the $Q_{\alpha }$ values used in the calculations are indicated.