Inner-shell ionization during $\alpha$ decay of superheavy isotopes from the tennessine ${}_{117}{}^{293}\mathrm{Ts}$ and oganesson ${}_{118}{}^{294}\mathrm{Og}$ chains

Presented here are calculations of probabilities of the $K$-, $L$-, and $M$-shell ionization during $\alpha$ decay of superheavy isotopes ${}_{117}{}^{293}\mathrm{Ts}$, ${}_{115}{}^{289}\mathrm{Mc}$, and ${}_{113}{}^{285}\mathrm{Nh}$ involved in the tennessine decay chain as well as ${}_{118}{}^{294}\mathrm{Og}$, ${}_{116}{}^{290}\mathrm{Lv}$, and ${}_{114}{}^{286}\mathrm{Fl}$ involved in the new oganesson decay chain. The ionization probabilities are of importance for handling data obtained by methods of the combined $\alpha$, $\gamma$, and conversion-electron spectroscopy used in the superheavy element synthesis analysis. Relativistic calculations are based on the quantum mechanical model. Electron wave functions are determined by the Dirac-Fock method. The $\alpha$-particle tunneling through the atomic Coulomb barrier is taken into account. Peculiarities of the $K$-, $L$-, and $M$-shell ionization are considered. Results demonstrate that the effect of tunneling through the Coulomb barrier for the $L$ and $M$ shells is of no significance as distinct from the $K$ shell, where the inclusion of the tunneling leads to a considerable decrease of the ionization probability. The probability of ionization from higher shells is larger than that from inner shells. However, the change from the $K$ shell to $L$ shell is much more significant than the change from the $L$ shell to $M$ shell. It has been found that only monopole and dipole terms of the radiative field $L=0,1$ make a contribution to the $K$- and $L_1$-shell ionization probabilities while contributions of all multipoles $L\le 4$ may be important for the $L_2$, $L_3$, and particularly for $M_1-M_5$ subshells.

Figure 1

The differential probability $d{P}_i\left(E_f\right)/d{E}_f$ of ionization during $\alpha$ decay of ${}_{118}{}^{294}\mathrm{Og}$ at $Q_{\alpha }=11.65\mathrm{MeV}$ for the $K$, $L$ (a) and $M$ (b) shells vs the continuum electron energy $E_f$. (a) Solid, the $K$ shell; large dashed, the $L_1$ subshell; middle dashed, $L_2$; small dashed, $L_3$. (b) large dashed, $M_1$; middle dashed, $M_2$; small dashed, $M_3$; large chain, $M_4$; small chain, $M_5$.

Figure 2

The probability of ionization $P_i\left(Q_{\alpha }\right)$ during $\alpha$ decay of ${}_{86}{}^{222}\mathrm{Rn}$ (a) and ${}_{118}{}^{294}\mathrm{Og}$ (b) vs the $\alpha$-particle energy $Q_{\alpha }$ for the $K$, $L_i$, and $M_i$ subshells. Solid, the $K$ shell; long-dashed, the $L_1$ subshell; middle-dashed, $L_2$; short-dashed, $L_3$; long-chain, $M_1$; middle-chain, $M_2$; short-chain, $M_3$; rare-dot, $M_4$; frequent-dot, $M_5$.