Effect of shell corrections on the $\alpha$-decay properties of ${}^{280\text{–}305}\mathrm{Fl}$ isotopes

The $\alpha$-decay half-lives of ${}^{285\text{–}289}\mathrm{Fl}$ isotopes and their decay chains are investigated by employing the generalized liquid-drop model (GLDM), the unified fission model, the Royer's analytical formula, and the universal decay law. For the GLDM, we take into account the shell correction. The agreement between the experimental data and the calculations indicates that all the methods we used are successful to reproduce $\alpha$-decay half-lives of ${}^{285\text{–}289}\mathrm{Fl}$. For the unknown nuclei, the $\alpha$-decay half-lives have been predicted by inputting $\alpha$-decay energies ($Q_{\alpha }$) extracted from the finite-range droplet model and the updated Weizsäcker-Skyrme-4 (WS4) model. It is found that the shell correction would enlarge the calculated $\alpha$-decay half-lives in the region from ${}^{292}\mathrm{Fl}$ to ${}^{298}\mathrm{Fl}$, where the shell effects are evident. We confirm that $N=184$ is the neutron magic number and $N=178$ is the submagic number by analyzing the $\alpha$-decay half-lives and the shell correction energies. The competition between $\alpha$-decay and spontaneous fission is discussed in detail and the decay modes of ${}^{280\text{–}283}\mathrm{Fl}$ and ${}^{290\text{–}305}\mathrm{Fl}$ have been predicted. Our calculations are in good agreement with the experiments for the decay properties of ${}^{284\text{–}289}\mathrm{Fl}$. We also predict ${}^{284,286}\mathrm{Fl}$ with both $\alpha$-decay and spontaneous fission. The ${}^{280\text{–}283,290\text{–}295,297}\mathrm{Fl}$ isotopes are $\alpha$ decay, ${}^{300\text{–}305}\mathrm{Fl}$ undergo spontaneous fission, and ${}^{296,298,299}\mathrm{Fl}$ would have both $\alpha$-decay and spontaneous fission. We also predict the decay chains of ${}^{280\text{–}283,290,291}\mathrm{Fl}$.

Figure 1

The $\alpha$-decay half-lives of even-even Fl isotopes calculated with FRDM [30] (a) and with WS4 model [31] (b). The solid circles are results calculated by GLDM. The open circles are calculated by GLDM including shell correction. The red squares are experimental data [10, 11, 12].

Figure 2

The shell correction energies of the even-even nuclei with $Z=114$. The WS4 data are from $E_{sh}$ in Ref. [31]. The FRDM data is adopted from $E_{\mathrm{mic}}$ in Ref. [30].

Figure 3

The predicted decay chains of ${}^{280\text{–}283,290,291}\mathrm{Fl}$ isotopes.