α-nucleus potentials, α-decay half-lives, and shell closures for superheavy nuclei

Systematic α-nucleus folding potentials are used to analyze α-decay half-lives of superheavy nuclei. Preformation factors of about several percent are found for all nuclei under study. The systematic behavior of the preformation factors and the volume integrals of the potentials allows predictions of α-decay energies and half-lives for unknown nuclei. Shell closures can be determined from measured α-decay energies using the discontinuity of the volume integral at shell closures. For the first time a double shell closure is predicted for $Z_{\mathrm{magic}}=132,N_{\mathrm{magic}}=194$, and $A_{\mathrm{magic}}=326$ from the systematics of folding potentials. The calculated α-decay half-lives remain far below 1 ns for superheavy nuclei with double shell closure and masses $A>300$ independent of the precise knowledge of the magic proton and neutron numbers.

Figure 1

The preformation factors P for several superheavy α emitters. The horizontal lines indicate an average value of $P\approx 8$% (full line) and typical uncertainties of a factor of 3 (dotted lines).

Figure 2

Phase shift ${\delta }_L$ for the $L=0$ partial wave for the system ${}^{212}\mathrm{Po}+{}^{208}\mathrm{Pb}$$\otimes \alpha$. The derived width from Eq. (7) is $\Gamma =3.52\times {10}^{-14}$ MeV. Note the extremely small step size of the calculation of $\Delta E=2.0\times {10}^{-15}$ MeV.

Figure 3

Volume integrals $J_R$ for superheavy nuclei as a function of $Z_D$ (upper), $N_D$ (middle), and $A_D$ (lower). Within a major shell one finds a smooth decrease of $J_R$ with a minimum value around $J_R\approx 280$ MeV fm${}^3$. From the fits to the data points one can directly see that $J_R$ drops below 280 MeV fm${}^3$ at $Z\approx 130,N\approx 192$, and $A\approx 322$, leading to the magic numbers $Z_{\mathrm{magic}}=132,N_{\mathrm{magic}}=194$, and $A_{\mathrm{magic}}=326$. The open circles are extrapolations for ${}^{294}$118 and the lower limit of $J_R>279$ MeV fm${}^3$ close to the next closed shells (see text). The open squares are nuclei with $Q=18$ (${}^{208}\mathrm{Pb}+{}^{204}\mathrm{Hg}$$\otimes \alpha$ ) and $Q=20$ (${}^{210}\mathrm{Pb}+{}^{206}\mathrm{Hg}$$\otimes \alpha$, ${}^{210}\mathrm{Po}+{}^{206}\mathrm{Pb}$$\otimes \alpha$).

Figure 4

Potential strength parameter λ (upper) and volume integrals $J_R$ (lower) around the shell closure $N=82$ for ${}^{130-136}$Xe$\otimes \alpha$ (diamonds), ${}^{132-142}$Ba$\otimes \alpha$ (circles), ${}^{134-144}$Ce$\otimes \alpha$ (triangles), and ${}^{140-146}$Nd$\otimes \alpha$ (squares) isotopes. One can clearly see the discontinuity at the shell closure $N=82$ (see text).

Figure 5

Potential strength parameter λ (upper) and volume integrals $J_R$ (lower) vs decay energy E for superheavy nuclei. Known nuclei are shown as full circles. The extrapolated doublymagic nucleus with $Z_{\mathrm{magic}}=132,N_{\mathrm{magic}}=194$, and $A_{\mathrm{magic}}=326$ is shown as an open circle. The open squares are nuclei with $Q=18$ and $Q=20$ (see also Fig. 3).

Figure 6

Potential strength parameter λ (upper) and volume integrals $J_R$ (lower) vs decay energy E around the shell closure $N=82$ for ${}^{130-136}$Xe$\otimes \alpha$ (diamonds), ${}^{132-142}$Ba$\otimes \alpha$ (circles), ${}^{134-144}$Ce$\otimes \alpha$ (triangles), and ${}^{140-146}$Nd$\otimes \alpha$ (squares) isotopes (see text; for description of symbols see Fig. 4).