Rate of decline of the production cross section of superheavy nuclei with $Z=114–117$ at high excitation energies

The production cross sections of superheavy nuclei with charge numbers 114–117 are predicted in the (5–9)$n$ evaporation channels of the ${}^{48}\mathrm{Ca}$-induced complete fusion reactions for future experiments. The estimates of synthesis capabilities are based on a uniform and consistent set of input nuclear data provided by the multidimensional microscopic-macroscopic approach. The contributions of various factors to the final production cross section are discussed. As shown, the specific interplay between survival and fusion probabilities unexpectedly leads to a relatively slow decline of the total cross sections with increasing excitation energy. This effect is supported by a favorable arrangement of fission barriers protecting the compound nucleus against splitting concerning energetic thresholds for the emission of successive neutrons. In particular, the probabilities of the formation of superheavy nuclei in the $5n, 6n$, and in some cases even $7n$ evaporation channels are still promising. This may offer a new opportunity for the future synthesis of unknown neutron-deficient superheavy isotopes.

Figure 1

The potential energy surface (PES), $E-E_{\mathrm{mac}}\left(\mathrm{sphere}\right)$, for ${}_{117}{}^{290}\mathrm{Ts}$. The crosses indicate the saddle point (blue) and the ground state (red).

Figure 2

The ratio $B_f/B_n$ vs the neutron number $N=A-Z$ for the SHN ${}_{114}\mathrm{Fl}, {}_{115}\mathrm{Mc}, {}_{116}\mathrm{Lv}, {}_{117}\mathrm{Ts}$.

Figure 3

The calculated (lines) excitation functions for $xn$ evaporation channels ($x=1$–9) of the indicated complete fusion reactions. The mass table of Ref. [12] is used in the calculations. The black triangles at the energy axis indicate the excitation energy $E_{\mathrm{CN}}^{*}$ of the CN at bombarding energy corresponding to the Coulomb barrier for the sphere-side orientation. The blue diamonds, green squares, red circles, and gray pentagons represent the experimental data [2] with error bars for $2n, 3n, 4n$, and $5n$ evaporation channels, respectively. The symbols with the arrow indicate the upper limits of evaporation residue cross sections.

Figure 4

The same as in Fig. 3, but for $xn$ evaporation channels ($x=5$–9) of the indicated complete fusion reactions.

Figure 5

The calculated fusion $P_{\mathrm{CN}}$ and survival $W_{xn}$ ($x=5$–9) probabilities as a function of the excitation energy for the ${}^{48}\mathrm{Ca}+{}^{244}\mathrm{Pu}$ complete fusion reaction.

Figure 6

The calculated ratios of the widths of neutron, proton, and $\alpha$-particle emissions to the total width as a function of excitation energy for the nuclei ${}^{284–287}\mathrm{Fl}$.

Figure 7

The calculated total cross section as a function of the excitation energy for the indicated reaction.