Production probability of super-heavy nuclei in fusion

Abstract

The synthesis of super-heavy nuclei (SHN) through fusion reactions is a critical area of nuclear physics, offering insights into nuclear stability and the limits of the periodic table. However, theoretical predictions of evaporation residue cross sections $ σ_{\rm {ER} }$ remain challenging due to large uncertainties arising from complex reaction mechanisms and sensitive model parameters. In this work, a new and analytical formula is proposed for systematically describing the production probabilities of SHN with atomic number $Z\ge 110$, based on barrier tunneling concept. Together with the empirical barrier distribution method for describing capture, an improved model, EBD3, reproduces 64 measured $ σ_{\rm {ER} }$ within one order of magnitude, with a root-mean-square deviation of 0.351. The model successfully captures key quantities in fission-like process, including fission barrier height, mass asymmetry, depth of capture pocket and the effective fusion barrier height. Predictions for the synthesis of element 119 are presented, identifying promising projectile-target combinations such as $^{45}$Sc + $^{249}$Cf with a maximum cross section of $107.5^{+120}_{-56.7}$ fb. The maximum cross section falls to $3.2^{+3.6}_{-1.7}$ fb for $^{54}$Cr + $^{243}$Am at the optimal incident energy of 244 MeV.

Figures (7)

• Figure 1: Contour plot of the macroscopic part $P_{\rm mac}$ of the DNS survival probability. The red circles and the blue ones denote known hot and cold fusion reactions producing SHN with $Z\ge 110$, respectively. The squares denote the three reactions leading to the synthesis of element 119: $^{54}$Cr+$^{243}$Am, $^{50}$Ti+$^{249}$Bk and $^{45}$Sc+$^{249}$Cf.
• Figure 2: (a) Predicted capture excitation function for $^{48}$Ca + $^{243}$Am with EBD3. The circles denote the production probability $P$ of SHN calculated by Eq.(2) (multiplied by $10^{10}$). (b) Comparison of the total evaporation residual cross sections $\sigma_{\rm {ER} }=\sum \sigma_{xn}$. The squares and circles denote the experimental data of Dubna Ogan15CaAm and the diamonds denote the data of CAFE2 in Lanzhou Gan26.
• Figure 3: Evaporation residual cross sections for cold fusion reactions $^{64}$Ni + $^{208}$Pb Hoff98Mori04, $^{64}$Ni + $^{209}$Bi Hoff02Mori04, $^{70}$Zn + $^{208}$Pb Hoff02, and $^{70}$Zn + $^{209}$Bi Mori09. The scattered symbols denote the experimental data. The curves denote the predictions of EBD3 and the shadows denote the uncertainties. The arrows denote the positions at $E_{\rm c.m.}=V_B+\Delta$.
• Figure 4: Total evaporation residual cross sections for hot fusion reactions $^{48}$Ca + $^{232}$Th CaTh, $^{48}$Ca + $^{238}$U CaU, $^{48}$Ca + $^{240,242,244}$Pu CaUCaPu240Ogan15, and $^{48}$Ca + $^{249}$Bk Ogan15. The squares and the curves denote the experimental data and the predictions of EBD3, respectively. The arrows denote the positions at $E_{\rm c.m.}=V_B+B_{\rm f}+\Delta$.
• Figure 5: The same as Fig. 4, but for $^{48}$Ca + $^{245,248}$Cm CaCmOgan15, $^{48}$Ca + $^{249}$Cf Ogan15, $^{50}$Ti + $^{242,244}$Pu Ogan25Ogan26TiPu, and $^{54}$Cr + $^{238}$U Ogan25.