Sub-barrier fusion enhancement due to positive Q-value four-neutron transfer

Abstract

The influence of positive $Q$-value four-neutron transfer (PQ4NT) effects on the sub-barrier capture cross sections is systematically investigated using the empirical barrier distribution (EBD2) method. For 13 fusion reactions with $Q_{4n}>0$, sustained neutron-pair transfer is found to reduce barrier heights and enhance capture cross sections at sub-barrier energies. In contrast, reactions such as $^{18}$O+$^{58}$Ni, which have $Q_{2n}>0$ but $Q_{4n}<0$, exhibit no enhancement due to the stalling of subsequent neutron-pair transfer after the initial 2n transfer. By incorporating PQ4NT effects into EBD2 for systems with $Q_{4n}>0$, the average deviation between predicted and experimental capture cross sections (113 datasets) is significantly reduced by $22\%$. Additionally, time-dependent Hatree-Fock (TDHF) calculations confirm greater barrier reduction in $^{40}$Ca-induced reactions ($Q_{4n}>0)$ compared to those induced by $^{48}$Ca.

Figures (5)

• Figure 1: Capture excitation functions for $^{16}$O+$^{154}$Sm Lei95, $^{48}$Ca+$^{154}$Sm Stef05, $^{18}$O+$^{116}$Sn Deb20, $^{28}$Si+$^{154}$Sm Gil90, $^{32}$S+$^{154}$Sm Gom94, $^{32}$S+$^{116}$Sn Trip01. The squares and curves denote the experimental data and predictions of EBD2, respectively.
• Figure 2: (a) Distribution of the discrepancies between the calculated barrier heights $V_B^{\rm th}$ with EBD2 and the extracted ones $V_B^{\rm exp}$Chen23. (b) Distribution of the mean-square deviation between the predicted cross sections with EBD2 and the experimental data in logarithmic scale. The blue and the red bars denote the results for the cases with $Q_{4n}<0$ and those with $Q_{4n}>0$, respectively.
• Figure 3: Capture excitation functions for reactions $^{40}$Ca + $^{94}$Zr Sef07, $^{40}$Ca + $^{96}$Zr Tim98, $^{40}$Ca + $^{124}$Sn Scar00, and $^{132}$Sn + $^{40}$Ca Kola12. The squares denote the experimental data. The solid curves and the circles denote the results of EBD2 and those with the PQ4NT effect being considered in the calculations, respectively.
• Figure 4: The same as Fig. 3, but for reactions $^{32}$S+$^{94}$Zr Jia14a, $^{32}$S+$^{96}$Zr Zhang10, $^{32}$S+$^{104}$Ru Pengo83, $^{32}$S+$^{154}$Sm Gom94, $^{32}$S+$^{182}$W Mis00, and $^{32}$S+$^{208}$Pb Das04.
• Figure 5: The same as Fig. 3, but for reactions $^{28}$Si+$^{154}$Sm Gil90, $^{28}$Si+$^{208}$Pb Hind95 and $^{30}$Si+$^{238}$U Nish10.