Refinement of an analytical capture cross section formula

Abstract

An analytical formula with high accuracy is proposed for a systematic description of the capture cross sections at near-barrier energies from light to superheavy reaction systems. Based on the empirical barrier distribution (EBD) method, three key input quantities are refined by introducing nuclear surface correction to the Coulomb parameter $z$ for calculating the barrier height, incorporating the reaction $Q$-value and shell correction into the barrier distribution width calculations, and considering the deep inelastic scattering effects of superheavy systems on the barrier radius. With these refinements, not only the accuracy of the calculated barrier height but also the accuracy of the predicted capture cross sections, is substantially improved. The average deviation (in logarithmic scale) between the predicted cross sections and the experimental data for a total of 426 reaction systems with $ 35 < Z_1 Z_2 < 2600$ is sharply reduced from 3.485 to 0.113.

Figures (6)

• Figure 1: (a) Relative deviations between the calculated barrier heights $V_B^{\rm th}$ and 382 extracted barrier heights Chen23$V_B^{\rm exp}$ for reactions induced by nuclei with $Z_1\ge 6$ and $Z_2\ge 6$. The squares and the circles denote the results of EBD Cap11EBD and those of EBD2, respectively. (b) Barrier radii $R_B$ scaled by $A_1^{1/3}+A_2^{1/3}$. The squares and the circles denote the extracted reduced barrier radii Chen23 and the predictions of EBD2 by Eq.(4), respectively. The line denotes the results of EBD Cap11EBD.
• Figure 2: Comparison of EBD and EBD2 predictions with measured capture cross sections for $^{16}$O+$^{16}$O Kuro87, $^{18}$O+$^{58}$Ni Jia25, $^{16}$O+$^{92}$Zr New01, $^{16}$O+$^{154}$Sm Lei95, $^{16}$O+$^{208}$Pb Mort99 and $^{64}$Ni+$^{238}$U Itkis22. The squares denote the experimental data. The dot-dashed curves and the solid curves denote the results of EBD and EBD2, respectively.
• Figure 3: (a) The same as Fig. 2, but for reactions $^{132}$Sn + $^{40,48}$Ca Kola12 and $^{40}$Ca + $^{48}$Ca Jiang10.
• Figure 4: (a) The same as Fig. 2, but for reactions $^{48}$Ca+$^{154}$Sm Stef05, $^{48}$Ca+$^{208}$Pb Prok08, $^{48}$Ca+$^{238}$U Nishio12Itkis22 and $^{48}$Ca+$^{248}$Cm Itkis22.
• Figure 5: Mean-square deviation between the predicted cross sections and the experimental data in logarithmic scale. The squares and the circles denote the results with EBD and EBD2, respectively.