Production probability of super-heavy nuclei in fusion

TL;DR

This paper introduces an analytical model for predicting the production probabilities of super-heavy nuclei via fusion, improving accuracy and providing specific predictions for element 119 synthesis.

Contribution

A new analytical formula based on barrier tunneling, combined with an empirical barrier distribution method, enhances prediction accuracy for super-heavy nuclei production cross sections.

Findings

Model reproduces 64 measured cross sections within one order of magnitude.

Successfully captures key quantities like fission barrier height and fusion barrier.

Predicts promising projectile-target combinations for synthesizing element 119.

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 $ \sigma_{\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 $ \sigma_{\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.