# Survival Mediated Heavy Element Capture Cross Sections

## TL;DR

This paper analyzes how the survival probability influences the calculation of heavy element formation cross sections in fusion reactions, emphasizing the impact of decay probabilities on the overall process.

## Contribution

It introduces a formal framework highlighting the role of survival probability in heavy element capture cross sections, emphasizing the importance of decay probabilities in the fusion process.

## Key findings

- Survival probability Wsur constrains the spin range for capture and fusion.
- Implications for calculating heavy element formation cross sections.
- Highlights the importance of decay probabilities in fusion models.

## Abstract

Formally, the cross section for producing a heavy evaporation residue, {\sigma}EVR, in a fusion reaction can be written as. \begin{equation} \sigma_{\rm EVR}(E)=\frac{\pi h^2}{2\mu E}\sum\limits_{\ell=0}^\infty (2\ell+1)T(E,\ell)P_{\rm CN}(E,\ell)W_{\rm sur}(E,\ell), \end{equation} where E is the center of mass energy, and T is the probability of the colliding nuclei to overcome the potential barrier in the entrance channel and reach the contact point. PCN is the probability that the projectile-target system will evolve from the contact point to the compound nucleus. Wsur is the probability that the compound nucleus will decay to produce an evaporation residue rather than fissioning. However, one must remember that the Wsur term effectively sets the allowed values of the spin, which in turn, restricts the values of the capture and fusion cross sections. We point out the implications of this fact for capture cross sections for heavy element formation reactions.