Survival Mediated Heavy Element Capture Cross Sections

Abstract

Formally, the cross section for producing a heavy evaporation residue, σEVR, in a fusion reaction can be written as. \begin{equation} σ_{\rm EVR}(E)=\frac{πh^2}{2μE}\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.