Survival-mediated capture and fusion cross sections for heavy-element synthesis

Abstract

The cross section for producing a heavy evaporation residue ${\ensuremath{\sigma}}_{\mathrm{EVR}}$ in a fusion reaction can be written as a product of three nonseparable factors, i.e., the capture cross section, the fusion probability ${P}_{\mathrm{CN}}$, and the survival probability ${W}_{\text{sur}}$. Each of these factors is dependent on the spin. However, one must remember that the ${W}_{\text{sur}}$ term is zero or very small for higher spin values, thus effectively limiting the capture and fusion terms. For a series of $\ensuremath{\sim}287$ reactions leading to heavy evaporation residues with ${Z}_{\text{CN}}\ensuremath{\le}110$, we point out the implications of this fact for capture cross sections for heavy element formation reactions. From a comparison of calculated and measured evaporation residue cross sections we deduce values of the fusion probability ${P}_{\text{CN}}$ for some of these reactions.