Tests of the fission-evaporation competition in the deexcitation of heavy nuclei

Abstract

In order to verify methods of calculating the fission-evaporation competition in reactions used to synthesize new super-heavy nuclei in ``cold'' $(1n)$ and ``hot'' $(3n,4n)$ fusion reactions, we present an analysis of existing experimental data on the evaporation-residue cross sections in two selected reactions, $^{208}\mathrm{Pb}$($^{16}\mathrm{O}$, xn) and $^{236}\mathrm{U}$($^{12}\mathrm{C}$, xn), for which complementary experimental information necessary to unambiguously calculate the survival probabilities is available: precisely measured fusion excitation functions and saddle-point energies of the fissioning nuclei, deduced from experiments. Standard statistical model calculations, with shell effects accounted for by the Ignatyuk formula, were carried out assuming the ground state shell corrections of M\"oller et al., and zero shell correction at the saddle configuration (resulting from the presented systematics). Good agreement of the calculated evaporation-residue cross sections with experimental data for different xn reaction channels at low excitation energies leaves no room for modifications of the conventional way of calculating the ${\ensuremath{\Gamma}}_{n}/{\ensuremath{\Gamma}}_{f}$ ratio, particularly for including into this ratio an additional preexponential factor (such as the Kramers fission hindrance factor or an effective collective factor) significantly different from 1.