Influence of deformed-nucleus level densities on statistical model calculations for high-spin fission

Inappropriate formulations for nuclear level densities, based in part on an assumption of spherical symmetry, have often been employed in statistical model calculations of the competition between decay modes of nuclei at high spin and excitation. We investigate the influence on such calculations of nuclear deformation effects in the level densities, at both the saddle-point shapes relevant to fission and the most probable shapes reached in particle evaporation. The deformation effects are included in a Fermi-gas formalism in two stages, first assuming complete independence of rotational and intrinsic degrees of freedom, and subsequently allowing for a deformation-dependent cutoff with increasing temperature in the collective enhancement of the level densities. The latter effect gives rise, in the absence of shell and pairing corrections, to a progressive increase with increasing temperature in the most probable daughter-nucleus deformation for particle emission. The most significant effects of the deformed-nucleus level densities on calculated decay properties for ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$+${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$→${}_{}{}^{203}{}_{}{}^{}\mathrm{Pb}$, at several bombarding energies, are an increase in the cross section and a decrease in the anisotropy for fission fragments. Ambiguities in the details of the collective cutoff yield a sizable uncertainty in the quantitative extent of the fission enhancement. Relative measurements for different entrance channels to the same compound nucleus which may be sensitive to the collective cutoff are illustrated by calculations for ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$+${}_{}{}^{180}{}_{}{}^{}\mathrm{Hf}$ vs ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$+${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$ fusion-fission.