Ratios of disintegration rates for distinct decay modes of an excited nucleus

This paper examines a prevalent departure from the standard transition-state treatment of Gamma(n)/Gamma(f), the relative rate of disintegration of an excited nucleus by neutron emission or fission. This departure is caused by what we believe is an erroneous treatment of shell structure corrections. According to the transition-state theory the shell correction in the excited compound nucleus cancels out identically in the ratio Gamma(n)/Gamma(f), whereas in the deviant treatment it leads to an energy-dependent fission barrier that modifies the expression for the partial width Gamma(f). Moreover, according to the transition-state theory, the partial width Gamma(n) depends on the shell effect in the residual nucleus that emitted the neutron, whereas in the deviant treatment this dependence is ignored. We illustrate explicitly the magnitude of the errors that the deviant treatment of Gamma(n)/Gamma(f) generates in typical nuclear reactions, errors that can reach orders of magnitude at low excitation energies. We take the opportunity to describe an accurate algebraic method of evaluating integrals over shell-affected level densities that appear in the transition-state theory. We also present a new derivation of Weisskopf's nucleon evaporation formula, based on the transition-state method rather than on the statistical principle of detailed balance used by Weisskopf. This unifies the theoretical treatments of fission and nucleon evaporation.