Angular momentum coupling in simple-fission transition states

Abstract

An efficient means is deduced for calculating RRKM microscopic reaction rates for simple-fission transition states by using a Hamiltonian consisting of the separate Hamiltonians for each moiety (A and B), hard-sphere interactions between A and B, and symmetric tops connected by a light rigid rod; the reaction coordinate is the breaking bond. This extension of the simple Gorin model takes exact account of the angular-momentum coupling between A and B and of the transition-state requirement that the density of states of the activated complex be evaluated with the reaction coordinate held fixed. Evaluation for typical systems shows that the simpler treatment where A and B are treated as independent rotors is both accurate and in accord with experiment, if both are small but breaks down when A and/or B are large. In the latter case, the variational calculation gives a rate coefficient that is highly sensitive to the assumed hard-sphere radii; although the model cannot then be used meaningfully for a priori prediction of experiment, it provides a useful means of fitting extant data to predict falloff behavior.