A scattering theoretical examination of the statistical theory of chemical reactions: competition between direct and resonance scatterings

On the basis of the formal scattering theory, the reaction probability of the chemical reaction of the complex-formation mode is derived. The probability is expressed as the sum of the contributions from the direct and resonance scatterings. The contribution from the latter is shown to coincide with the reaction probability predicted by the conventional statistical theory of chemical reactions. The balance between the direct and resonance scatterings is governed by the parameter of the overlapping resonance, , where is the average partial width and is the density of resonance states. It is shown that the prediction of the statistical theory is realized when the condition of the critical overlap of resonances, , is fulfilled. The setup and conclusion of the formal theory are illustrated by a numerical example of a simple model.