Theoretical studies of hot-atom reactions. III. Solution of the integral reaction probability equation for quantum-mechanical nonreactive scattering

Abstract

A mathematical technique by which the previously derived IRP equation for a multicomponent mixture can be solved accurately for the integral reaction probability, when quantum‐mechanical oscillations are included in the model for nonreactive scattering, is described. The kernel corresponding to a quantum‐mechanical hard‐sphere model for nonreactive scattering is developed. The known functions required for the calculation of the kernel are analyzed for the case of hot tritrium reactions with isotopic hydrogen molecules in the presence of rare‐gas moderators. The algebraic method of solution of the IRP equation is general and can be applied to any inhomogeneous Volterra equation of the second kind. It is particularly recommended when the kernel is oscillatory and/or asymmetric.