Abstract
The quantum mechanical coupled channel τ operator formalism has been used to derive coupled integral equations for three-body reactions in three dimensions (neglecting dissociation). These integral equations differ significantly from the usual Lippmann-Schwinger integral equations in that they are already essentially Fredholm equations of the second kind. (That is, the ‘kernel’ for these equations does not involve the appearance of ‘lesser’ and ‘greater’ radial variables.) The formalism is used to calculate total reactive scattering cross sections for a three-dimensional model for a three-body system. Results are presented over a range of energies from about 0·2 eV to 1·2 eV.
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