On the Lippmann–Schwinger equation for atom–diatom collisions: A rotating frame treatment

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Abstract
The use of a rotating frame description of molecular collisions is reconsidered within the framework of the Lippmann–Schwinger equation for the transition or T operator. The present approach explicitly displays the proper boundary conditions which apply to descriptions of such collisions in the rotating frame whose Z axis follows the scattering vector. The resulting body frame equations are shown to lead naturally to the introduction of ’’body frame Bessel and Hankel functions,’’ 𝒥Jjλλ′ and ℋJjλλ′ (BFBF), which are solutions of the unperturbed Hamiltonian for the collision transformed to the rotating frame. It is found that the BFBF can be defined in several ways differing by phase factors that affect their asymptotic form. Two particular choices are examined, one of which leads to a simple asymptotic form of the wavefunction, and the other leads to a somewhat more complicated form. Both are shown to yield the jz-conserving coupled states equations of McGuire and Kouri but slightly different approximations are required in the two cases. The implication of these results as to the accuracy of the jzCCS method are discussed.