On the coupled states and infinite order sudden approximations to the body frame wavefunction

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Abstract
New CS and IOS approximations to the total angular momentum body frame radial wavefunction ψJ(jλ‖j0m0‖R) are derived. The new expressions for ψCSJ(jλ‖j0m0‖ R) and ψIOSJ(jλ‖j0m0‖R) are not diagonal in λ, m0 and they lead to the proper exact solution when the potential is set equal to zero. In addition, since ψJCS and ψJIOS are linear combinations of ψlm0(j‖j0‖R) and ψIOSlm0(j‖j0‖R) for all l satisfying ‖J−j‖⩽l⩽J+j, one expects improved behavior for larger J (especially for elastic elements where j=j0). It is explicitly shown that the present nondiagonal expressions for ψJCS(jλ‖j0m0‖R) are consistent with the Shimoni–Kouri expressions for the bodyframe T matrix TJCS(jλ‖j0m0), which is also not diagonal in λ, m0. The present results are expected to provide the basis of an improved CS and IOS theory of reactive scattering.