Approximations for the rotational excitation of molecules by atoms

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Abstract
The applicability of the effective close‐coupling approximation of Rabitz and the centrifugal decoupling approximation of McGuire and Kouri is examined for a system which models the rotational excitation of molecular nitrogen in collisions with helium atoms. For small values of the rotational quantum number both methods are more accurate for total elastic scattering cross sections than for inelastic and neither is capable of providing reliable inelastic cross sections close to the rotational threshold. Agreement with the close‐coupling cross sections improves with increasing impact energy. The accuracy of the centrifugal decoupling approximation appears to be stable with respect to the magnitude of the repulsive anisotropy whereas the effective close‐coupling method is sensitive to it and the approximation becomes inaccurate when the anisotropy is large. The detailed‐balancing relationship is not satisfied by the effective close‐coupling method and modifications that depend upon energy and upon the magnitude of the anisotropy are needed.