Abstract
The coupled states or centrifugal sudden (CS) approximation1-3 is widely recognized as the most accurate of a general class of angular momentum decoupling approximations developed over the past decade for the purpose of treating molecular collisions. Considerable effort has been expended in clarifying the approximation and determining its optimum form.3-8 It has been established that the CS parameter \( \overline \ell \), which enters when the centrifugal potential operator L2/2MR2 is approximated by the form1 \( \overline \ell \left( {\overline \ell + 1} \right)^2 /2MR^2 \), must retain the character of an orbital angular momentum quantum number.3-8 Furthermore, it has been shown that the technique of l-labelling [i.e., choosing the CS \( \overline \ell \) parameter as a function of the initial (l) and final (l′) values of the orbital angular momenta when calculating a particular Arthurs-Dalgarno9 T matrix element TJ(j′l′|jl)] and the proper choice of phase enables one to (a) satisfy exactly the proper asymptotic boundary conditions,3-8,10-12 (b) ensure time reversal symmetry,13,14 (c) obtain exact results in the limit of zero potential anisotropy (thereby ensuring that the helicity transitions induced by tumbling of the atom-diatom system in space are exactly described15) and (d) build back in effects of the rotation of the scattering vector (in an approximate fashion) so that the resulting CS approximation to the T matrix in the coordinate representation is no longer local (diagonal) in the angles.16
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References
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Khare, V., Fitz, D.E., Kouri, D.J., Evans, D., Hoffman, D.K. (1981). On CC and CS Descriptions of Phase-Sensitive Cross Sections: Computations for He + HCl. In: Truhlar, D.G. (eds) Potential Energy Surfaces and Dynamics Calculations. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-1735-8_30
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DOI: https://doi.org/10.1007/978-1-4757-1735-8_30
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