On representative orbital angular momentun quantum numbers in the definite parity j z CCS approximation

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Abstract
A detailed study of the role of representative orbital angular momentum quantum numbers ? (J,j) in a definite parity jz CCS approximation (DPjz) is presented. First the DPjz equations are derived by a procedure which establishes the validity for kjR≫Jj in place of kjR≫[(J+j)/2]2 in the original derivation of Kouri, Heil, and Shimoni. Then expressions for integral and differential cross sections within the DPjz approximation are derived. This analysis points up the importance of choice functions ? (J,j), which determine the representative orbital angular momentum quantum numbers associated with given values J,j. Computations for the He+H2 system are carried out for various choices of ? (J,j) and results are compared with exact close coupling (CC). Analyses of trends in the results suggest (a) the median choice ?=max(J,j) gives best results at the integral cross section level (if one disregards parity), (b) elastic cross sections for given j depend on the numerical value of ? and not on the l̄′ values occurring for other rotor states j′, (c) averages of both partial and integral cross section results with respect to choice function ? (j,J) lead to excellent agreement with CC results, (d) by noting (b) above, an alternative average over ? values can be achieved by relabeling amplitudes by ?,j rather than J,j, (e) this last average can be made using the results obtained with a single choice function.