Reduced matrix elements collision potentials

The Q-projected Green s function (7.111) in the polarisation potential (7.115) contains the collision Hamiltonian H, but practical implementation of it involves the weak-coupling approximation (7.132). A second-Born calculation is equivalent to a calculation of the polarisation potential with Q=1 and Vopul being the reduced matrix element of U. This has... 

Effective collision cross sections are related to the reduced matrix elements of the linearized collision operator It and incorporate all of the information about the binary molecular interactions, and therefore, about the intermolecular potential. Effective collision cross sections represent the collisional coupling between microscopic tensor polarizations which depend in general upon the reduced peculiar velocity C and the rotational angular momentum j. The meaning of the indices p, p q, q s, s and t, t is the same as already introduced for the basis tensors In the two-flux approach only cross sections of equal rank in velocity (p = p ) and zero rank in angular momentum (q = q = 0) enter die description of the traditional transport properties. Such cross sections are defined by... 

The first matrix element in this product is calculated on the energy shell. It could be directly obtained from a study of scattering by the potential (6.3.1). It will be admitted, in the static approximation, that the nucleus is at the origin of coordinates (rA = 0). Then the second matrix element in the product reduces to the quantity (y a) = dy[l. The collision amplitude which appears in (6.3.8) can be written... 

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