For the conventional homogeneous target experiments, the resonant molecular
as a function of the target temperature,
is written as [147,4]:
The popular choice of the interaction operator has been:
The use of the dipole operator in H' was criticized by Petrov et al. [144,145,146] and by Scrinzi , who each proposed alternative forms of the operators, but the accuracies of simplifications adopted were in turn questioned by Faifman et al. [134,71]. Faifman and his colleagues recently included the quadrupole corrections in the interaction operator in Ref. , and those are what we used in our analysis of the experimental data. We note that the perturbative formulation used by Faifman as well as by Petrov and by Scrinzi were criticized by Lane  and Wallenius [45,46]. Lane  also criticized the formulation of earlier work by Cohen and Leon . In fact, Wallenius in his thesis goes as far as calling Menshikov and Faifman's justification for the Born approximation ``nonsense.'' Wallenius concludes, however, that different ``working formulae'' in the literature actually end up to be equivalent (presumably due to cancellation of what he calls mistakes), and would yield the same cross sections, if no further approximations were made .
Thus theorists seem to agree, though maybe for different reasons, at least on the form of the starting formula they use to calculate the matrix elements. For actual evaluations, however, further approximations are necessary in the interaction operators, such as the multipole expansion as mentioned above, or in the wave functions as discussed next.