Resonant energy transfer cross sections formulated in terms of form factors: An appraisal of the first Born approximation

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Abstract
In the Born approximation without exchange the differential cross section of energy transfer between two molecules is expressible in terms of the generalized oscillator strengths (f) for the excitation of individual molecules by electron impact. Thus, the Born cross section can be unambiguously calculated using electron impact data. In the absence of such data, an approximate expression of f can still be obtained from experimental values of transition moments, ionization potentials, and excitation energies based on the first term of Lassettre’s series representation of f. It is shown, in the case of dipole–dipole energy transfer, that the cross section calculated with the approximate f corresponds to scattering from a shielded dipole–dipole intermolecular potential, with the correct asymptotic behavior at both large and small r. Hence, it appears that even when approximate f’s are used, the present method is superior to the dipole–dipole theory of Cross and Gordon. The validity of the Born approximation at thermal energies is discussed. It is argued that the Born approximation should work best in the calculation of near resonant dipole–dipole energy transfer. Two numerical examples are given to test the above argument. In the case of energy transfer between Ar 3,1P1 and H2, HD, or D2, the Born results are in reasonable agreement with the data of Fink, Wallach, and Moore when the energy gap is ≲30 cm−1. In the second example, energy transfer between p‐difluorobenzene and ketones, due to the absence of electron impact data, approximate f’s are used and the calculated cross section is a lower bound of the Born value. Exchange effects on the Born approximation is studied. It is concluded that the exchange amplitude has the same symmetry property as the direct term. Thus, contrary to the Dexter approximation, the cross term between direct and exchange contributions do not vanish in the expression of the energy transfer cross section.

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