I know it involves an integration of the impact parameter with respect to energy. I also know how to calculate the lower limit of integration using the effective intermolecular potential with centrifugal term. But I can't find details of the calculations.
To my mind, the simplest temperature-independednt esimate is Pi*((d1+d2)/2)^2
cross section, where d1 and d2 are WDW dimeters of colliding particles.
The WDW diameters of small particles can be determined by the Cambi equation (http://dx.doi.org/10.1063/1.461035)
For large species simple correaltion formula can be recommended (DOI:10.1080/13647830.2012.663102).
Furthermore, the expression for the thermally average capture constant for binary collision using the effective intermolecular potential with centrifugal term is given in (DOI:10.1080/13647830.2012.663102) (~T^(1/6)).
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