The Relationship between Rate Constants and Cross Sections

The Relationship between Rate Constants and Cross Sections 

A most useful general review of this topic by Light et has 

Consider an excitation function a v) of an ion-molecule reaction for which, in order to simplify the discussion, any consideration of internal energy may be ignored. This can be included (and must be for any real system). It complicates the situation and some indication of this is given in the footnotes accompanying the following discussion. The excitation function, which summarizes the energy dependence of the integral reactive cross section for the particular reactive channel under consideration, is the fundamental measure of the total reaction efficiency for that 

When the relative velocity distribution remains constant throughout the reaction period, the rate constant k is related to the microscopic cross section (t(v) by the familiar expression 

For a slow reaction occurring in a system maintained at constant temperature T or for a slow or fast reaction between dilute solutions of reactants in an inert buffer gas held at constant temperature,/(t ) is of course given by the Maxwell distribution at this temperature T. Under the conditions specified above, this distribution will not be disturbed by the reaction and it is appropriate to write Eq. (2) as 

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