Rate constants in scattering theory

To connect the scattering properties discussed above to rate constants, the asymtotic form of the (energy normalized) outgoing wave is analyzed  

Here E,nr scattering wavefunction corresponding to an incoming reactant state rir at energy the wavefunction for the internal degrees of 

This flux can be expressed as the expectation value of a flux operator F defined by  

The rate constant for reacting from an initial quantum state at an energy E can be calculated from the flux of the corresponding scattering wavefunction  

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