Stationary-state scattering theory for electrons by molecules

2 Stationary-state scattering theory for electrons by molecules 

The fixed nuclear approximation is extremely useful, not only for the bound states, but also for the treatment of electronic scattering by molecules. For instance, stationary-state scattering theories within the fixed nuclear approximation have been extensively developed for molecular photoionization [18, 250, 336, 516] and electron scattering from polyatomic molecules [210, 418, 419]. These scattering phenomena are quite important in that they are widely foimd in nature as elementary processes and even in industrial applications using plasma processes. These scatterings may be referred to as stationary-state electron dynamics in fixed nuclei approximation. 

As usual, the total electronic Hamiltonian H we consider can be written as 

16) the first and second terms are the electron repulsion and electron-nuclei attraction, respectively. We would like to solve the stationary state Schrodinger equation 

The major differences of this equation from Eq. (2.11) is that (1) E of Eq. (2.17) is not an eigenvalue but a parameter that specifies the experimental collision energy, and (2) has a nonzero component in the asymptotic 

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