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assuming I have the potential for a diatomic molecule in the groundstate i=o and excited state i=1

[itex]V_i( r ) = D( 1 − exp[ −β ( r − r_i)] )^2+ C_i[/itex]

Using collisional excitation with fast electrons.

What is the vibrational quantum number of the state the molecule will most likely be excited to?

All under low pressure gas discharge.

I first assumed I could use Franck Condon principle, but this is not the case as I am not radiating on the molecules and thus dipole approximation is not allowed.

I cant use Lippmann–Schwinger equation either because I have no futher information on the interaction.

Can anyone help me?

Thank you,

kuecken