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Instantaneous Intervalley Transition just at the Franck-Condon State in the Conduction Band of GaAs

We propose two possible quantum microscopic mechanisms for intervalley transitions just at the Franck-Condon state in GaAs. The first is the simultaneously combined coulombic elastic transitions of two electrons,from the originally photo-excited $Γ$ valley to the mutually opposite L and -L valleys in the Brillouin zone. The second is the "elastic" scattering of an electron from the $Γ$ valley to the L one by the frozen phonon, which is not newly created in the excited state, but already exists, being inherited from the starting ground state, according to the Franck-Condon principle of the photo-excitation. Surprisingly, we can theoretically show that such the elastic electron-phonon scattering gives extremely fast time constant of the order of a few tens femtoseconds, as well as the above elastic electron-electron scattering does.