Theory of Dissociative Attachment

Abstract

A fairly comprehensive theoretical treatment of the dissociative attachment (DA) of electrons to diatomic molecules ($AB+e\to A^{-}+B$) is given, going from general formalism to explicit cross-section formulas and comparison with experimental results. Using the Born-Oppenheimer separation, the process is understood as an electronic transition from a continuum to a discrete electronic state, which then dissociates. The final discrete state, being degenerate with a continuum, is necessarily a resonance. Accordingly, the theory is derived from a general rearrangement formalism which is based on projection operators onto this resonance state (defined along the lines of Feshbach) and uses the Born-Oppenheimer separation. This formalism, which is applicable to a fairly wide class of collision processes, is characterized by its extreme simplicity and practical usefulness. Exact transition matrix elements are derived for DA, together with its inverse and competing processes, in terms of the resonance and "potential scattering" wave functions. Finally, a certain adiabatic approximation is considered for the potential scattering function, which neglects the indirect influence of other inelastic processes on the resonance transition, treating them as higher order effects. After this approximation, the classical nature of the nuclear motion makes it possible to eliminate the nuclear wave functions in a fairly trivial way and to derive a simple explicit formula for the DA cross section from an arbitrary initial vibration-rotational state of the molecule. For the most interesting case, the ground vibrational and rotational state, this formula is in complete agreement with the previous result of Bardsley, Herzenberg, and Mandl. Later this adiabatic approximation is partly relaxed and more general formulas derived. Various implications of the results are also considered, such as the relation to experimentally observed isotope effects and temperature effects. The "vertical onset" threshold phenomenon which occurs when the resonance potential curve is attractive is also discussed.