Theory of molecular photofragmentation

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Abstract
In this paper we advance a unified theoretical scheme for the description of direct photodissociation and predissociation of polyatomic molecules. In the case of direct photodissociation we consider energy‐resolved variables. i.e., the cross sections for photon absorption, for elastic and inelastic photon scattering, and for the populations of different dissociative channels. For predissociation we consider both time‐resolved and energy‐resolved experimental observables. The various cross sections relevant for the description of a direct photodissociation process were formally expressed by introducing a distorted wave basis to specify the eigenvalues of the nuclear states on the dissociative potential and advancing a general wave operator which is completely defined within the dissociative potential surface. Explicit expressions for the cross sections were derived with a proper account for radiative coupling effects. Utilizing projection operator techniques we have demonstrated that to a low (second) order in radiative interactions, which costitute an excellent$approximation to the problem at hand, the photodissociation process is isomorphous with a coherent superposition of full collision processes on the electronically excited nuclear potential surface. Similar theoretical techniques are utilized for the study of energy‐resolved and time‐resolved observables in predissociation. Subsequently, we have invoked a set of systematic approximations to reduce the formal expression to a tractable form. The Heitler K matrix formalism is utilized, and the introduction of the first‐order approximation for the K matrix results in explicit expressionss for the time‐ and energy‐resolved observables in photofragmentation, where the cross sections are expressed in terms of products of an initial coupling matrix, the wave operator matrix, and a radiative interference matrix. This formalism is then adopted for the special case of linear photofragmentation of triatomics. Analytical, quantum mechanical expressions for the experimental observables and, in particular, for the vibrational energy distribution of the photofragments were derived for a linear triatomic, where the interfragment replusion is exponential and the diatomic fragment is characterized by a harmonic potential. The effects of intercontinuum coupling on the vibrational energy distribution in the predissociation of XCN (X=H, Cl, Br, and I) molecules in the energy range ∼6.5–10.5 eV were investigated.

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