On the separation of resonance Raman scattering into orders in the time correlator theory

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Abstract
A detailed study is carried out of the separation of resonance Raman scattering into orders within the time‐correlator formulation of Hizhnyakov and Tehver (HT). This formulation is exact for a multimode system at all temperatures and for all electron–phonon coupling strengths within well‐defined ’’standard assumptions.’’ As in any Raman theory, the full m‐phonon Raman scattering involves the electron–phonon coupling to infinite order, owing to virtual phonon transitions accompanying the m real final state phonon transitions. The HT separation into orders is seen to correspond to a particularly convenient grouping of the contributions, such that the full m‐phonon scattering is expressed as a power series in explicit orders of the electron–phonon coupling, but with each term of the series also containing factors involving the electron–phonon coupling implicitly to infinite order. Each term of this series except the first vanishes for T→ 0, with the result that the (explicitly) mth order scattering and the full m‐phonon scattering are identical at T = 0. Most importantly, at any temperature the contributions from each order to the resonance Raman excitation profile line shapes are obtainable from the optical absorption in a direct and simple way. We have previously stressed the usefulness of the first‐order version of this feature for the analysis of experimental data, and here that work is contrasted with recent work of Hassing and Mortensen, who expressed the full one‐phonon series for a single‐mode system in a different form. For completeness, a detailed derivation of the entire theory is given, including proofs via phonon many‐body techniques of the two fundamental identities upon which the HT approach rests and which were not proven in HT’s rather condensed presentation of their time‐correlator formulation.