Statistical theory of electronic Raman resonance scattering by oriented atoms

A statistical scattering theory approach to the angular distribution and polarisation of inelastically scattered electromagnetic radiation is presented. The authors' theory, which is also applicable to fluorescence, accounts for the influence of the orientation of the target atoms on the radiation pattern of the scattered photons. Their analysis is based on a relativistic generalisation of Placzek's scattering tensor formalism (1934) and on the multipole expansion of the photon-electron interaction. The state of the incoming photons is described by a density matrix and the orientation by statistical tensors. As a result the differential cross section is expressed as a weighted sum of geometrical scattering factors which describe the directions and polarisations of the incoming and scattered radiation. The weight factors are statistical expectation values of dynamical scattering tensors with respect to the oriented initial atomic states. The non-relativistic dipole approximation is considered in detail for weak and strong orientating fields. Illustrative examples of the radiation pattern of K X-ray Raman resonance scattering from oriented systems are given and possible implications of the authors' work with regard to future experiments are pointed out.