The results of work in two different aspects of Raman spectroscopy are presented.

Part I describes a systematic and comprehensive calculation of selection rule tables for three- and four-photon Raman interactions. As a preliminary step, explicit quantum-mechanical expressions for the scattering tensors are obtained, enabling- the symmetry of the tensors to be analysed. It is found that these tensors do not possess the symmetry previously ascribed to them in the literature. Selection rule tables are calculated using standard group theoretical techniques. The results show that it may be possible to measure, by means of high-order Raman spectroscopy, energy levels which cannot be measured directly by conventional spectroscopic techniques.

In Part II, an experimental investigation of the Co²+ ion in CdCl₂, MnCl₂, CoCL₂ and CdBr₂ using conventional Raman spectroscopy is described. In these crystals, the Co²+ ion experiences a trigonal crystal field which gives rise to a low-lying manifold of six doubly-degenerate energy levels with a total splitting of about 1000 cm⁻¹. Spectra have been recorded at room, liquid air and liquid helium temperatures for varying concentrations of Co²+ ions in the host crystals, enabling all energy levels to be measured in each of the four cases. Close fits with crystal field theoretical calculations are achieved. The results are compared with those previously obtained by infrared absorption experiments, and the superiority of Raman spectroscopy as a technique for measuring low energy transitions is shown. A preliminary investigation of antiferromagnetic Cocl₂ is presented.