Dipole irreducible three-body component

Theoretical estimates of the three-body moments may be obtained from the well-known pair dipole moments. These do not include the irreducible three-body components which are poorly known. Interestingly, in every case considered to date, the computations of the three-body spectral moments y[3 are always smaller than the measurements, a fact that suggests significant positive irreducible three-body dipole components for all systems hitherto considered [296, 299] further details may be found in Chapter 5. 

Binary and ternary spectra. We will be concerned mainly with absorption of electromagnetic radiation by binary complexes of inert atoms and/or simple molecules. For such systems, high-quality measurements of collision-induced spectra exist, which will be reviewed in Chapter 3. Furthermore, a rigorous, theoretical description of binary systems and spectra is possible which lends itself readily to numerical calculations, Chapters 5 and 6. Measurements of binary spectra may be directly compared with the fundamental theory. Interesting experimental and theoretical studies of various aspects of ternary spectra are also possible. These are aimed, for example, at a distinction of the fairly well understood pairwise-additive dipole components and the less well understood irreducible three-body induced components. Induced spectra of bigger complexes, and of reactive systems, are also of interest and will be considered to some limited extent below. 

For easy reference we also plot theoretical three-body moments of H2-H2-H2 which are computed from first principles based on the assumption of a pairwise-additivity, Figs. 3.46 and 6.2 (heavy curves). The pair dipole moments have been shown to allow a close reproduction of measured binary spectra from first principles in the hydrogen fundamental band, for temperatures from 20 to 300 K these are believed to be reliable. Interestingly, the pairwise-additive assumption is not sufficient to reproduce the experimental three-body moments from theory, except perhaps at the lowest temperatures. With increasing temperature, rapidly increasing differences between measured and computed moments are observed, a fact which suggests the presence of an irreducible three-body dipole component of the overlap-induced type [296]. 

The three-body spectra and their associated correlation functions may be considered to be a superposition of three components of different nature. One part arises from two-body dynamics where the third atom acts strictly as a perturbing field. The second part represents the contributions of the irreducible three-body dynamics to the pairwise-additive induction. The third part is due to the three-body induction mechanism and contains the irreducible dipole. These agents vary differently with temperature and could in principle be separated on that basis. 

Ternary moments have been computed for several systems of practical interest [314, 422]. Recent studies are based on accurate ab initio pair dipole surfaces obtained with highly correlated wavefunctions. Because not much is presently known about the irreducible ternary components, it is important to determine to what extent the measured three-body spectral components arise from pairwise-additive contributions [296, 299]. 

We have seen above that the pairwise-additive parts of the ternary induced dipole component are well known for a number of systems. The irreducible, ternary components, on the other hand, are poorly known, for any system. Even less is known about the N-body irreducible components of the induced dipole for N > 3. Attempts exist to model three- and four-body dipole components on the basis of classical relationships, but the evidence indicates that overlap effects are important the known many-body dipole models do in general not account for quantum effects. 

---