Biphonons local

Let us assume that the anharmonicity constant A is large compared to the width T) = 2T (where T is the half-width) of the phonon band. In this case, as was shown in Subsection 6.2.2, the width of the biphonon band is of the order of T /A, i.e. small compared to the width T of the band of optical phonons. Important here is, however, the comparison of the width of the biexciton band with isotope shift. Indeed, in the limiting case of strong anharmonicity, the biphonon energy is E ss 2hui — 2A and the biphonon state 2) is just the coherent superposition of the states of two-fold excited molecules. It is clear then that an elementary generalization of an equation of the type (6.89) can be used to find biphonon local states. Specifically, the equation for the frequency of a local biphonon io, i.e. the localized state split off the biphonon zone, can be written as follows ... 

A generalization of biphonon theory beyond the Van Kranendonk model was made later (14)—(17). Subsequently, the effect of biphonons on polariton dispersion in the spectral region of two-particle states was investigated in a number of papers (18)—(22), and the contribution of biphonons to the nonlinear polarizability of a crystal was discussed in (23)-(25). Problems of the theory of local and quasilocal biphonons in disordered media were discussed in a number of papers (14), (26) -(28). The influence of anharmonicity in crystals on the spectra of inelastically scattered neutrons was considered by Krauzman et al. (29), Prevot et al. (30), and in Ref. (31). 

Local biphonons in crystals with isotopic substitution impurities... 

We begin, in this section, a discussion of features of the biphonon spectrum in imperfect crystals. For the sake of simplicity we shall assume that the crystal contains only the simplest point defects isotopic substitution impurities. Before going over to a theory of local biphonons, we shall make several qualitative remarks concerning the effect of anharmonicity on the spectrum of local vibrations... 

Since the states of the biphonon, like those of the phonon, are characterized by only a value of the wavevector, an analysis of eqn (6.90) is analogous to that of eqn (6.89). On the basis of the result of such an analysis, which we have already used for phonons, it can be contended that the level of a local biphonon is formed if... 

Local biphonon in an 1ANHiBr crystal containing the isotopic substitution impurity 15N... 

We already mentioned the experimental research conducted by Belousov et al. (77). In these investigations they studied the spectrum of local states in the frequency region w m 2800 cm-1 in a 14NH4Br crystal (a cubic crystal of group Tj) having as an impurity the isotope 15N. It was first shown experimentally in these investigations that, in accordance with predictions (14), anharmonicity actually can led to the formation of a local biphonon under conditions in which no local phonons exist. 

An additional line at lux = 2788 cm-1 was found even in a crystal with a natural content of the isotope 15N by Belousov cl, al. (77). When the concentration is increased to x = 0.05 and x, = 0.3, the integrated intensity of this line increases (see Fig. 6.16b). It is exactly this fact that enables us to regard this line as being correspondingly coupled to the impurity of the two-phonon state (local biphonon). 

---