Energy Transfer by Non-Resonant Processes

In order to be complete, we shall now describe non-resonant processes where there is a large mismatch in energy of the oscillators. The first analogue for energy transfer was formulated by Orbach (1967). This corresponds to the situation shown as follows  

Even though there is no overlap of vibronically-coupled energies, energy transfer can occur as (dd), (dq) or Hexchange. through coupling of each 

In other words, two mismatched multipoles can readjust their ener states (within certain limits as determined by li 2 n ooi, the energy of the 

In addition, n (which is a function of allowed directions in the lattice), and k and 3 (which are the phonon coupling vectors) describe the number of phonons involved in the process. Note that what we have done is to include phonon processes as part of the energy transfer process integral. The actual evaluation of Heff. is very complicated and will not be 

Suffice it to say that both Heff. (actually Hdd, Hdq as the case may be) and Heiec.- vibr. (a Hamiltonian describing vibronic coupling) must be included. Nevertheless, this type of energy transfer involving phonon creation and destruction at two sites where the oscillators are not originally coupled has been observed experimentally and occurs in many cases where energy transfer between excited and unexcited centers occurs. 

---