Phonons atom-multiphonon scattering

The atom-multiphonon component of the inelastic scattering can be obtained from the theory of Manson [44] by subtracting off the zero- and first-order terms from the power series expansion of the exponential displacement correlation function. With the assumption that the major contribution to the multiphonon scattering is due to low-energy, long-wavelength phonons, he is able to arrive at an expression with a very simple form for the transition rate. 

---