Deformation potential approximation

Note in passing that the common model in the theory of diffusion of impurities in 3D Debye crystals is the so-called deformational potential approximation with C a>)ccco,p co)ccco and J o ) oc co, which, for a strictly symmetric potential, displays weakly damped oscillations and does not have a well defined rate constant. If the system permits definition of the rate constant at T = 0, the latter is proportional to the square of the tunneling matrix element times the Franck-Condon factor, whereas accurate determination of the prefactor requires specifying the particular spectrum of the bath. 

The role of two-phonon processes in the relaxation of tunneling systems has been analyzed by Silbey and Trommsdorf [1990]. Unlike the model of TLS coupled linearly to a harmonic bath (2.39), bilinear coupling to phonons of the form Cijqiqja was considered. In the deformation potential approximation the coupling constant Cij is proportional to (y.cUj. There are two leading two-phonon processes with different dependence of the relaxation rate on temperature and energy gap, A = (A Two-phonon emission prevails at low temperatures, and it is... 

Acoustic Phonons. We assume that acoustic phonons can be adequately described by a Debye spectrum cut-off frequency ojpj and the electron-phonon coupling is given by the deformation potential approximation... 

In the framework of the model, the difference Ei — E is within the acoustic phonon bandwidth, and that is why Skinner and Trommsdorff [21] reasonably assumed that the longitudinal acoustic modes could influence the tunneling proton transfer. The interaction potential (22) was chosen in the form of the deformation potential approximation (see Ref. 74)... 

A stress applied to a crystal results in a strain. A phenomenological description of the electron energy levels under elastic strain was developed by Bardeen and Shockley [12]. It is referred to as the deformation potential approximation (DPA), in which the one-electron Hamiltonian is developed in a Taylor s series of the strain components The perturbation is written in cartesian coordinates, for a linear order in strain, as ... 

The interaction between a free electron in a metal and the ionic displacements u is frequently given by the deformable potential approximation (E.g.92), p. 128). If the potential felt by the electron in position r is V 0) without the lattice being distorted, then upon distortion of the lattice to an extent of u(r), the potential experienced by the electron is y(r-u). Another approximation views the potential as the sum of separate ionic potentials based on the instantaneous positions X(k) + u(k) of each ion... 

For interaction with long wavelength, low-energy phonons the deformation potential approximation, frequently in use for covalent compounds with spherical energy surfaces E = E(k), leads to the form45 88)... 

The Deformation Potential Approximation and Its Applications to Different Poiymers... 

If one substitutes equation (9.24) obtained in the deformation potential approximation into expression (9.47) for relaxation time, one obtains the latter quantity in the form... 

The relaxation time rph for positron scattering off phonons can be calculated using the deformation potential approximation [126]... 

---