Kramers approximation relaxation

The problem of the electron spin relaxation in the early work from Sharp and co-workers (109 114) (and in some of its more recent continuation (115,116)) was treated only approximately. They basically assume that, for integer spin systems, there is a single decay time constant for the electron spin components, while two such time constants are required for the S = 3/2 with two Kramers doublets (116). We shall return to some new ideas presented in the more recent work from Sharp s group below. 

It has been claimed that reactions in proteins can, as an approximation, be formulated within the Kramers reaction theory of barrier crossing [106]. The highly nonexponential relaxation pattern can now be explained by our model,... 

For M = 1 this yields t = (/c R ie ) S which is exactly the low-friction generalized Kramers result. (The friction y is replaced here by the more general fcvR. which incorporates non-Markovian effects if present. In this low-friction limit i = Eg.) For intermediate large values of n Eq. (6.72) may be approximated by vibrational relaxation rate kyg(E) = dE/dt,... 

III.G., the WKBJ approximation is applied to retrieve the analytic expression derived by Brown using the Kramers transition state theory for the longest relaxation time for uniaxial anisotropy in the limit of high potential barriers. This is also extended to yield the formula for the relaxation time for high uniaxial anisotropy in the presence of a longitudinal field. 

Velocity relaxation effects can be accounted for in an approximate fashion by going to a phase-space description in terms of Fokker-Planck or Langevin equations. Perhaps the best known study of this type is due to Kramers, who studied the escape of particles over potential barriers as a model for certain types of isomerization or dissociation reaction. 

Raman Process of Spin-Lattice Relaxation. In addition to the one-phonon process described above, a two-phonon scattering process according to Fig. 14 b can also occur. The temperature dependence of this Raman process of sir can be approximated (for the non-Kramers situation) at low temperature and for AE phonon energies to A(Raman) - T [97,224,227]. Also, this process has been observed experimentally [224, 227, 230, 231]. At very low temperature and in the presence of a fast direct process, Raman scattering can usually be neglected. 

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