Kubo-Tomita theory

A similar approach, also based on the Kubo-Tomita theory (103), has been proposed in a series of papers by Sharp and co-workers (109-114), summarized nicely in a recent review (14). Briefly, Sharp also expressed the PRE in terms of a power density function (or spectral density) of the dipolar interaction taken at the nuclear Larmor frequency. The power density was related to the Fourier-Laplace transform of the time correlation functions (14) ... 

Kubo R and Tomita K 1954 A generai theory of magnetio resonanoe absorption J. Phys. Soc. Japan 9 888-919... 

The stochastic theory of lineshape has been developed by Anderson and Weiss [157], by Kubo [158], and by Kubo and Tomita [159] in order to treat the narrowing of spectral lines by exchange or motion, a generalized formulation having been subsequently presented by Blume [31]. We consider below an application of the theory of Blume to the specific problem of relaxation between LS and HS states in Mossbauer spectra of powder materials which is based on the formulation by Blume and Tjon [32, 33], Accordingly, the probability of emission of a photon of wave vector Ik and frequency m is given as [160] ... 

Caspers has developed a theory of spin-spin relaxation starting from the general expressions established by Kubo and Tomita.23 His results however differ from those of Hartmann and Anderson and have been criticized recently by Tjon.11 We shall first outline the main points of Caspers method and then examine the basis on which it may be criticized. 

Lindner presented an important paper on this type of systems already in mid-1960s (102). She considered the whole system as an ensemble of microcrystallites with different orientations of the principal axis of the ZFS tensor with respect to the magnetic field and applied the linear response theory of Kubo and Tomita (103). The expression for the nuclear Ti for the case of S = 1 could be written as ... 

The measurement of relaxation times 7j and T2 and the subsequent application of the theory formulated by Bloembergen et al. (236), and extended by Kubo and Tomita (272) and Torrey (288), leads to the determination of motional and thermodynamic parameters such as mean times between molecular jumps, diffusion coefficients, and activation enthalpies for translation. For example, Resing and Thompson (289, 290) used this... 

Such behavior of the spectrum fully corresponds to the predictions of the theories of motional narrowing of Anderson, Kubo and Tomita and others [10,11]. With temperature increase the transition rate between different JT conformations... 

Actually the measurements of the temperature dependence of spin-lattice and spin-spin relaxation times is preferred since it allows the exploitation of a wider range of frequencies for the reorientational motions occurring in the solid state. The quantitative comprehension of the effect of molecular motion on relaxation times Tx and T2 is described by the Bloenbergen, Purcell and Pound (BPP) theory [15]. For example if one considers a specific motion that contributes to proton relaxation, the Kubo and Tomita equation [16]... 

Fig. 34. Comparison of the measured c-values for Gd,Y,, P, Gd,, Se,, P and Gd,Y, jAs (0.2

ESR linewidth is expected to show a significant frequency dependence when the external field Hz and the exchange field Hgx are of comparable size. In the framework of a linear response theory Kubo and Tomita (1954) calculated this factor c. The result is shown in fig. 34 and compared to experimental results of the Gd-resonance experiments in YP, ScP and YAs. Figure (34) clearly demonstrates that almost all data fall onto an universal curve which is discussed in detail by Sperlieh and Jansen (1974). For Hg -C Hz the value of c approaches 1 and for Hg Hz, c amounts to 10/3. The numerical calculations yield He = 36.0 and 40.3 kG for the Gd-Gd exchange in GaP and GdAs, respectively. 

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