Note on the Stochastic Theory of Resonance Absorption

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The stochastic theory of magnetic resonance absorption developed recently by P. W. Anderson is examined here further in some details. The fundamental idea of the theory is that the resonating units suffer transitions among their possible states each of which is characterized by a proper frequency of the magnetic moment. The transition is assumed to be described by a Markoffian process. The fundamental equation for the auto-moment or the auto-correlation of the magnetic moment is rederived and transformed. Some general properties of the absorption spectrum are discussed on the basis of this equation. In particular, the narrowed spectrum for the case of rapid transition is proved to be Lorentzian with a half width determined by the equilibrium distribution of the units and the transition matrix of the Markoffian jumps. If the relaxation time of the transition is assumed to be completely degenerate, the resonance spectrum is given by<BR>I(ω)=\frac1π\ extRe∫\fracP(ω′)dω′ωe+i(ω−ω′)\bigg⁄\left{1−∫\fracωeP(ω′)dω′ωe+i(ω−ω′)\ ight}<BR>where P(ω) is the intensity distribution in the limit of slow relaxation, 1/ωe being the relaxation time. Although this idealization is not quite physical, the result is useful for qualitative understanding of the changes in line shapes due to the motional effect. The limit of Gaussian-Markoff case is also discussed.

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