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The final stage is to express (Q) as the left side of (5.5) and to reverse the procedure which led from (El) to (E2), obtaining an equation of the form d r (6) x-, - = y expi(X*i+X6*+Efe^)where [see also (6.1) J we have used the notationIn (E4), the operator 5^ comes out to be the complete curly bracketed Fokker-Planck operator on the righthand side of (5.7) after all derivatives higher than the second have been discarded. Extraction of the integrand of (E4) by Fourier transform yields (5.7). Carrying out the above procedure, we find that passage from 5i to 9^ entails the following set of sub-stitutions :along with the conjugates of the first four. These replacements are made without disturbing the order of factors. In 3i, products of field quantities times atomic quantities such as /3*9TC and £9li occur, but these give no ordering problems since their replacements commute.After the replacements, all derivatives higher than the second are discarded.Lattice relaxation measurements have been made for Ce 3+ , Nd 3+ , and Yb 3+ at axial sites in CaWCU by a novel spin-echo method. In this method the spin system is inverted by adiabatic rapid passage, and the magnetization is later sampled by a two-pulse echo sequence. Temperatures were in the range from 1.4 to 9°K, the transfer of cold helium gas being used to maintain temperatures of 4.7°K and above. The relaxation behavior of all the ions appeared to be best described by a direct process (w oc T) going over into a Raman process (w oc T n ) in the vicinity of 4°K. The results could not, however, be fitted to the T 9 law, which arises in simple theoretical treatments of the Raman process, but yielded powers of the absolute temperature between 10 and 11. Orbach processes did not seem to be relevant. Two causes for this behavior are considered: dispersion in the phonon spectrum, and the inadequacy of an approximation which is commonly made in treating the denominator of the Raman integral. The Yb relaxation rate showed a marked angular variation in the Raman region. This is discussed in terms of a possible admixture of the two processes which, in the simple theory, lead to T 7 and T 9 laws.

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