Tensor space reduction

This is not consistent with the relative diffusion coefficient of noninteracting particles Dab = >a + because the tensor relationship between and D is broken upon reduction of the FPE to one dimension, that is, Dj Dab except for particles with /ka = Wb a = b- Nevertheless, (Jab from Eq. (2.34) is appropriate for relative momentum relaxation, whereas Dab appropriate for configurational relaxation at large separations. The problem is resolved by splitting configuration space into two regions at a separation R such that for I > / the diffusion coefficient is given by Dab- For R < R, the friction can... 

The effective operators defined in (10.35) extend the standard Judd-Ofelt effective operators by the interactions via the crystal field potential within the spin part of the space. The reduction to the non-relativistic case is easily seen when all of the ranks of operators acting within the spin space are equal to zero. Indeed, setting ki = k2 = 3 = 0 results in = 1 k2 = t and k = k. In such a situation, the rank of effective unit tensor operator is even, the... 

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