On the theory of spin-spin relaxation I

Abstract

A method is developed that enables us to determine the asymptotic form for large times of the so-called relaxation function of spin systems, in the case of a large external magnetic field H . The spin-spin relaxation phenomena are described within the framework of the spin hamiltonian; we restrict ourselves to those systems for which all g-tensors appearing in the spin hamiltonian are isotropic. Most attention will be paid to those systems in which all ions are identical and occupy aequivalent lattice sites. For these systems the asymptotic form of the relaxation function is given by a function of the type: A exp ( − t τ ) + B , in which expression τ is the spin-spin relaxation time. For the quantity 1/τ we find a series expansion: 1 τ = Σ ∞ n=1 1 τn , in which the different terms 1 τ n correspond to different relaxation processes. For more complicated systems the ions are divided into groups, according to the kind of ion and the occupied lattice site. When all ions have the same g-value and the interaction between the different groups is strong enough, the asymptotic form of the relaxation function will be, in a good approximation, of the type indicated above, that means that there is only one relaxation time. If this coupling is small there will be in general a number of different relaxation times, this number being equal to the number of groups. The same will be true for systems, containing different groups, corresponding with different g-values.