On possibility of using the reduced description of the anisotropic Heisenberg paramagnet spin dynamics, and the NMR line-shape in solids

The problem of free induction decay calculations in solids is solved in quadratures. Existence of this solution is the consequence of the similarity relations between time correlation functions appearing in the infinite chain of the gearing differential equations. Thus, the reduced description of spin dynamics for the most spreading kinds of crystals becomes appropriate. General characteristics of the system are investigated and some theorems are proved. Theoretical results obtained for the present theory are in good agreement with experimental data.