Many-Body Aspects of Dipolar Interaction in Crystal Lattices

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Abstract
The moment expansion of the magnetic resonance line and the semi-invariant expansion of the free energy of a dipolar lattice are expressed in powers of the Hamiltonian. The expansions are looked at from the point of view of the number of particles in each term. Intercomparison is made of the terms in a density expansion and the moment expansions. The third and fourth semi-invariants of the simple cubic dipolar lattice are evaluated by a computing machine. The results suggest the general conclusion that the cycle diagrams predominate for dipolar interaction and a general formal expression for the contribution of the nth order diagram is derived. The calculation of the higher order moments and semi-invariants is, thus, simplified but still remains formidable. For the short-range exchange potential, on the other hand, the cycle diagrams do not predominate.