Multilinear interactions in high-resolution spectra
The most general interaction of a collection of nuclear magnetic moments, invariant under the operations of the pure rotation group in three dimensions, is shown to be a linear combination of basic invariants that are multilinear in the components of the nuclear spin vectors. For an even number of spins each basic invariant is proportional to a product of scalar products, whereas for an odd number of spins each basic invariant is proportional to a scalar triple product multiplied by a product of scalar products. Representation theory for the group of proper rotations is used to determine the exact number of independent basic invariants for a given number of spins. The implications of time-reversal invariance and the consequences of including multilinear interactions in the Hamiltonian are investigated. In particular, the high-resolution spectrum of the AA'XX' system when quadrilinear interactions are included is examined. Copyright 1998 Academic Press.