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Multilinear Interactions in High-Resolution Spectra

✍ Scribed by P.L. Corio

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
169 KB
Volume
134
Category
Article
ISSN
1090-7807

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✦ Synopsis

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 AAXX system when quadrilinear interactions are included is examined.

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