Multipole operators for an arbitrary number of spins

Basis states and operators composed of n, in general, different nuclear spins of integer or half-integer values are explicitly constructed. Various coupling schemes are discussed, and transformations between them derived. Following this, a complete set of irreducible tensor operators T(k){V} is constructed which can be used as a basis for expanding operators which depend on n nuclear spins. It is further shown that decomposition of the tensor’s components T(k)q{V} into a sum of products of two irreducible tensor components involves transformation matrices between different coupling schemes. Various properties and commutation relations of the T(k)q{V}’s are given along with a discussion of their reduced matrix elements.