Symmetry Properties of the Spin-Spin Contact Hamiltonian

The spin-spin contact Hamiltonian has been separated into operators having well-defined symmetry properties. Analysis of the form of the spin-spin contact Hamiltonian shows that fewer symmetry operators are actually required in this separation than would be indicated by simple group-theoretical arguments. Matrix elements of most of those operators are evaluated by considering the Casimir operator ${\mathrm{Sp}}_{4l+2}$; the remaining operators are evaluated by exploiting a proportionality to matrix elements of the Coulomb operator.