Abstract
Two-body double-tensor (TBDT) operators are introduced in the LS- and jj-coupling schemes following Racah's definition of irreducible tensor operators. These operators are shown to contain well-known one-body double tensors as a subset. The result of applying parity, charge conjugation, and time reversal to the TBDT operators is investigated so as to obtain selection rules for their matrix elements. On the basis of their rotation properties, these Hermitian tensor operators are shown to satisfy an SU(2) algebra, and consequently the Wigner–Eckart theorem is applied to calculate their matrix elements. The derivation of the reduced matrix elements is provided. We show some examples of interactions investigated in the literature that can be represented as TBDT operators. For one such operator, the spin-correlated crystal field, a detailed numerical evaluation of its matrix elements is given.
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