OPERATOR REPRESENTATIONS IN KRAMERS BASES

Using the time-reversal symmetry operation, we introduce the time-reve rsal adapted Kramers basis operators X(pq)+ which are the natural expa nsion set for any relativistic Hermitian or anti-Hermitian one-electro n operator and thus replace the spin-adapted basis operators of non-re lativistic quantum mechanics. Depending on the time-reversal symmetry or Hermiticity of the one-electron operator, either X+ or X-, but neve r both of them, appear in the expansion, thus causing the symmetry blo cking that is important for computational saving in relativistic elect ronic structure calculations. We determine the combinations of X opera tors that become irreducible tensor operators in the non-relativistic limit and we use the particle-hole expansion case to offer an interpre tation of the new basis as operators that describe simultaneous excita tion and deexcitation of particle-hole states with opposite spin-polar ization in the non-relativistic limit.