My question concerns the interpretation of occupation numbers in the Kondo problem in presence of crystal fields.

(1) Consider first a Ce4f electron in a hexagonal crystal field (CF) without Kondo interaction. Owing to the symmetry, the |mj> states will not be mixed but merely split in Kramers doublets (neglecting artificial degeneracy). Thermal occupations of the CF states (and related termodynamic quantities) are readily computed with usual statistical methods.

(2) Now admit some hybridization to a metallic host (still in hexagonal symmetry). It will give rise to the Kondo effect. Within the NCA (noncrossing approximation), each of the 4f states is now represented by its spectral density, resulting in a Kondo (or Abrikosov-Suhl) resonance. Due to their finite width, the excited levels acquire a larger occupation than in (1), remaining finite as T->0 (strictly speaking, the latter cannot be a NCA result, I know).

How to view/interpret these "non-thermal occupation numbers"?

(a) we have interaction induced hoppings to the different |mj> states and therefore "non-thermal" but statistical occupations

(b) all the |mj> states are quantum-mechanically (qm) mixed by the Kondo interaction (with temperature dependent amplitudes) despite the hexagonal symmetry. This would mean that (in general) all the |mj> states are part of the Kondo singlet ground state.

I'd appreciate your opinions and/or pointers to pertinent literature. For some properties as e.g. specific heat or magnetic susceptibility the answer to the question might be irrelevant. But an experiment able to produce interference terms from a qm mixture of states might be able to tell the difference (?!).