“…These interactions are expressed using Racah tensor algebra methods and their effects are evaluated using perturbation theory. The entire Hamiltonian used to investigate the structure of electronic energy levels is provided by: 53 H = H 0 + H ee ( B , C ) + H Trees ( α ) + H CF ( B , C , Dq) + H SO ( ζ 3d ) H 0 is the Hamiltonian configuration, H Trees ( α ) is the Trees correction Hamiltonian, and H ee ( B , C ) is the Coulomb interaction including electron–electron repulsions. This Hamiltonian gives the 2S+1 L terms: two quartet terms ( 4 P excited state and 4 F ground state) and six doublet excited terms ( 2 G, 2 H, 2 D, 2 F, 2 D′ and 2 P) with a 3d 3 configuration for the Cr 3+ ion.…”