Abstract: The LSQ coupled states of l-shell are constructed by (U,D)L-LSQ scheme, where U(D) is the total orbital angular momentum of spin up(down) electrons, the LS and Q are the total orbital angular momentum, spin and quasispin respectively, the (U,D) L-LSQ is unitary transformation. The scalar operators which commute with the total orbital angular momentum, spin and quasispin operators, are constructed from 4 creation-annihilation operators, and the LSQ coupled states are further or complete classified by its eigenvalues. The complete classifications of coupled states for f- and g-shell are obtained, the primary results of complete classifications of coupled states for g-shell are listed.

Key words: atomic physics, classification of coupled states, shell model, second quantization