Hamiltonian, subshell

As a second example, we can think of the case where the one-electron Hamiltonian has spherical symmetry. Then the Kramers pair creation operator corresponding to the shell n and subshell l is given by... 

When the discussion is limited to a single open subshell and to perturbations within such a shell, an interesting formulation of the many-electron atomic problem can be achieved that exhibits useful particle-hole symmetry. The summations in the perturbation term of the hamiltonian then run only over electron states nlmu) of the open subshell (nQ. This means that the electron repulsion integrals can be expressed as... 

As in the subshell hamiltonian in Eq. (4.150), there should be an interaction parameter V(7Z/5) corresponding to the electron pair operators. The possibility exists to introduce parameters that couple pair states of equal L and S but different 7 s. We require that the two-particle part of the hamiltonian commutes with the parity operator... 

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