ABSTRACT
Let us now consider the case of both valence protons and valence neutrons outside closed shells within the LS-coupling scheme. We consider charge independent Hamiltonians which do not depend explicitly on the spin and isospin variables of the nucleons. Such Hamiltonians are invariant under permutations of the space coordinates of nucleons. As before, eigenfunctions of these Hamiltonians, being functions of space coordinates which are transformed into each other under permutations, have the same eigenvalue. Such eigenfunctions belong to irreducible representations of the group of permutations. Wave functions which are fully antisymmetric, according to the generalized Pauli principle, are linear combinations of these spatial eigenfunctions multiplied by spin-isospin functions which belong to the dual Young diagram. The theory of such Hamiltonians, presented in the following, is due to Wigner (1937) and Hund (1937).
