Particles and holes equivalence for generalized seniority and the interacting boson model

An apparent ambiguity was recently reported in coupling either pairs of identical fermions or hole pairs. This is explained here as due to a Hamiltonian whose lowest eigenstates do not have the structure prescribed by generalized seniority. It is shown that generalized seniority eigenstates can be equivalently constructed from correlated J = 0 and J = 2 pair states of either particles or holes. The interacting boson model parameters calculated can be unambiguously interpreted and then are of real interest to the shell model basis of interacting boson model