Abstract
Generalized seniority gives good description of the lowest states of semimagic nuclei. Recently, a very large fraction of eigenstates obtained with random two-nucleon matrix elements were shown to have the structure prescribed by generalized seniority, also for lower values of isospin. To study such states, this concept is generalized to states of nuclei with valence protons and neutrons in the same major shell. States of generalized seniority are defined and constructed. Conditions are derived on charge-independent shell-model Hamiltonians which have such states as eigenstates. From these conditions follow directly the corresponding eigenvalues. Even without an underlying group structure, these eigenvalues have the same form as in the case of protons and neutrons in the same j-orbit.
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