Excitation spectrum associated with a generalized antisymmetrized geminal power ground state

Self-consistent polarization-propagator approximations (i.e., those based on a proper vacuum) are compared to conventional time-dependent Hartree-Fock — random-phaseapproximation ones, with special attention to the fulfillment of the $f$-sum rule. The effect on the properties of the consistent propagator, based on a general-antisymmetrizedgeminal-power vacuum, when degeneracies occurring in the first-order reduced-density matrix of this vacuum are examined. The foregoing analysis shows that low-lying electronic states can be expected to become degenerate with the vacuum in conjunction with superphenomena in extended systems and oscillator-strength anomalies in finite ones.