Inelastic-resonance quasiprojection operators

An explicit form of quasiprojection operator $\hat{Q}$ is given for the calculation of resonances in the domain of inelastic scattering of electrons from atoms and atomic ions. This operator allows the calculation of the resonant spectrum through the diagonalization of $\hat{Q}H\hat{Q}$ with as many inelastic states projected out as desired. The technique gives rise to a limited number of spurious states, but they can be unambiguously identified and thus eliminated. The elimination procedure is illustrated in the case of three-electron (i.e., heliumlike target) ions whereby we explicitly determine the number of spurious states that arise in inelastic scattering below the $3{}_{}{}^3{}_{}{}^{}S$ state of the target.