Resonant-state perturbation formalisms

Three different formalisms for determining bound-state, virtual-state, and resonant-state energies of a perturbed system are developed. Two of the formalisms are based on expansions of the unperturbed Green function in terms of bound-state, resonant-state and deformed-continuum-state contributions of the form developed by T. Berggren. The third formalism is based on a Mittag-Leffler expansion of the unperturbed Green function. The three formalisms are compared and the relative merits of calculation schemes based on them are examined. (orig.)