Construction of resonance projection operators: Application to two-electron targets

Feshbach projection approach to study plasma effects on doubly excited autoionizing states in helium

“…The Feshbach projection method [26,27] provides a powerful method to deal with resonance phenomena in scattering processes. Most of the known applications in atomic and molecular physics are reduced to two-electron (see, for instance, [27] and references therein) and three-electron systems [28,29]. Additionally, it has shown to be a remarkable method not only as a time-independent approach but also in the time domain [30,31].…”

Core effects in atomic resonances. A comparison between 1,3P (3l 3l′) states of He-like and Be-like systems

“…This is a well-known effect3 1 of the partial screening of the lr core electrons, which results in an effective nuclear charge Zeff > Z -2, with the corresponding stabilizing effect on the energies. It is also apparent that while the absolute difference between the resonance positions of He-and Be-like systems increases with Z, the relative differences diminish; this follows directly from the simple quantum defect expression for the energy of He-and Be-like resonances: (19) where Zeff = Z -a and a is the corresponding screening constant. Taking into account that a is practically constant along the series, and n* -+ n as Z -+ 00, it follows that t:.E=E Be -EHe =O(Z) whilet:.EIE Be =O(Z-I).…”

Doubly excitedPeandDo

“…The QHQ method is known as providing good approxima-tions to the energies of closed-channel (Feshbach) The projection operator Q corresponds to a closed-channel space and is the complement of the projector P (P + Q = 1) projecting onto the open-channel space according to where g, (r' ') is a channel wave function in which the (N -1)-electron target-state wave function P, is coupled to the angular momentum l and spin of the incoming (or outgoing) electron, as defined by Temkin and Bhatia [12] and applied in Ref. [10].…”