By G. Wendin
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As a consequence, the excited electron m will feel the potential of two core holes (V N-2 potential). Furthermore, the two core holes i and k must be allowed to relax properly. This involves in principle a two-core hole self-energy which describes relaxation, correlation, decay, screening of the hole-hole repulsion etc. and it also affects the interaction with the excited electron m. b) As discussed in Sect. 1 (Fig. 3) an electron-hole excitation may become strongly modified by the dielectric response of the system.
38)-(40), giving E4~ 2 E4_a(ASCF) - (F°(4d; 4d) - 2 A ~ ) ~ (56 a) = 2 E~_F - F°(4d; 4d) + 4dS~ (56b) For some elements we also used the ASCF method involving two core holes (Eq. (41)). The results are shown in Fig. 15. We now have the tools for constructing the spectralfunction A4p(E). ~ = R e 2 ~ ( E ) + Re2-~aE(E) (57 a) + _ so RePOt(E)_ =A42 (57b) E - E4E(ASCF) - Re z4DEI(E) (58) Re z4Dpl(E), Im ~;4Dd(E)and the straight lines E - E4B(ASCF) (j = 1/2, 3/2) are shown for a number of representative elements in Fig.
Although this may look like hiding the difficulties, it is really a way of organizing the difficulties, collecting them into physically relevant quantities. We shall now break down the renormalized self-energy diagram in Fig. 19 c in terms of effective two-body interactions suitable for explicit calculations. In analogy with the Dyson equation in Fig. e. one-particle-two-hole (phh), i i __B = (o) (b) (c) (dl (e) (f) (O) (h) Fig. 19 a-i. Expansion of the self-energy in terms of effective interactions (see text) (i) 32 Core-Hole Self-Energy2'i(E): Formal Theory and Approximative Treatment interaction FPhh(E) in Fig.