Fano configuration interaction

The advances in this field are related with the development of the theory of configuration interaction between different excitation channels in nuclear physics including quantum superposition of states corresponding to different spatial locations for interpretation of resonances in nuclear scattering cross-section [7] related with the Fano configuration interaction theory for autoionization processes in atomic physics [8],... 

Fano, U., Effects of configuration interaction on intensities and phase shifts, Phys. Rev. 1961, 124, 1866 1878... 

Real energy hermitian approaches. Extension of Fano s K-matrix, configuration interaction theory... 

Fano, U., Effects of configuration interaction on intensities and phase shifts, Phys. Rev., 124, 1866,1961 Fano, U., Sullo spettro di assorbimento del gas nobili presso illimite dello spettro d arco, Nuovo Cimento, 12, 154, 1935 in Enghsh at Fano, U., Pupillo, G., Zannoni, A., and Clark, C.W., On the absorption spectrum of noble gases at the arc spectrum limit, 7. Res. Natl. Inst. Stand. Technol, 110, 583, 2005. 

U. Fano. Effects of Configuration Interaction on Intensities and Phase Shifts. Physical Revew 1961 Dec 15 124(6) 1866-1878. 

Another type of such coupling is the configuration interaction (CI) between a true discrete excitation and a continuum excitation. This autoionization phenomenon is clearly within the TDLDA framework, A nice example can be found in copper where 3d -> ef, ep excitations interfere with the 3p -> 4s transition, The resulting 3d partial photoionization cross section is shown in Figure 8, In addition to the prominent Fano line shape, an overall diminultion (relative to the LDA) of the cross section is found due to intrashell 3d polarization. The interesting dip around 80 eV is again a Cl effect, but this time the 3d ef,ep excitations interfere with the continuum channels, 3p es,ed. 

Fig. 3.4. Example of a Lu-Fano graph involving more than two interacting series, and consequently more than one avoided crossing. This particular graph occurs in the spectrum of Yb, and involves doubly-excited configurations, discussed in chapter 7. The number of series in the graph is equal to the number of intersections of the curves with the diagonal, i.e. 3 in this case (Kaenders and Connerade - unpublished).

Theoretical formulae for the matrix elements of the electrostatic interaction within and between all possible types of three-electron configurations were constructed by Z.B. Goldschmidt, both in explicit form (Z.B. Goldschmidt, 1968a Fano et al., 1963) and as linear combinations of two-electron matrix elements (Z.B. Goldschmidt, 1968a, 1971). These quite lengthy formulae will not be included here. 

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