Feynman Dyson amplitudes

Eigenfunctions that accompany these eigenvalues have a clear physical meaning that corresponds to electron attachment or detachment. These functions are known as Dyson orbitals, Feynman-Dyson amplitudes, or generalized overlap amplitudes. For ionization energies, they are given by... 

The principal part of the eigenvectors, Ca, contains the combination of coefficients that is required to build Feynman-Dyson amplitudes (Dyson orbitals) from the reference Hartree-Fock orbitals. Dyson orbitals as they result from (1.12) are not normalized, i.e., the sum... 

The shape resonances are believed to result when the impinging electron is temporarily captured in an unoccupied orbital of the target /17-19/. While qualitative correlation between orbital shapes and electron-scattering resonances has been attempted earlier /17,18,64/, a quantitative investigation of the resonant orbital(s) has not been undertaken so far since any study of this nature first and foremost, requires a reliable mechanism for an unequivocal identification of the resonant orbital from other unoccupied (virtual) orbitals of the target. We have shown that the dilated electron propagator based on the bi-variational SCF may be successfully used to isolate the resonant or-bital/Feynman Dyson amplitudes which characterize the 2P shape resonances in e-Be, e-Mg and e-Ca scattering /25,26,39-41/. 

In this section we investigate the factors affecting the formation and decay of shape resonances by examining the radial charge density /120/ plots from the Feynman Dyson amplitudes corresponding to the resonant poles identified earlier /22,25,26,40,41/ in sections 3.1 and 3.2 for different atomic and molecular resonances. 

Corresponding residues are related to the Feynman-Dyson amplitudes (FDAs), where... 

Figure 8. The X2A1 Feynman-Dyson amplitude of CaBH4 [55]. The Ca atom is to the right and the in-plane BH2 part of the BH4 group is to the left. [Reprinted from ref. 55, with kind permission from Elsevier Science-NL, Sara Burgerhartstraat 25, 1055 KV Amsterdam, The Netherlands.]...

The Feynman-Dyson amplitudes directly associated with the various electron binding energies are then... 

---