Electron propagator dilated

Characterization of Shape and Auger Resonances using The Dilated One Electron Propagator Method. 

The Orbital Picture of Resonances from different Decouplings of the Dilated Electron Propagator... 

Analogous to the previous treatments /69/ the Fourier transformed equation of motion of the dilated electron propagator may now be written as... 

This demonstrates the equivalence of this development to that of the undilated electron propagator. The structural equivalence at any order of perturbation theory between the dilated propagator G(r/) and the unrotated case, demonstrated by the corresponding choice of projection manifolds and density operators, guarantees the ease with which the dilated propagator coalesces into the undilated one for 0 = 0 at any level of approximation. For example, choosing p = pQ, h = h1 h3, and h = h1 h3 with... 

Particular choices for p and alternative partitionings of H lead to various decouplings of the dilated electron propagator with different actualizations for A and E /71 / and in the following subsections we briefly categorize these different approaches to the construction of G(tj, E). 

The bi-orthogonal dilated matrix electron propagator G( /,E) may be expressed as /22/... 

Approximation of H by H0 in eqn. (62) results in the second order approximation to the dilated electron propagator /26,39/ with... 

Finally, in terms of the eigenfunctions and eigenvalues of L, the spectral representation of the dilated electron propagator is... 

The spectral representation of the dilated electron propagator in strict analogy to eqn. (1) is given by /20-23/ ... 

While the resonant pole of the dilated electron propagator is persistent once uncovered and should be invariant to further changes in the complex... 

Figure 2. Theta trajectories for the e-Be 2P shape resonance and a nearhy scattering root from the second order decoupling of the dilated electron propagator /26/.

Since the complex scaling of the exponents of the primitive basis set will lead to a complex primitive basic set u and hence to the loss of biorthogonality central to our constructions, the Moiseyev-Corcoran approach has been adopted by us /44-46/ and Donnelly /21,47-50/ in the construction of the molecular dilated electron propagator. 

The 2P shape resonance in e-Be scattering has served as the test case for almost all the theoretical approaches to the treatment of electron scattering resonances and the earliest applications of the dilated electron propagator have also focused on this system /21,26,40/. Theta trajectories from different decouplings of the bi-orthogonal dilated electron propagator are displayed in fig. 4. The optimal value of a = 0.75 has been determined through a separate a-trajectory /26/. 

Second order Dilated Electron Propagator based on real SCF /21/ 0.57 0.99... 

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