Interchannel coupling, with

If there are no interchannel couplings, R = 0, corresponding to the fact that the i channels have quantum defects of and occur when v, = 0. In general the R matrix is a real symmetric matrix with zeroes on the diagonal. 

To account for the interchannel coupling, or, which is the same, electron correlation in calculations of photoionization parameters, various many-body theories exist. In this paper, following Refs. [20,29,30,33], the focus is on results obtained in the framework of both the nonrelativistic random phase approximation with exchange (RPAE) [55] and its relativistic analogy the relativistic random phase approximation (RRPA) [56]. RPAE makes use of a nonrelativistic HF approximation as the zero-order approximation. RRPA is based upon the relativistic Dirac HF approximation as the zero-order basis, so that relativistic effects are included not as perturbations but explicitly. Both RPAE and RRPA implicitly sum up certain electron-electron perturbations, including the interelectron interaction between electrons from... 

Figure 18 Calculated [33] RPAE results for the Xe 5s photoionization cross section of Xe Cgo obtained in the A-potential model at the frozen-cage approximation level. (a) o 1" A iro), complete RPAE calculation accounting for interchannel coupling between photoionization transitions from the Xe 4d10, 5s2 and 5p6 subshells (b) 5 A ( >), the same as in (a) but with the 4d - f, p transitions being replaced by those of free Xe, for comparison purposes (c) o AA(

Figure 28 Relativistic RPAE calculated results [30] of the 6s dipole photoelectron angular distribution parameter of Hg at two different levels of truncation with regard to RRPA interchannel coupling (a) including channels from the 6s2 subshell alone, Aa, and (b) including channels from the 6s2 and 5d10 subshells of d>Hg, as in Figure 27. Confinement effects were accounted for in the A-potential model at the frozen-cage approximation level.

Complex adiabatic energies (a) compared to resonance energies (b) for a model of a closed and an open channel described in reference (30). The zeroth order energy has been subtracted out. Unit cm , Interchannel coupling 200 cm . Crossing diabatic energy equal to the energy of the level with v = 18. 

There is, of course, no objection in principle to the occurrence of energy-dependent parameters, provided this dependence is weak 2 after all, the constancy of p was the approximation in the first place, as the numbers in table 2.1, in the absence of perturbations, show quite clearly. However, the consequence of an energy dependence is that the variations in pi and p2 are no longer perfectly periodic, and it may then become unclear which part of the variation with energy is intrinsic (i.e. existed before interchannel coupling was turned on) and which part is produced by coupling between channels. 

In addition to this important effect, the inner-shell excitations from the 6s and 5d subshells also overlap in energy with each other, giving rise to prominent interchannel coupling and examples of the q reversal effect which will be discussed in chapter 8. The 5d spectrum of Tl is thus unexpectedly rich and interesting. 

Molecular applications have thus far involved the calculation of the electronic structure and potential energy surfaces of negative ion "compound states" and of "diabatic states" in the continuous spectrum of polyelectronic diatomics and triatomics and of energies and partial widths with interchannel coupling of vibrational shape and predissociating resonances of diatomics. The same principles and methodologies can be applied to many more such cases. 

COMPUTATION VIA THE CESE SSA. MANY-BODY EXPANSION AND PARTIAL WIDTHS WITH INTERCHANNEL COUPLING... 

One of the useful consequences of the CESE approach, in conjunction with the related many-electron analysis, is the fact that it solves in a simple way the problem of computing partial decay widths, without or with interchannel coupling. In order to see this, I draw from the theory published in Refs. [37b, 101, 118-121]. 

The calculafions of Ref. [118,119] still remain the only ones in which complex scaling and square-integrable complex functions have been employed for the determination of the complex eigenvalue and its breakdown in its partial widths, without and with interchannel coupling, of an inner-hole resonance sfafe of a sysfem with many interacting electrons. 

We point out that since the structure of the CESE-SSA is such that it requires well-defined mafrix elements and computations that are practical and economic, its first-principles implementation has been extended to prototypical cases, such as the determination of partial and total autoionization widths in series of high-lying DESs [120] and Section 9.4, and of partial widths with interchannel coupling for fhe predissociation of excimer molecules [121]. 

X If symbolizes fhe "asymptotic" correlation that is function spaces that represent the energetically open channels and contain the information about the interaction of fhe free electrons with the core state and about the possible interchannel couplings. It is zero when the state is discrete. For quantities where the open continuum is important, such as the energy-dependent photoabsorption cross-sections, or for fhe full description of resonance states, the proper computation and consideration of X are essential. 

Equation (32) keeps a formal resemblance with expression (16). The coupling operator K)(H originates from the interchannel couplings gathered in V (28). On the other hand, Gq( 2 ) contains the information concerning the energy shifts and the energy densities. When there is no interaction inside and between the continua, i.e., V=0, Eq. (32) reduces to... 

For AD the molecule is left in a 2-hole state with a -I- 2 charge, but the +1 ion also can be produced by coupling of the shape resonance to the valence electron ionization continuum. The co re hole shape resonance then relaxes by interchannel decay (ICD). AD and ICD can be distinguished by the... 

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