Frozen-cage approximation

In the framework of the A-potential model, combined with the frozen-cage approximation, the problem is solved simply. Namely, HF wavefunctions and energies of the encaged atom, solutions of the extended to encaged atoms Hartree-Fock equations (2), must be substituted into corresponding formulae for the photoionization of an nl subshell of the free atom, Equations (18)-(26), thereby turning them into formulae for the encaged atom (to be marked with superscript " A") rrni(o>) —> a A(co), Pni(fi>) Yni o>) - and 8ni((o) - 8 A(co). This accounts... 

In the frozen-cage approximation, the carbon cage is considered totally invisible to the incoming electromagnetic radiation. However, as was explained earlier, following [38-40,43,44], when A C60 is exposed to the external electromagnetic field, the latter polarizes the carbon cage,... 

Following the previous discussion, the following notations are maintained in this section calculated results obtained within the A-potential model at the frozen-cage approximation level are marked as a A, P A, y A and 8 A to distinguish them from the results of the 5-potential model, a s, f) s, y s and 8 s, respectively. 

Figure 17 The Cgo dynamical screening function F (to) [40] along with the RPAE calculated 5p photoionization cross section of free Xe, CT eefei, encaged Xe both at the frozen-cage approximation...

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(

The quintessence of the reversed electron correlation effect is illustrated in Figure 20 by nonrelativistic HF and RPAE calculated data of the 4s photoionization cross section of free Ca and encaged Ca, Ca C60 near threshold, both at the frozen-cage approximation level, afs A, [20] and dynamical-cage approximation level, afsA [64]. 

At the dynamical-cage approximation level (see the lower main panel in Figure 20), the role of the dynamical screening of the incoming radiation by the C60 cage is tremendous [64], resulting in the impressively enhanced 4s photoionization cross section afsA compared to that calculated at the frozen-cage approximation level. 

The RRPA calculated [29] valence ras photoionization cross sections for both the free and encaged atoms, at the frozen-cage approximation level, are displayed in Figures 22-24. To demonstrate the importance of electron... 

Ca C60, ofs A, are displayed in the lower panel of Figure 26. The dynamical screening effect is seen to increase very much quantitatively, although does not alter qualitatively, the photoionization probability of Ca at the autoionizing resonance energies compared to the predictions of the frozen-cage approximation. 

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.

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