## 5 Time-Resolved Coherent Excitation and Decay of Strongly Correlated Autoionizing States
### The Relative Time Delay in the Neon Problem: The Role of Doubly Excited Resonances
#### 6.3.1 The Relative Time Delay in the Neon Problem: Comparison of Theory with Experiment  
The quantitative discrepancy between the experimental and theoretical results reported in [11] evidently presented a scientific challenge. On page 465 of [3], I commented as follows:  
_\"The enigma stemming from the reported difference between the experimental and the theoretical findings in [11] remains to date, in spite of subsequent theoretical investigations by a number of researchers. It is challenging to both theory and experiment. In this context, it is worth noting that the same theoretical number, [to that of the SSEA], i.e., **6.4** as, was reported recently by [PERSON] et al. [60] who carried out very large R-matrix type calculations, including a series of resonance states near and far from the critical region of 106 eV. Their results confirm the original theoretical predictions which were made in [11; 17].\"_  
The \"enigma\" stated above was resolved recently with the publication by [PERSON] et al. [10] of new measurements with high spectral resolution, which allowed the disentanglement of the direct 2 ionization from the two-electron process of ionization plus excitation to a \(3p\) state [10]. The qualitative conclusions of [PERSON] et al. [10] as to the sequence of emission of electrons from the \(2s\) and \(2p\) subshells of neon confirm the original experimental and theoretical predictions of [PERSON] et al. [11]. However, the new experimental number [10] is about **10** as, much closer to the theoretical result first predicted via the theory and the SSEA calculation in [11] than to the experimental value [11]. Here, a parenthetical clause is necessary. The authors of [10] present the discrepancy between the theoretical and experimental TD as a \"puzzle\" that came to the fore after calculations that followed the publication of [11] produced such a result. (The theoretical work in [10] used the many-body perturbation theory.) In fact, this was already known and reported explicitly, with specific numbers, in the seminal publication [11], which demonstrated, conceptually and quantitatively, the presence of the relative TD in neon, both experimentally and theoretically. (See the paragraph from [3] quoted above.) The calculations by other groups that appeared after the publication of [11], (quoted in [10]), simply confirmed its theoretical finding, which was obtained based on the analysis outlined in Section 6.2.2. It is gratifying to see that, once the phenomenon was understood and presented in [11], later large-scale calculations by [PERSON] et al. [60], [PERSON] et al. [39], and others, produced a number that is the same as, or very close to, the theoretical numbers (6.4 as and 8.7 as) reported in [11]. 6.3.2 The Relative Time Delay in the Neon Problem: Self-Consistent Orbitals and Electron Correlation  
I quote from [3], page 464:  
_\"Contrary to our initial anticipation, the results for this system did not show a strong dependence on details of electron correlation beyond the MCHF level, or on interchannel coupling. For example, whereas the final result due to the pump step was 6.4 as, the result without interchannel coupling, i.e., using just the dipole matrix elements connecting the initial state-specific orbitals, calculated at the MCHF level, to their corresponding final state channel, was 4 as (see page 1661 of [11]).\"_  
In other words, we found that the cause of the bulk of the relative (\(2s\),\(2p\)) TD in neon is already produced at the level of state-specific HF-MCHF wavefunctions for initial and final states, even though the _hole-filling_ electron correlation, \(2p^{2}-2s\overline{d}\), normally important for transition processes is present only in the case of photoionization from the \(2s\) subshell. \(\overline{d}\) is a one-electron function of \(d\) symmetry representing the sum of the \(d\) orbitals of the discrete and the continuous spectrum calculated in the term-specific N-1-electron HF potential.