Multiply excited states

G.F. Gribakin, S. Sahoo, Mixing of dielectronic and multiply-excited states in electron-ion recombination A study of Au24+, J. Phys. B 36 (2003) 3349. 

It is clear, however, from the discussion involving Eqs. (7)—(9) and from the sudden approximation sum rule that the spectrum associated with the photoionization of a core electron should not, in fact, necessarily consist only of a single line some data observed for RbCl and RbF (40) are shown in Fig. 16. The narrow peaks are the Rb 4s24 6(1S) - -4s14 >6(2S) excitation and the broad peaks, approximately equal in intensity, arise from multiple electron excitation , that is, the production of final states such as 4s24 4 s(2S), where n > 5. Even though the photoemission event is just a one-electron dipole process, multiple excitation can occur because the wavefunction of the instantaneous intermediate state of the (TV—1)-electron ion [Eq. (7)] has overlap with wavefunctions of such multiply excited states that is, i has components which are eigenfunctions, n(N—1), of multiply... 

Fourth, the predominantly one lectron nature of the phenomena lends Itself to theoretical treatment sy realistic. Independent-electron methods (2,4-9), with the concomitant flexibility In terms of complexity of molecular systems, energy ranges, and alternative physical processes. This has been a major factor In the rapid exploration In this area. Continuing development of computational schemes also holds the promise of elevating the level of theoretical work on molecular Ionization and scattering and. In so doing, to test and quantify many of the Independent-electron results and to proceed to other circumstances such as weak channels, multiply-excited states, etc. where the slimier schemes become Invalid. 

It is worth pointing out that the idea of searching directly for a state-specific solution for the wavefunctions of multiply excited states (MES) implies projections on distinct function spaces with separate optimization of some type, thereby avoiding serious problems having to do with the undue mixing of states and channels of the same symmetry. This idea has since been a central element of our analyses and state-specific computations. In fact, in recent years, such concerns have led to appropriate modifications of conventional methods of quantum chemistry, such as perturbation or coupled-cluster. 

An addifional remark has fo do with the quantum chemistry of doubly or multiply excited states embedded in channels of series of Rydberg and scattering states. In such cases, the SPSA has been implemented by first dividing the total function space into two parts One containing the separately optimized valence states and the other containing the physically relevant channels. The theory for this approach and applications to prototypical cases can be found in Refs. [8,10,22-25]. A discussion on special topics concerning MES is given in Section 4. 

Centrifugal barriers have a profound effect on the physics of many-electron atoms, especially as regards subvalence and inner shell spectra. One aspect not discussed above is how energy degeneracies arising from orbital collapse can lead to breakdown of the independent electron approximation and the appearance of multiply excited states. Similarly, we have not discussed multiple ionisation (the ejection of several electrons by a single photon) enhanced by a giant resonance. Both issues will be considered in chapter 7. 

In summary the discussion includes formalism and analysis contributing to the understanding of the nature of unstable states, as well as indicative theoretical and numerical examples from applications to atoms and molecules, and related comparisons with other methods, concerning prototypical problems of autoionization, predissociation, series of isolated and overlapping resonances, structure and spectroscopy of doubly and multiply excited states, multiphoton ionization, field-induced polarization, etc. 

The topic of multiply excited states (MESs) has attracted both experimental and theoretical interest over the last few decades. In a series of publications, we have produced results of SSA calculations for a variety of MESs, based on the analysis and computations of their By the word "multiply" 1 mean not only the normally examined DESs of He-like systems (Section 9.4), but also novel structures where three or four electrons occupy higher-lying subshells [153-156] and references therein. 

In the late 1980s, this three-electron excitation was cited by other researchers as a heuristic case to argue that, "as far as we can tell, a multiply excited state such as 3p is virtually inaccessible by single-photon absorption." Yet, small-size (for reasons of economy) SSA calculations show that the state-specific HF result, which is of course obtained from an independent electron model with no electron correlation, produces nonzero values for the probabilities of the three transitions. Furthermore, the order of magnitude of the HF transition probabilities is the same as that from computations that include some part of electron correlation. Specifically, the results of the SSA calculations for the oscillator strengths, using only approximate wavefunctions for the oS, are ... 

Similarly, intense lasers make it possible to study the early stages in the multiphoton ionization of molecules through multiply excited states. Above-threshold ionization gives rise to a quasi-free electronic wavepacket state, and the recombination (collision) of such an electronic wavepacket with the remaining cation species results in the high harmonic... 

Keywords Electronic correlation Relativistic effects Isotopic effects Multiply excited states Hollow atoms B-spline basis set Charge transfer Photodissociation Radiative association... 

From doubly to multiply excited states in hollow atoms... 

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