Resonance multiply excited states

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 information on the bulk of the interparticle interactions is contained in I o, even though the decay properties are obtained only after input from Xas has been added, it follows that its accurate and systematic computation is of prime importance, instead of following procedures of brute-force diagonalization, the calculation of I o for electronic structures is done directly, via the solution of state-specific Hartree-Fock (HE) equations under special orbital constraints. The practicality of this approach even for open-(sub)shell multiply excited resonances was demonstrated in the 1972 paper, thereby opening the way for later computations that start with state-specific mul-ticonfigurational HF equations and tackle efficiently the MEP and electron correlation in the context of appropriate formalisms for resonance states. 

The TDMEPs that are of concern in this review acquire their serious difficulty not only from the fact that the eigenfunctions of the states of real systems, have many-electron structures and are not solvable one-electron models but also from the fact that many discrete states may be involved while the multichannel continuous spectrum, including resonances with multiply excited structures, becomes critically important. 

As is shown schematically in Eigure 6.3, inside both the discrete and the continuous spectrum there are states labeled by doubly or multiply excited valence electron configurations or by inner-hole configurations, whose energy is embedded inside the channels of single-electron excitation of the same symmetry. Their mixing produces perturbation of the discrete Rydberg wavefunctions and spectra or the appearance of resonances in the continuous spectrum. 

Superradiance. We consider a system of several two-level atoms occupying a volume the dimension of which is small compared to A. In this case the total radiating dipole is given by eq. (36), multiplied by the difference of atom populations in the excited state and in die ground state. If the external resonant field is stopped at t-nHQa, we shall create a macro dipole given by ... 

Figure 8.1 A Photoelectron Spectrum (PES) of HC1, excited by the He I resonance line. This PES displays rotational substructure in A2E+ state vibrational transitions. The intensity of the spectrum in dashed lines is multiplied by 10. The sharp peak at 18.07 eV is due to CO2 (from Edvardsson, et al., 1995).

Two of the three laser ionization methods have already been discussed, namely one-photon PI and multiphoton MPI. The third type is resonance enhanced MPI, or REMPI. In the latter method the laser is tuned so that an intermediate state of the molecule is excited with one, two, or perhaps three photons. The excitation of the intermediate state determines the overall cross section for the process because the absorption of additional photons to reach the ionization continuum is generally rapid. In contrast to PI and MPI, REMPI is state selective if the absorption process is resonant between two bound and reasonably long-lived states of the molecule. It is an extremely sensitive method for product detection because the result of the REMPI process is an ion which can be detected with near 100% efficiency. Not only is the ion collection efficiency of the detector (e.g., by channeltron electron multiplier or a multichannel plate detector) extremely high (ca. 50%), but all ions regardless of their initial velocity vector can be collected by the application of appropriate electric fields. This is a major advantage... 

The imaginary part has a Lorentzian profile of halfwidth centred at exact resonance. This Lorentzian line shape comes from the assumed form for the damping terms, and more realistic models should be used in Equation [14] when studying line shapes. The spectral shape is the same as for spontaneous Raman lines. The real part of is multiplied by the detuning, and shows a dispersive line shape. depends on the population difference, instead of just the population of the initial state as does spontaneous Raman. This dependence can lead to saturation whenever appreciable population is transferred to the excited level. 

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