Inner-hole states

The phrase relative sense implies the consideration of electronic structure and notions from perfurbafion theory, such as energy differences and strengfh of first-order interaction matrix elements. For example, when inner-hole states are considered, all kinds of possible mixings involving both valence and inner spin orbitals are in principle present. In a related investigation concerning photoelectron spectroscopy [27a-27c], we wrote ... 

Fig. 4 Shift AF. of inner-hole state due to the interaction with the Auger continuum...

The calculations were performed using a double-zeta basis set with addition of a polarization function and lead to the results reported in Table 5. The notation used for each state is of typical hole-particle form, an asterisc being added to an orbital (or shell) containing a hole, a number (1) to one into which an electron is promoted. In the same Table we show also the frequently used Tetter symbolism in which K indicates an inner-shell hole, L a hole in the valence shell, and e represents an excited electron. The more commonly observed ionization processes in the Auger spectra of N2 are of the type K—LL (a normal process, core-hole state <-> double-hole state ) ... 

Th. Mercouris, Y. Komninos, C.A. Nicolaides, Time-resolved hyperfast processes of strongly correlated electrons during the coherent excitation and decay of multiply excited and inner-hole excited states, Phys. Rev. A 76 (3) (2007) 033417. 

With rn( only the total decay rate or, equivalently, the total level width of an inner-shell hole-state has been considered so far. In general, the system has different decay branches. In many cases these branches can be classified as radiative (fluorescence) or non-radiative (Auger or autoionizing) transitions, and even further, by specifying within each group individual decay branches to different final ionic states. (Combinations of radiative and non-radiative transitions are also possible in which a photon is emitted and simultaneously an electron is excited/ ejected. These processes are termed radiative Auger decay (see [Abe75]).) As a result, the total transition rate Pnr and, hence, the total level width is composed of sums over partial values ... 

Ionization of inner valence orbitals In this regime, where several matrix elements have comparable strength, the self energy has a sequence of poles, and has several solutions with comparable residues. A qualitative explanation is given in Fig 3 there are configurations shown in part (b) of the figure that have the same energy as the hole state shown in part (a). 

In an excitation process, the electron and the hole can remain bound, producing an exciton state just below the conduction band. Indeed, the mass of an inner hole is considered as infinite and the exciton binding energy is thus almost zero with reference to the absorption threshold energy. If the resonance lines were excitonic type transitions, the emission spectmm should be exactly the reverse of absorption. We would see that this is not the case although a localized excited Mjy state has a large probability of existing, sometimes the resonance Mjy lines are absent, whereas the resonance My lines are the most intense of the spectrum (77). 

We have seen that the inner hole can produce a perturbation of the electronic distribution relatively to that of the unperturbed solid. Various analyses have shown the importance of the final-state configuration on the spectra and the electron-hole interactions which can, in some cases, alter their shape. Thus, the rare earth 3 d photoabsorption spectra present a number of structures which spread over several eV. They can be interpreted as the components of multiplets because of the exchange coupling between the 3 d and 4/shells. The perturbation weakens as the hole lies in a deeper inner shell. In fact, the exchange interaction strength depends on the overlap between the wavefunctions of the inner hole and the localized 4/holes the weaker... 

Fig. 2 shows a diagram summarizing the various transitions which can be observed in the Mjjj and My spectra of a metal as well as in the 3 d Auger spectra. The Mjjj and My absorption transitions are shown in Fig. 2a and b the energy of the Mjjj discontinuity corresponds to the transfer of an inner 3p i2 electron to the Fermi level and its shape involves the 6d unoccupied distribution the energy of the My absorption line is exactly that of the 5/" -> SJjyj excitation transition. The My emission is shown in Fig. 2e an inner 3 d i2 hole is created and a 5/electron transits to this hole with the emission of a photon. In the corresponding non-radiative transition, there is simultaneously the 5/ electron transition, and the excitation or ionization of a 5/electron (or 6p or 6 s) (Fig. 2f). The My resonance line is represented in 2c the excited 5/electron drops back to the inner hole the corresponding emission line then coincides with an absorption line. The competing non-radiative transition is shown in 2d this is an Auger transition in the excited atom the final state has only one hole in an outer shell and the configuration is the same as in a photoemission process.

It is thus possible to emphasize the following points When the excited electron jumps in a wide conduction band, i.e. in itinerant states, the electronic speed in the band is sufficiently large for the electron to have a very small probability of returning to the inner hole. No resonance line is observed this is the general case in the solid. 

In the same way we have determinated the position of resonance lines with respect to the Fermi level. If one supposes that the perturbations caused by 3p and 3d holes are the same, it appears that the 5/excited states involved in the R lines are situated largely beyond the Fermi level for Th and Pu. Then the resonance lines are not of an excitonic type moreover, they are not due to a stabilization of 5/empty states by the inner hole because the excited states should then drop below Ep. On the contrary, in a—Pu, the R line is in coincidence with the R absorption line and not with the Rj line. However, a lowering of the position of 5/ excited states as a consequence of the formation of the inner hole must be present and the distance between the resonance line and the Fermi level gives only a minimum value of the 5/ states — Ep distance. 

Secondly, photoelectron spectroscopy gives the distribution of all mixed states and the spectrum is disturbed by the photoionization probabilities of the various symmetries as a consequence, it is sometimes difficult to interpret the results. On the other hand, the X-ray spectra involve the distributions of known symmetries, i.e. those states from which the transitions toward the inner hole are possible considering the transition probabilities. 

In the approximation (2), A indicates that the two quantities on the right-hand side are obtained by computing separately the initial and the final (hole) states. I note that in the 1970s and early 1980s, the problem of determining the BE of the Is electron in the Be metal (in general, of inner electrons in metals), which is measured via photoelectron spectroscopy, was mostly tackled via models of the independent particle type, with... 

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