Auger final state

Rgure 3 Experimental and calculated results (a) for epitaxial Cu on Ni (001). The solid lines represent experimental data at the Cu coverage indicated and the dashed lines represent single-scattering cluster calculations assuming a plane wave final state for the Cu IMM Auger electron A schematic representation lb) of the Ni (010) plane with 1-5 monolayers of Cu on top. The arrows indicate directions in which forward scattering events should produce diffraction peaks in (a). 

These are produced by autoionization transitions from highly excited atoms with an inner vacancy. In many cases it is the main process of spontaneous de-excitation of atoms with a vacancy. Let us recall that the wave function of the autoionizing state (33.1) is the superposition of wave functions of discrete and continuous spectra. Mixing of discrete state with continuum is conditioned by the matrix element of the Hamiltonian (actually, of electrostatic interaction between electrons) with respect to these functions. One electron fills in the vacancy, whereas the energy (in the form of a virtual photon) of its transition is transferred by the above mentioned interaction to the other electron, which leaves the atom as a free Auger electron. Its energy a equals the difference in the energies of the ion in initial and final states ... 

Auger spectra, involving electrons of outer open shells. Specific for Auger spectra is the interaction of the electronic configuration with two vacancies in final state of an ion, first of all, with quasidegenerated configurations, particularly if they are energetically close. 

It should be pointed out that the chemical shifts observed in AES are not usually the same as in XPS for the same atoms in the same chemical state. Often, they are larger because of the two-hole nature of the final state in the Auger process. The difference between the XPS and Auger chemical shift has been termed the Auger parameter (17) and is an additional useful guide to the chemical state of the atom concerned. 

Figure 6.1 Schematic representation of one of the channels of the Is-1 Ne+ Auger decay one of the valence electrons (2s) is filling the core vacancy while another one (2p) is ejected into continuum. The same final state results also from the 2p —> Is recombination and 2s ionization (not shown here). The former ( direct ) and the latter ( exchange ) contributions interfere due to electron indistinguishability.

In summary, the dynamics of the electronic decay of inner-shell vacancies in a charged environment, such as created by interaction of a cluster with a high intensity FEL radiation, can be qualitatively different from the one induced by a low-intensity source. If the emitted electrons are slow enough to be trapped by the neighboring charges, the familiar exponential decay will be suppressed by quantum beats between the initial state and the quasi-continuum of discrete final states. Physically, the predicted oscillations correspond to creation of the initial vacancy due to the reflections of the emitted electron by the charged cluster potential and the subsequent inverse Auger transition. 

G. Howat, T. Aberg, O. Goscinski, Relaxation and final-state channel mixing in the Auger effect, J. Phys. B 11 (1978) 1575. 

The dominant non-radiative branches for the filling of the created ls-hole in neon are the K-LL Auger transitions. As can be seen in Fig. 2.5 there are different ways for the two holes to be distributed in the final state in the L-subshells L L2 3, and the corresponding Auger transitions can be grouped into K-L,L,... 

Within the two-step model, one can say that the intermediate photoionized state is the initial state for the Auger transition. For the K-LL spectrum of neon this initial state is described by ls2s22p6 2Sj/2. For the final state the possible electron configurations of the ion were shown in Fig. 2.5. Within the LS-coupling scheme which applies well to neon, these electron configurations yield the following final... 

The selection rules have to be fulfilled for the transition from the ls2s22p6 2Se initial state to the possible final states. Thus, the final state contains one of the final ionic states listed in Table 3.2 and the wavefunction for the emitted Auger electron in its partial wave expansion (see equ. (7.28b)). Due to the selection rules, only a few t values from the partial wave expansion contribute. In the present case there is only one possibility which will be characterized by si. Therefore, one... 

The theoretical expression for the transition probability will be evaluated for the simplest one of these Auger transitions, K-LjLj 1St0. The transition operator Op of equ. (3.3) connects the wavefunctions of the initial and final states, JjMj) and km -)> given by... 

Because the Coulomb operator is a two-particle operator, the transition matrix element Mn is non-zero only for cases in which at most two orbitals differ in the initial- and final-state wavefunctions. For normal Auger transitions it will turn out that these are just the electron orbitals used to characterize the Auger transition, including the Auger electron itself. To show this for the K-LfLf 0 transition one starts with the matrix element... 

This result shows that the original matrix element containing the orbitals of all electrons factorizes into a two-electron Coulomb matrix element for the active electrons and an overlap matrix element for the passive electrons. Within the frozen atomic structure approximation, the overlap factors yield unity because the same orbitals are used for the passive electrons in the initial and final states. Considering now the Coulomb matrix element, one uses the fact that the Coulomb operator does not act on the spin. Therefore, the ms value in the wavefunction of the Auger electron is fixed, and one treats the matrix element Mn as... 

A PCI is the energy gain for the Auger electron, but the energy loss for the photoelectron.) It should be pointed out that this situation differs considerably from the case of electron impact ionization with subsequent Auger decay. Following electron impact, there are three free particles present in the final state... 

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