Auger capture

Fig. 12. Schematic of Auger capture at a one-electron trap (a) and of Auger recombination from there (b).

Finally, by substituting equation (21) into equation (18) and making use of the standard expression relating the imaginary part of the susceptibility v(t >, z,/) for interacting electrons (screened susceptibility) to the density operators 8n(q, z) and 8n(q, z ), the final expression for the Auger capture rate is obtained as... 

Another possible simplification to the full calculation of the Auger capture rate consist of the use of the asymptotic long-distance limit of... 

We also conclude that a detailed calculation of the different mechanisms operating in the ion-metal charge exchange processes depends on a careful description of the ion levels as a function of the ion-metal distance. In this paper, these levels as well as the ion-metal hopping interactions and the Auger capture rates, have been presented for the H/Al and He/Al systems. 

In the self-energy formalism, the probability of Auger capture per unit time r can be calculated in terms of the screened Coulomb interaction W(r,r [19]... 

Fig. 4. Schematic picture of the Auger capture process. An electron is captured from a valence band state lipi) to a state bound to the ion I An electronic excitation (either an electron-hole pair or a collective excitation) is created at the same time in the medium.

To make a connection with experimental measurements [15] we consider that the Ne ion has only one K-shell elecuon. We also assume that, once the ion has entered the solid, its M shell (if bound) is rapidly filled. The electronic configuration of the Ne ion then has the mentioned K-shell hole and a given number of L-shell holes. We plot in Fig. 5 the L-shell Auger capture rate El for Ne ions in a FEG of = 1.5 and 2.0, as a function of the... 

Fig. 5. Probability (per unit time) of Auger capture to the L shell of a Ne ion embedded in a FEG El as a function of the number of L-shell electrons bound to the ion before the capture. El is in atomic units. Two different values of the electronic density = 1.5 and 2 are shown.

In the same way that the rearrangement of charge is crucial to determine the Auger capture rates from the valence band of a metal, it is reasonable to assume that it should also be of great importance to calculate radiative rates from the metal valence band. Nevertheless, the theoretical approach is simpler because the energy associated to the decay is released in the form of photons, and no electronic excitations are created in the medium. The radiative capture process is shown schematically in Fig. 8. We call radiative capture to the process in which the initial state of the electron is a valence-band state, the final state is a bound state of the ion, and the energy balance is compensated by the emission of light. 

Fig. 11. Differential transition rate AF/Ak (in atomic units) as a function of the initial momentum of the electron (normalized to the Fermi momentum) fej /fef for an Auger capture process from a free electron gas of = 2 to the 3p state of an Ar ion. Solid lines include the Ar in the calculation of the response function. Dashed lines are the unperturbed free electron gas results. Thick lines are calculated with the self-consistent response function while thin lines show the results using the Hartree response xq (the latter are multiplied by 0.5 before being plotted).

Fig. 3.1 The calculated dependences of the Auger capture cross-section solid line - E = 50 eV dotted line - E = 20eV) on orbital number I for different n values for incident a" energies 20, 50 eV...

Fig. 3.3 The calculated Auger capture cross-section in dependence upon the principal quantum number n after summation on all orbital moment values for different muon energies (the digits in figure - the muon energies ineV)...

Fig. 3.4 Total cross-section of a capture in dependence on an energy our data (the Auger capture cross-section) - curve 7 (elastic and inelastic scattering cross-sections) - curves 2,3 cross-section of capture by Copenman and Rogova (curve 5) the HaF data by Cherepkov-Chemysheva -curve 1 inelastic scattering cross-section by Rosenberg -curve 4 the transport cross-section - x...

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