Quantum-mechanical time-dependent calculation for Auger processes in the volume of metals

Abstract

Auger charge-transfer processes occurring in the volume of metals have been formulated in full quantum mechanically. The time-dependent Hamiltonian describing these processes is written down using the jellium model, and solved using the Keldysh Green function formalism. Our calculated self-energies take into account single-particle and plasmon excitations. We find the mathematical conditions under which the quantummechanical solution will be well approximated by the semiclassical solution of a rate equation. We perform numerical calculations for the He/Al system, and find that the semiclassical solution is an excellent approximation in this case.

Interference between resonant and Auger mechanisms for charge-exchange processes near surfaces

“…Details have been published elsewhere. 12,27,28 Let us only summarize here that the basic quantity we need is the two-times retarded self-energy ⌺(t,tЈ). This quantity can be found using the equations of motion method and, as in the static case, keeping terms to lowest order in the interaction integrals.…”

“…Both use the exact but much more affordable calculation of ⌺ A (t,tЈ) in the bulk of the metal done in Ref. 28 and assume an exponential decay away from the surface when either t or tЈ are such that the corresponding perpendicular distance is outside the jellium edge. As we said before, this exponential decay is found approximately in explicit calculations of the Auger transition rates.…”

“…As we said before, this exponential decay is found approximately in explicit calculations of the Auger transition rates. 24 In our first Ansatz ⌺ AC,AL (t,tЈ) are written down 28 as (tϪtЈ) are the exact bulk self-energies, ⌬ AC (t) is the static full width at half maximum ͑FWHM͒ of the peak in the static density of states calculated in Sec. II and t j is the time at which the ion coordinate perpendicular to the surface equals the jellium edge position z j .…”

“…This Ansatz implies to use the SCA outside the jellium edge and it is justified because in Ref. 28 the SCA was found to be a vey good approximation for describing Auger processes alone. With respect to Auger loss processes, these processes can only take place when the final position of the energy level is above the Fermi level and this is inside the jellium edge in our case: hence Eq.…”

“…This Ansatz has the problem that the Auger self-energies are discontinuous functions of t and tЈ at t j which leads to discontinuities in the derivative of the atomic occupancy at t j . 28 To ascertain how serious the problem is we make a second Ansatz in which the Auger self-energy has a form similar to the resonant selfenergy. We notice in Eq.…”