Manifestations of Collective Properties of the Degenerate Electron Gas in the (e,2e) Quasielastic Knockout Process

Abstract

It is shown that quasielastic knockout (e t 2e) of electron by a fast electron from a thin solid film presents direct information about both the k and oo dependence of the singleparticle, spectral-weight function A(k,<jo) of target electrons. We discuss the expected manifestation of Mahan-Nozieres edges and their plasmon satellites in an (e,2e) experiment side by side with that of plasmaron hole states.The high-energy, quasielastic knockout of nucleons or nucleon clusters [(£, 2/>), (p,pd),etc.] is a powerful tool for nuclear-structure research. 1 Several years ago the {e, 2e) quasielastic knockout process was proposed by Smirnov and one of the authors 2 for the investigation of electron wave functions in atoms, molecules, and thin solid films. Its advantage in comparison with the methods of positron annihilation and Compton scattering profiles 3 consists in the possibility of obtaining the momentum distribution of the target electron for the fixed value of its binding energy side by side with the fixed orientation of its quasimomentum in a monocrystal. The disadvantage of the {e, 2e) method is that it cannot be used for the investigation of thick solid (d > 250 A) or liquid targets.Subsequent papers have exhibited both various theoretical aspects of the problem mentioned 4 ** 6 (in particular the manifestation of the band structure of solids 2 * 5 * 6 ) and the first experimental results for solid 7 and gas 8 targets (with the best energy resolution at present 8 A£ ^1-2 eV). Rather rapid further experimental progress is to be expected.The first problem considered in the present paper concerns the Mahan-Nozikres edges 9 and their plasmon satellites. 10 The main difference between the (e, 2e) process and x-ray absorption considered earlier 9,10 is that the final electron is not near the Fermi surface but is ejected into the high-energy (a few keV) continuum described by plane waves. Thus only the polarization of the degenerate electron gas by the suddenly appearing deep hole is present as a collective effect (high-energy x-ray photoemission would be, of course, similar in this respect). In terms of Ref. 9 we obtain information about singularities of the deep-electron spectral-weight function Z(w) itself.For describing this effect we should generalize the formulas of our previous papers. 2,6 Namely, we should replace the quantity 6(w -£*) 6£* entering into equations for the Sommerfeld model of a degenerate electron gas 2,6 by the general electron spectral-weight function yl(k, a;). 11 We obtain d 5 a 2ink 2 (do dSl^figaE l dE 2 du> {2-nhf \aQ l A'F6(£ 0 -Ey -E 2 -(jo)A(k, OC)as the (e,2e) cross section for a unit crystal volume containing A electrons (V is the volume of the 995

Semi-relativistic (e,2e) study with twisted electron beam on Cu and Ag

“…around 1960 [1]. Originally derived for the (p, 2p) spectroscopy in nuclear physics [2], where p represents a proton, it was proposed in 1966 by Smirnov and co-workers [3] for the investigation of atomic wave functions [4], upon the replacement of the protons by electrons. Since then, it has enjoyed a widespread applications such as electron momentum spectroscopy [5].…”

A Review of (e,2e) Studies in Thin Films and Some Recent Results

“…More generally, the wavefunction would be made up of a linear combination of atomic orbitals, with the result that (4) is the Fourier transform of this characteristic orbital. The differential cross section is then (Neudatchin et al 1969) …”