A simple model for SMC-and SMD-processes including quasiparticle and phonon excitations is presented. Emission spectra and angular distributions are calculated without free parameters for 93-Nb(n, n'), (n, p) and incidence energies between 5 and 26 MeV.

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,), (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

The process of quasielastic knock-out of an electron by the projectile electron (e, 2e) allows one to study the k-and also &-dependence of the single-particle spectral density A ( k , E ) . The plasmaronhole excitations of the metal conduction band and the modification of Mahan-NoziBres singularities in the production of a deep hole in a metal are considered as examples. Depending upon the experimental procedure the (e, 3e) and (y, 2e) processes of knocking out the electron pair provide direct information either about the two-hole spectral density B(k,, k,, E ) or about the Fourier image f k , k , ( q ) of the electron-electron correlator f ( r 2 ) .Der ProzeB des quasielastischen ,,Herausbrechens" eines Elektrons durch ein Projektilelektron (e, 2e) erlaubt, die k-und auch die E-Abhangigkeit der Einteilchenspektraldichte A ( k , E ) zu untersuchen. Die Plasmaron-Loch-Anregungen des Metall-Leitungsbandes und die Modifizierung der Mahan-NoziBres-Singularitaten bei der Erzeugung eines tiefen Loches in einem Metal1 werden als Beispiele betrachtet. In Abhangigkeit von dem experimentellen Verfahren liefern die (e, 3e)-und (y, 2e)-Prozesse des Herausbrechens eines Elektronenpaares direkte Informationen entweder iiber die Zwei-Locher-Spektraldichte B(k,, k,, e ) oder iiber das Fourierdiagramm f k , k , ( q ) des ElektronElektron-Korrelators f ( r 2 ) .

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