Inelastic x-ray scattering from copperK-shell electrons at intermediate momentum transfers

Abstract

We give experimental spectra for 70-and 62-keV x rays inelastically scattered from the A^-shell electrons of copper. The x rays scattered from the K shell were selected by fluorescence coincidence. The scattering is in a momentum-transfer regime in which the impulse approximation is not valid, and atomic binding effects are important. The data are in agreement within experimental uncertainties in absolute scattering strength and spectra shape with a Hartree-Fock-Slater calculation. In contrast to previous work we do not see separate spectral features attributable to Compton and Raman scattering.PACS numbers: 32.80.Cy, 32.80.Hd At high momentum transfers inelastic x-ray scattering is well described by the impulse approximation x in which the spectrum of scattered x rays is determined by the momentum distribution of the electronic initial state. The aim of this work was to examine the x-ray scattering process beyond the impulse-approximation regime by inelastically scattering x-rays from deeply bound A'-shell electrons of orbital radius a at intermediate momentum transfers (qo^\/a). 2 In this momentum-transfer regime, unlike the limit qoa^>\, the electron is excited to a state which is not well described as a free-electron plane wave. Furthermore, we are sensitive to electricdipole-forbidden transitions, which are not revealed in x-ray photoabsorption spectroscopy (which is spectroscopically equivalent to the limit qa <C 1 of inelastic scattering). 3 We eliminate inelastic scattering from outer-shell electrons by detecting scattered x rays in coincidence with A'-fluorescence x rays.Previous measurements have studied the breakdown of the impulse approximation in scattering from A'-shell electrons of Cu and Fe 4,s and Ge. 6 The work on Cu and Fe by Namikawa and Hosoya 5 at q$a« 1.0, which motivated this work, indicated the existence of two features in the scattering spectrum: A "Raman" peak at small energy transfer and a separate "Compton" feature of roughly equal magnitude at large energy transfer. We show that such a splitting of the scattered x-ray spectrum would contradict a standard one-electron description of x-ray scattering from a bound electron. Our measurements, which cover a range of momentum transfers 0.53 < q$a < 1.11, do not show the separate Compton feature at high energy transfers, in agreement with the one-electron model. Manninen 7 has criticized the previous experimental results on the basis of possible false coincidences.This scattering experiment was performed on the A2 line at the Cornell High Energy Synchrotron Source. The incident beam, at energy Eo=70 or 62 keV, was obtained from wiggler radiation selected by a Si(400) double crystal monochromator tuned to a fundamental energy of 35 or 31 keV. A Cu filter attenuated the funda-mental component by a factor of 300 relative to the second harmonic. The flux in the second harmonic was estimated at ~ 10 8 photons/sec. The energy bandwidth was less than the resolution of the scattered-photon detector.Two energy-resolving detectors viewed a 7.1-fim Cu...

Compton scattering of photons by inner-shell electrons

“…We note several recent experiments involving x-ray [2][3][4] or y-ray [5] scattering in which deviations from the commonly used A 2 approximation would be expected. There are two recent experiments on Zr (Z = 40), one on the K shell [4] and the other on the L shell [3].…”

“…Suric, (a(2) P. M. Bergstrom, Jr., (2) K. Pisk, (1) and R. H. Pratt (2) Ruder Boskovic Institute, 41000 Zagreb, Yugoslavia (2) Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260 (Received 28 January 1991)…”

“…There has been considerable recent interest [2][3][4][5] in measuring the inelastic (Compton) scattering cross sections on bound atomic electrons, in circumstances in which the composite structure of the initial atomic state modifies the scattering from free particles. Accurate theoretical cross sections for Compton scattering by bound inner-shell electrons are needed as basic data with which experiments may be compared, to provide insight into the nature of the response of the composite system and to separate this process from others of experimental concern.…”

Maximum-entropy analysis of one-particle densities in atoms

“…specially by means of photon-photon or photon-electron coincidence experiments [5][6][7], high resolution Compton scattering [8], angular correlation of positron annihilation radiation [9], (e, 2e) coincidence spectroscopy [10] and magnetic Compton scattering experiments [11]. However, the main problem is that the Compton profile J(q) can only be measured up to some finite value of the momentum transferred q which depends on the type of experiment.…”

Compton profiles and momentum space inequalities

“…Moreover, in the last decade the electron momentum distribution of atomic and molecular systems has been shown to be experimentally accessible [2][3][4]. Let us just remark here that the atomic Compton profiles can be obtained by means of photon-photon or photon-electron coincidence measure-ments [5][6][7], high resolution Compton scattering [8], angular correlation of positron annihilation radiation [9], (e, 2e) coincidence spectroscopy [10] and magnetic Compton scattering experiments [ 11 ].…”