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INELASTIC X-RAY SCATTERING FROM COPPER K SHELL ELECTRONS AT INTERMEDIATE
MOMENTUM TRANSFER
V. Marchetti, C. Franck
To cite this version:
V. Marchetti, C. Franck. INELASTIC X-RAY SCATTERING FROM COPPER K SHELL ELEC-
TRONS AT INTERMEDIATE MOMENTUM TRANSFER. Journal de Physique Colloques, 1987, 48
(C9), pp.C9-855-C9-858. �10.1051/jphyscol:19879153�. �jpa-00227265�
JOURNAL DE PHYSIQUE
Colloque C9, supplBment au n012, Tome 48, dBcembre 1987
INELASTIC X-RAY SCATTERING FROM COPPER K SHELL ELECTRONS AT INTERMEDIATE MOMENTUM TRANSFER
V. MARCHETTI and C. FRANCK
Laboratory of Atomic and Solid State Physics and Materials Science Center, Cornell University, Ithaca, NY 14850, U.S.A.
Abstract:
We have used a coincidence technique to measure the inelastic x ray scattering spectrum from copper K-shell electrons at an incident energy of 70 keV. We cover a range of momentum transfers tLq over which 0.5
5
qa5
1.1, where a is the Bohr radius of the copper K-shell. This is a momentum transfer regime in which the impulse approximation is no longer valid. The data presented are compared to the results of a one-electron calculation and agree well in both spectral shape and absolute cross section. In contrast with previous work of this type we do not see separate spectral features attributable to Raman and Compton scattering.The scattering of x rays by bound electrons is, in the case where the binding energy is small compared to the free electron Compton shift, described- well by the impulse approximation, in which the spectrum of scattered x rays yields the Compton profile, which is directly related to the momentum distribution of the electron initial state. The above condition is
,
for electrons in hydrogenic orbitals, equivalent to the conditionI
30 40 50 60 70
Scottered X Roy Energy (Lev)
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19879153
C9-856 JOURNAL DE PHYSIQUE
where Aq is the momentum change of the x ray upon scattering, and a is the radius of the electron orbital. Here we present data for a case in which q a w 1 and the impulse approximation is no longer valid. The spectrum of scattered x rays agree well, in both shape and absolute magnitude, with a simple one electron model. A more complete description of this work is published elsewhere.[l] The scattering is of 70 keV x rays from the K shell electrons of copper. The scattering from the K shell is isolated by detecting scattered x rays in coincidence with the characteristic K fluorescence x ray emitted in the decay of the K shell hole. A similar experiment has been performed for 59.6 keV x rays scattered from the K shell electrons of Fe and Cu.[2] However, the spectra in that work were distorted by false coincidences possibly caused by detector to detector scattering.[3] That work claimed to show two distinct features in the scattered x ray spectrum: A peak near the threshold energy (i.e. the incident x ray energy Eo minus the K shell binding energy EB), termed the Raman peak; and a separate broader feature at lower energies termed the Compton peak. The position of this Compton peak was roughly what would be predicted from an energy and momentum conservation argument similar to that which yields the free electron Compton shift, but including the binding energy term. This double structure has been supported by an OPW calculation.[4]
The results of our work are in direct contradiction with these earlier results.
Fig 1 b
I
30 40 50 60 70
Scattered X Ray Energy (keV)
Fig l c
This experiment was performed at the Cornell High Energy Synchrotron Source (CHESS) using 70 keV incident x rays derived from wiggler radiation. Two solid state detectors viewed a 7.7 pm copper
foil target. An intrinsic Germanium (IG) detector detected x rays scattered through angle 8. A Si(Li) detector detected characteristic copper K fluorescence x rays. A fast-slow coincidence system enabled the recording of events in which a scattered x ray was emitted in coincidence with a fluorescence x ray. Accidental events were measured by taking equivalent spectra with the scattered x ray detector output delayed with respect to the output of the fluorescence detector.
The spectra of inelastically scattered x rays were measured a t incident energy Eo = 70 keV at four scattering angles 6' = 49", 70°, 89", and 118", and at Eo = 62 keV for 8 = 89'. These spectrn are shown in Figs. la-le. The solid curves in each case are the result of a one electron model calculation of the inelastic scattering cross section[5] in the Hartree-Fock-Slater approximation using Herman-Skilman atomic potentials. The triple differental cross section which is the ordinal unit in Figs la-e results from considering the process as differential in the solid angles of the emitted fluorescence x ray. The theoretical cross sections were converted to this scale using:
where U K is the K shell radiative de- cay efficiency.[b] The implicit assumption here is that the fluorescent decay follow- ing photoabsorption is isotropic and oc- curs with the same efficiency as in decay following other excitation processes. The experimental data were normalized inde- pendently of the theory by measuring total fluorescent rates; the normalization scales have an estimated uncertainty of f 40%.
This error in normalization is the same for
L 1 I
30 40 50 60 70
Scattered x Roy Energy (keV)
Fig 1 d
30 I 40 50 60 70
Scattered X Roy Energy (keV) Fig le
Fig la-e Inelastic scattering cross section of x rays from copper K shell electrons. See text for explanation of units of ordinate axis. Scattering is at incident energy Eo, scattering angle 8. Momentum transfer qoa corresponds to an elastic scattering from the K she1 at that energy and scattering angle; hqo = 2 E o / c sin(8/2), a is the copper K shell Bohr radius.
C9-858 JOURNAL DE PHYSIQUE
all spectra displayed. A typical spectrum (lb) contains a total of 1677 coincidence counts and represents x 6.5 hrs. of data acquisition time a t an incident photon flux of 1 x 10' ylsec.
Possible sources of false coincidences have been considered. These include detector-to-detector scattering, in which a high energy x ray scatters from the fluorescence x ray detector into the scattered detector. The recoil energy deposited in the fluorescence x ray detector mimics a copper K fluorescence x ray.
This was avoided by placing 3.2 mm. lead shielding between the detectors. A test of this shielding was made by blocking the direct path from sample to scattered x ray detector so that a signal observed could only come from directions other than the sample. The signal observed with the sample blocked was statistically consistent with there being no such signal from directions other than the sample direction. Another source of false coincidences is a scattering event into the scattered x ray detector followed by a fluorescence emission when the Compton recoil electron ionizes another copper atom. Our estimate [I] of this process showed that it contributes a negligible
signal in this system. A third source of false coincidences is photoabsorption (followed by fluorescent decay), and a bremsstrahlung photon emitted by the photoelectron into the scattered photon detector. Our estimate of this process [I] yielded the result that it is negligible in the region near threshold, but could be responsible for some of the scattering signal seen below 35 keV
.
These spectra, which cover a range of momentum transfers 0.53 2 qoa 5 1.11, a range in which the impulse approximation is no longer valid in describing the ihelastic scattering process, show only a single feature; a broad peak which is cut off by the threshold edge required by energy conservation. We do not see a second peak at lower scattered x ray energy (higher energy transfer) corresponding to a 'Compton' peak. This form of the spectrum is supported by a simple one- electron model calculation of the inelastic scattering from the copper atom K shell.
This work was supported by the U.S. National Science Foundation through the Materials Science Center at Cornell and through additional N.S.F. support for V.M.
[ I ] V. Marchetti and C. Franck, Phys. Rev. Lett. 59, 1557 (1987).
[2] K. Namikawa and S. Hosoya, Phys. Rev. Lett. 53, 1606 (1984).
131 S. Manninen, Phys. Rev. Lett. 57, 1500 (1986).
[4] Y. Ohmura and S. Sato, J. Phys. Soc. Jpn. 56, 1657 (1987).
[5] P. Eisenberger and P.M. Platzman, Phys. Rev. A2, 415 (1970).
[6] W. Bambynek et al., Rev. Mod. Phys. 44, 716 (1972).
