BL Practice: BL08W, Cherion School 2015

Compton scattering measurement withLaue‐geometry spectrometer
Masayoshi Itou, Marek Brancewicz, Yoshiharu Sakurai (JASRI / SPring‐8)
Abstract
When A.H. Compton discovered "Compton scattering", a broadening of scattered X‐raypeak was also captured. Now, the broadening is used for studies of electronic states ofatoms. In high energy beamline BL08W, a Laue‐geometry wave dispersive spectrometeris installed for Compton scattering measurement. In the practice, we will measure
one‐dimensional projections of electron momentum density distribution of a single
crystal.

Introduction to Compton scattering
Compton scattering is a phenomenon of inelastic scattering of a photon on a free or
weekly bounded electron. During this process photon is transferring a part of his energy
to the electron, which is knocked out from the atom. To fulfill this condition energy ofthe photon must be significantly bigger than the binding energy of the electron.
Therefore the hard X‐rays high‐energy synchrotron radiation or γ‐rays radioactive
isotopes are the most commonly used sources of photons in Compton spectroscopy.
Scattered photon energy can be calculated using quantum approach to the energy andmomentum conservation rules. In the simplest case, when scattering of a photon on
is equal to:electron at rest is considered this energy

1whereis an incident photon energy,

1

cos

(1)

511

is electron rest mass andis ascattering angle. This means that in the spectrum of scattered photons two lines will beobserved. The one of energy ω corresponding to elastically scattered photons without

energy transfer and the lower energy

corresponding to the inelastically scatteredphotons.
But the electrons in matter are never at rest. When electron is considered as a movingobject, the energy of scattered photons′

where′ can be expressed as:

111c(2)cos

is an electron energy. As can be easily observed an additional term appears

compared to the equation 1 that is dependent from the electron momentum z
component, where z axis is specially chosen to be a scattering vector

direction.

Scattered photon energy is not constant anymore and the spectral shape of its line isbroadened due to the Doppler effect from the moving electrons and is usually called theCompton profile

Fig. 1 .
10.4
0.2
0050

elastic scattering

0.6

Compton scatteringcounts0.8

fluorescence X-rays

105 ]100150energy (keV)

Energy profile of Nb (E0 =115.5keV =165 deg)

Fig. 1. X‐ray energy spectrum from Nb measured by Ge‐SSD with a scattering
angle of 165 degrees. The incident X‐ray energy is 115.5 keV at elastic peak andthe Compton scattered X‐ray line at 80 keV is broadened by Doppler shift incollision between the photons and moving electrons.

Electron energy and momentum are strictly connected with a state of this electron in
atom band structure . Therefore it is easily to conclude that the Compton scattering ona different materials different atoms and band structures will give the different shapeof a Compton peak. This shape is directly connected with an electron momentum density
distribution:

(3)and is schematically shown on Fig. 2.

Fig. 2. Schematic drawn of the relationships between the 3D electron,and 1D
momentum density distribution
its 2D projection
projection
Compton profile .

Electron momentum density distribution is anisotropic. This anisotropy comes from theanisotropic electron wave functions and the influence of a crystal potential. For thisreason Compton profiles measured along the different crystal orientations are slightlydifferent. In order to get the full 3D or 2D electron momentum density one needs tomeasure an adequate number of directional Compton profiles and use one of thereconstruction methods

eg. Direct Fourier transformation method or maximum

entropy method . The more Compton profiles measured the better reconstruction
results are usually obtained.

Compton experiment
Most of the Compton experiments require high incident photon energy especially forheavy materials study. The only beamline in SPring‐8 that can provide this is the BL08W
station with the multipole wiggler as a source of high energy X‐rays 110 – 300 keV .
The main equipment on this station is a high resolution Cauchois‐type Compton
spectrometer dedicated for Compton scattering measurements Fig. 3 .

Fig. 3. High energy 115.6 keV synchrotron radiation and high resolution 0.10
a.u. Cauchois‐type X‐ray Compton spectrometer at SPring‐8 beamline
BL08WPracticeIn the beamline practice BL08W , we will measure a series of directional Compton
profiles for vanadium crystal cubic along the crystallographic directions between
100 and 110 . The aim of this experiment is to observe Compton profile anisotropy
differences between the measured Compton profiles and reconstruct the 2D electron
momentum density distribution in the

100 ‐ 110plane using direct Fouriertransformation program widely used on the BL08W.

Literature
1 “X‐ray Compton Scattering”, eds M. J. Cooper et al., Oxford University Press, 2004
2 “Compton Scattering: Tool for the Investigation of Electron Momentum Distribution”,
ed. B. Williams, McGraw‐Hill International Book Co., 1977