Roland Ribberfors

Calculation of scattering cross sections for increased accuracy in diagnostic radiology. I. Energy broadening of Compton‐scattered photons

In this work, scattering cross sections differential with respect to both the scattering angle and the energy of the scattered photon are derived in the relativistic impulse approximation for the light elements H, Be, and Al, and photon energies between 30 and 200 keV. The energy broadening of the scattered photons reflects the momentum distribution of the target electrons. It increases with both increasing atomic number of the scatterer and with scattering angle. Even in light elements, the energy broadening is comparable with the intrinsic energy resolution of modern Ge spectrometers. In reconstructing primary photon energy spectra by means of a Ge spectrometer and Compton scattering techniques, i.e., by measuring the photons incoherently scattered at a given angle, the energy resolution is markedly impaired compared to direct measurements in the primary beam. This is usually explained as an effect of the nonzero acceptance angle of the detector. It is shown, however, that the fundamental energy broadening of the scattered photons is alone sufficient as an explanation. The Compton scattering technique is valuable in determining energy spectra in clinical situations. Aspects of its optimal performance are discussed. The commonly used scattering angle of 90 degrees seems adequate. At small scattering angles, the incoherent-scattering cross section is badly known due to electron-electron interactions and, for photon energies less than 100 keV, coherent scattering contributes appreciably to the total scattering even in media of low atomic number. In cases where coherent scattering dominates and where the energy degradation of the incoherently scattered photons is small compared to the energy resolution of the spectrometer, the reconstruction is simplified. The double-differential cross sections derived can be used to simplify calculations of the Compton component of the mass-energy absorption coefficient.

Compton spectroscopy in the diagnostic x-ray energy range. II. Effects of scattering material and energy resolution.

The overall performance of a Compton spectrometer and, in particular, its energy resolution are investigated both experimentally and theoretically for different scattering materials. Using low-Z (less than or equal to 8) scatterers of moderate sizes (scatterer diameter d less than or equal to 5 mm), there are negligible disturbances due to coherent and/or multiple scattering at 90 degrees scattering angle and photon energies above 20 keV. Two factors contribute to decreasing the energy resolution compared with that in direct measurements: (i) the velocity distribution of the electrons in the scatterer and (ii) the scattering geometry. Of these, (i) is dominant for photon energies less than or equal to 100 keV. The optimal scattering material is a metal of as low Z as possible, i.e. beryllium. However, polyethylene and lucite are normally sufficiently good scatterers. The scattering geometry may become the dominating factor decreasing energy resolution at high photon energies hv greater than or equal to 150 keV.

A compton scattering spectrometer for determining X-ray photon energy spectra

With the use of more sophisticated diagnostic technologies it is becoming increasingly important to know the energy spectra of the primary photons from clinical x-ray tubes. At the high fluence rates used under working conditions, it is necessary to greatly reduce the number of photons to the detector per unit time in order to avoid pulse pile-up. The Compton scattering method is very suitable for this reduction and hence it has been further developed in this work in the primary-photon energy range 20-200 keV. The movement of the electrons in the scattering target causes an energy broadening of the Compton scattered photons. This broadening results in a decreased energy resolution, which is particularly seen as a smearing out of the characteristic x-ray peaks of the anode material. Comparison between the spectrum obtained using a Compton spectrometer and unfolded with our reconstruction and the spectrum measured directly in the primary beam shows very good agreement even though relatively simple reconstruction algorithms have been used.

Compton component of the mass-energy absorption coefficient: corrections due to the energy broadening of compton-scattered photons

The velocity distribution of atomic electrons causes an energy broadening of photons Compton scattered through a given angle. The energy distribution of the photons is peaked at the Compton energy (that of photons scattered against free electrons at rest). Doubly differential incoherent scattering cross sections calculated in the relativistic impulse approximation show that the broadening is asymmetric around the Compton energy, particularly for photon energies <200 keV and when energy transfers are in the neighborhood of an absorption edge in the atom. Here, doubly differential cross sections are used in calculations of the incoherent energy absorption cross section

Measurements of high energy photon spectra of synchrotron radiation from a storage ring

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A study of a rotating rod carrying a collar using Lagrange's equation of motion and variational calculus

. The values derived deviate considerably from those in standard tabulations. Neglect of the energy broadening leads to an underestimate of the true energy transferred to Compton electrons and hence to too low values of

Relativistic Compton scattering from a relativistic maxwellian distribution of electrons

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Relationship of the relativistic Compton cross section to the momentum distribution of bound electron states

. Since photoelectric absorption predominates in cases when the energy broadening su...

Relationship of the relativistic Compton cross section to the momentum distribution of bound electron states. II. Effects of anisotropy and polarization

Abstract A new method for measuring the photon fluences and polarization degree, in different points, from high energy synchrotron radiation has been developed. Radiation from a beam of photons was scattered under right angles in two independent directions and the scattered radiation was measured and deconvoluted in order to obtain information about the original spectra. The results agree very well with theoretical calculations using experimental parameters for the National Synchrotron Light Source (NSLS) at Brookhaven National Laboratory (BNL), USA.

The compton spectrometer

In this paper we use Lagranges equation of motion to study a rotating rod carrying a collar. The focus is on how the shape of the rod affects the velocity of the collar. The calculus of variations is used to find the shape that gives the least time of travel along the rod.