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Scofield's theory confirmed

Measuring partial photoionization cross sections makes X-ray-analytical laboratory investigations more reliable

PTB-News 3.2015
Especially interesting for

non-destructive analysis of materials

process control

manufacturers of X-ray-analytical laboratory devices

validating models in nuclear physics

By means of improved measurement procedures, PTB employees from the field of spectrometry with synchrotron radiation have succeeded – in cooperati-on with partners from industry – in experimentally confirming the different energy dependences of partial photoionization cross sections which could so far be predicted only by theoretic calculations. Due to this, the quantification approach of an energy-independent ratio of the partial cross sections, which is often used in particular in X-ray fluorescence analysis, has been refuted.

Comparison of different data for the partial photoionization cross sections of the palladium L1 subshell. At higher excitation energies, the approach of an energy-independent ratio (red) shows deviations of up to a factor of 4.

X-ray fluorescence (XRF) analysis is frequently used to analyze materials in the lab in order to measure the total content of certain elements or the mass per area. Hereby, the content of certain elements is deduced from the intensity of element-specific X-ray fluorescence curves. The quantitative indication of this content is done using Sherman's fundamental parameter approach which was drawn up in 1955. Here, atomic fundamental parameters – such as photoionization cross sections and fluorescence yields – describe the probabilities of X-ray excitation and of X-ray fluorescence decay in the interaction between X-radiation and matter.

The partial photoionization cross section indicates the probability of the excitation of an electron from a specific subshell to be excited. There are two different approaches to describe the way the cross sections depend on the energy of the exciting X-ray photons for different subshells. For simplification purposes, the approach stating that the ratio of the cross sections is assumed to be constant for different subshells is often selected. Model computations in nuclear physics realized by Scofield had, however, predicted as early as in the 1970s that this does not apply to subshells with orbitals of different symmetry and that the relation with the exciting photon energy changes in this case.


In PTB's laboratory at the electron storage ring BESSY II, this predicted energy dependence has now been successfully demonstrated experimentally for the first time by using radiometrically calibrated XRF instrumentation. The results clearly show that the different energy dependences must be taken into account for a reliable elemental analysis with small uncertainties.




Philipp Hönicke
Department 7.2 Cryophysics and Spectrometry
Phone: +49 (0)30 3481-7174
E-mail: philipp.hoenicke(at)ptb.de


Scientific publication

P. Hönicke, M. Kolbe, M. Müller, M. Mantler, M. Krämer, B. Beckhoff: Experimental verification of the individual energy dependencies of the partial L-shell photoionization cross sections of Pd and Mo. Physical Re-view Letters 113, 163001 (2014)