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Fundamental Parameter Initiative

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Overview and calculation of X-ray K-shell transition yields for comprehensive data libraries

142,143,144,36,145,146,97,41L. Martins, P. Amaro, S. Pessanha, M. Guerra, J. Machado, M.L. Carvalho, J.P. Santos, P. Indelicato
X-Ray Spectrometry 49(3), 398-423, 2020

The simulation of atomic relaxation relies on data libraries with tabulated partial fluorescence yield values of radiative transitions, commonly derived from the Evaluated Atomic Data Library (EADL). However, recent studies support that the data library EADL could be improved by adopting Scofield's Hartree-Fock calculations instead of current Scofield's Hartree-Slater calculations. This work presents a bibliography overview of relevant atomic parameter values in order to verify the partial fluorescence yields presented in EADL. The references include libraries and articles, in which the atomic parameter values were theoretically calculated, experimentally measured, or obtained with semi-empirical and empirical fitting formulas. We present a comparison of total K-shell fluorescence yields and partial K-L2, K-L3, K-M2, K-M3 fluorescence yields that are either obtained directly from its references, or are derived from atomic parameters presented in these references. Additionally, we obtain comprehensive partial fluorescence yield values from the combination of semi-empirical and empirical fitting functions from different references. The comparisons performed in this work confirm that total K-shell, partial K-L2, and partial K-L3 fluorescence yield values, obtained from Scofield's Dirac-Slater calculations have better agreement with the most recent empirical values. Partial K-M2, and partial K-M3 fluorescence yield values obtained from Scofield's Dirac-Fock calculation have better agreement with the most recent empirical values. Therefore, further studies should be performed before changing the EADL data library.

DOI:10.1002/xrs.3123  Keywords: K-shell

Experimental determination of L fluorescence yields of gadolinium

78,62Y. Ménesguen, M.-C. Lépy
X-Ray Spectrometry 49(5), 596-602, 2020

The fluorescence yields are useful X-ray atomic fundamental parameters for X-ray spectrometric purposes but suffer from large tabulated uncertainties, and this is the first time to our knowledge that all three subshell parameters are measured together. We determined the three L partial fluorescence yields and the associated Coster-Kronig transition probabilities of gadolinium, by selectively ionizing the three L subshells with a tunable monochromatic photon beam. We found ω 1 = 0.099(3), ω 2 = 0.162(4), and ω 3 = 0.159(3) that are in good agreement with tabulated values, but our derived uncertainties are significantly reduced.

DOI:10.1002/xrs.3157  Keywords: fluorescence yield 64Gd

Valence-to-core X-ray emission spectroscopy of titanium compounds using energy dispersive detectors

185,188,189,190,184,186,187,191,91,193,194L. Miaja‐Avila, G.C. O'Neil, Y.I. Joe, K.M. Morgan, J.W. Fowler, W.B. Doriese, B. Ganly, D. Lu, B.D. Ravel, D.S. Swetz, J.N. Ullom
X-Ray Spectrometry , 1-12, 2020

X‐ray emission spectroscopy (XES) of transition metal compounds is a powerful tool for investigating the spin and oxidation state of the metal centers. Valence‐to‐core (vtc) XES is of special interest, as it contains information on the ligand nature, hybridization, and protonation. To date, most vtc‐XES studies have been performed with high‐brightness sources, such as synchrotrons, due to the weak fluorescence lines from vtc transitions. Here, we present a systematic study of the vtc‐XES for different titanium compounds in a laboratory setting using an X‐ray tube source and energy dispersive microcalorimeter sensors. With a full‐width at half‐maximum energy resolution of approximately 4 eV at the Ti Kβ lines, we measure the XES features of different titanium compounds and compare our results for the vtc line shapes and energies to previously published and newly acquired synchrotron data as well as to new theoretical calculations. Finally, we report simulations of the feasibility of performing time‐resolved vtc‐XES studies with a laser‐based plasma source in a laboratory setting. Our results show that microcalorimeter sensors can already perform high‐quality measurements of vtc‐XES features in a laboratory setting under static conditions and that dynamic measurements will be possible in the future after reasonable technological developments.

DOI:10.1002/xrs.3183  Keywords: valence‐to‐core, XES, X‐ray emission spectroscopy 22Ti

Diagram, valence‐to‐core, and hypersatellite K β X‐ray transitions in metallic chromium

140,38,23,116,155,156,49,36,96,84,41,68,97F. Zeeshan, J. Hoszowska, J.-C. Dousse, D. Sokaras, T.-C. Weng, R. Alonso‐Mori, M. Kavčič, M. Guerra, J.M. Sampaio, F. Parente, P. Indelicato, J.P. Marques, J.P. Santos
X‐Ray Spectrometry 48, 351– 359, 2019

We report on measurements of the K β diagram, valence‐to‐core (VtC), and hypersatellite X‐ray spectra induced in metallic Cr by photon single and double K ‐shell ionization. The experiment was carried out at the Stanford Synchrotron Radiation Lightsource using the seven‐crystal Johann‐type hard X‐ray spectrometer of the beamline 6‐2. For the K β diagram and VtC transitions, the present study confirms the line shape features observed in previous works, whereas the K h β hypersatellite transition was found to exhibit a complex spectral line shape and a characteristic low‐energy shoulder. The energy shift of the hypersatellite relative to the parent diagram line was deduced from the measurements and compared with the result of extensive multiconfiguration Dirac–Fock (MCDF) calculations. A very good agreement between experiment and theory was found. The MCDF calculations were also used to compute the theoretical line shape of the hypersatellite. A satisfactory agreement was obtained between the overall shapes of the experimental and theoretical spectra, but deviations were observed on the low‐ and high‐energy flanks of the hypersatellite line. The discrepancies were explained by chemical effects, which were not considered in the MCDF calculations performed for isolated atoms.

DOI:10.1002/xrs.3019  Keywords: K-shell, satellite lines, synchrotron radiation 24Cr

Precise x-ray energies of gadolinium determined by a combined experimental and theoretical approach

78,62,42,137,34,177,178,179,180,41,68,96,36,84,97Y. Ménesguen, M.-C. Lépy, Y. Ito, M. Yamashita, S. Fukushima, M. Polasik, K. Słabkowska, Ł. Syrocki, E. Wȩder, P. Indelicato, J.P. Marques, J.M. Sampaio, M. Guerra, F. Parente, J.P. Santos
Journal of Quantitative Spectroscopy and Radiative Transfer 236, 106585, 2019

We combined different experimental techniques with a theoretical approach to determine a consistent set of diagram lines energies and binding energies. We propose an original approach consisting in determining the mass attenuation coefficients in an energy range covering the L-, M- and N- absorption edges, including a detailed evaluation of the associated uncertainties, to derive precisely the binding energies. We investigated the Lα, Lβ and M spectra of Gd with an independantly calibrated high-resolution anti-parallel double-crystal x-ray spectrometer. All the lines were identified and found in excellent agreement with the binding energies previously derived. Morever, we identified for the first time M5−O2, M4−O2,3 and M4−N2,3 diagram lines.

DOI:10.1016/j.jqsrt.2019.106585  Keywords: diagram line energies, diagram lines, MAC, mass attenuation coefficients 64Gd

Experimental determination of line energies, line widths and relative transition probabilities of the Gadolinium L x-ray emission spectrum

100,52,40,147,148,130,9M.L. Wansleben, Y. Kayser, P. Hönicke, I. Holfelder, A. Wählisch, R. Unterumsberger, B. Beckhoff
Metrologia 56(6), 065007, 2019

In this work the most intense x-ray lines of the L-emission spectrum of gadolinium with respect to line energies, natural line widths, and relative transition probabilities were investigated using monochromatized synchrotron radiation. The measurements were realized in the PTB laboratory at BESSY II by means of an in-house built von Hamos spectrometer based on up to two full-cylinder HAPG mosaic crystals. The von Hamos spectrometer is calibrated by means of elastically scattered photons from the employed synchrotron radiation beamline leading to a well-defined energy scale and an experimentally determined spectrometer response. A selective excitation of the gadolinium L subshells was carried out to ensure a robust deconvolution of neighboring emission lines of different L subshells. The experimental results are discussed in the context of existing data from common databases and published values since significant deviations, especially for the Lγ2 and Lγ3 emission lines, are observed. We further substantiate and discuss two satellite lines at the low-energy side of the Lβ2,15 and Lγ1 emission lines arising from the N4,5 subshell.

DOI:10.1088/1681-7575/ab40d2  Keywords: L shell, line width, satellite lines, synchrotron radiation 64Gd

A combined experimental and theoretical approach to determine X-ray atomic fundamental quantities of tin

78,62,96,68,84,36,41,97,40,9Y. Ménesguen, M.-C. Lépy, J.M. Sampaio, J.P. Marques, F. Parente, M. Guerra, P. Indelicato, J.P. Santos, P. Hönicke, B. Beckhoff
X-Ray Spectrometry 47(5), 341-351, 2018

The knowledge of atomic fundamental parameters, such as the mass attenuation coefficients or fluorescence yields with low uncertainties, is of decisive importance in elemental quantification involving X-ray fluorescence analysis techniques. For example, several databases giving the mass attenuation coefficients are accessible and frequently used within a large community of users. These compilations are most often in good agreement for photon energies in the hard X-ray ranges. However, they significantly differ for low photon energies and around the absorption edges of the elements. In the case of the fluorescence yields, some authors made a review of measured values found in the literature. However, reliable measurements are not so many illustrating the inherent difficulties. Mass attenuation coefficients of tin were determined experimentally in the photon energy range from 100 eV to 35 keV by using monochromatized synchrotron radiation at SOLEIL (France). The fluorescence yields of the 3 L-subshells of tin were also determined using a reflection geometry setup and the X-ray fluorescence setup of Physikalisch-Technische Bundesanstalt. The Coster?Kronig factors for the tin L-shells were also experimentally determined. The application of high-accuracy experimental techniques resulted in low uncertainty mass attenuation coefficients and L-subshell fluorescence yields that are directly compared with existing databases and with updated relativistic configuration mixing Dirac?Fock calculations including Quantum electrodynamics (QED) corrections.

DOI:10.1002/xrs.2948  Keywords: fluorescence yield, MAC 50Sn

Advances in the measurements of the mass attenuation coefficients

78,24,62Y. Ménesguen, C. Dulieu, M.-C. Lépy
X-Ray Spectrometry 48(5), 330-335, 2018

The knowledge of atomic fundamental parameters, such as mass attenuation coefficients or fluorescence yields with low uncertainties, is of decisive importance in elemental quantification involving X-ray fluorescence analysis techniques. Several databases providing the mass attenuation coefficients are accessible and frequently used within a large community of users. These compilations are most often in good agreement for photon energies in the hard X-ray ranges. However, they significantly differ for low photon energies and around the absorption edges of the elements. Mass attenuation coefficients of several elements were determined experimentally in the photon energy range from 100 eV to 35 keV by using monochromatized radiation at the SOLEIL synchrotron (France). The application of high-accuracy experimental techniques resulted in low uncertainty mass attenuation coefficients. The results are compared with tabulated data.

DOI:10.1002/xrs.2991  Keywords: MAC

Relative L3 transition probabilities of titanium compounds as a function of the oxidation state using high-resolution X-ray emission spectrometry

130,40,86,79,9R. Unterumsberger, P. Hönicke, B. Pollakowski-Herrmann, M. Müller, B. Beckhoff
Spectrochimica Acta Part B: Atomic Spectroscopy 145, 71-78, 2018

The relative transition probabilities of the L3-fluorescence lines from different titanium oxides were determined using high-resolution X-ray emission spectrometry. A reliable deconvolution of the X-ray emission spectra, by means of both experimentally determined response functions and absorption correction, reduces the relative uncertainties of the relative transition probabilities to 10% for titanium and 15% for titanium dioxide. The relative L3 transition probability of metallic titanium amounts to 0.66 ± 0.07 for the Ll fluorescence line and 0.34 ± 0.07 for the L[alpha] fluorescence line, respectively. Respective database values from existing literature vary up to a factor of 3, which shows that a determination of the fundamental parameters in the soft X-ray range with low uncertainties is needed in particular with respect to surface sensitive X-ray spectrometer methods. The relative L3 transition probability for titanium dioxide is slightly changed to 0.56 ± 0.08 for the Ll fluorescence line and 0.44 ± 0.08 for the group of fluorescence lines associated to the L3 transition of titanium dioxide that can be considered equivalent to the metal L[alpha] fluorescence line.

DOI:10.1016/j.sab.2018.04.008  Keywords: transition probabilities 22Ti

Accurate experimental determination of gallium K- and L3-shell XRF fundamental parameters

130,40,20,43,100,79,9R. Unterumsberger, P. Hönicke, J.L. Colaux, C. Jeynes, M.L. Wansleben, M. Müller, B. Beckhoff
J. Anal. At. Spectrom. 33(6), 1003-1013, 2018

The fluorescence yield of the K- and L3-shell of gallium was determined using the radiometrically calibrated (reference-free) X-ray fluorescence instrumentation at the BESSY II synchrotron radiation facility. Simultaneous transmission and fluorescence signals from GaSe foils were obtained, resulting in K- and L3-shell fluorescence yield values (ωGa,K = 0.515 ± 0.019, ωGa,L3 = 0.013 ± 0.001) consistent with existing database values. For the first time, these standard combined uncertainties are obtained from a properly constructed Uncertainty budget. These K-shell fluorescence yield values support Bambynek's semi-empirical compilation from 1972: these and other measurements yield a combined recommended value of ωGa,K = 0.514 ± 0.010. Using the measured fluorescence yields together with production yields from reference Ga-implanted samples where the quantity of implanted Ga was determined at 1.3% traceable accuracy by Rutherford backscattering spectrometry, the K-shell and L3-subshell photoionization cross sections at selected incident photon energies were also determined and compared critically with the standard databases.

DOI:10.1039/C8JA00046H  Keywords: fluorescence yield 31Ga

Experimental and theoretical determination of the L-fluorescence yields of bismuth

78,62,96,68,84,36,41,97Y. Ménesguen, M.-C. Lépy, J.M. Sampaio, J.P. Marques, F. Parente, M. Guerra, P. Indelicato, J.P. Santos
Metrologia 55, 621-630, 2018

The knowledge of atomic fundamental parameters such as the mass attenuation coefficients or fluorescence yields with low uncertainties, is of decisive importance in elemental quantification involving x-ray fluorescence analysis techniques. For example, several databases giving the mass attenuation coefficients are accessible and frequently used within a large community of users. These compilations are most often in good agreement for photon energies in the hard x-ray ranges. However, they significantly differ for low photon energies and around the absorption edges of the elements. Some review articles present compilations of measured fluorescence yields values found in the literature. However reliable measurements are not so many illustrating the inherent difficulties. Mass attenuation coefficients of bismuth were determined experimentally in the photon energy range from 100 eV to 30 keV by using monochromatized synchrotron radiation at SOLEIL (France). The fluorescence yields of the three L-subshells of bismuth were also determined using a reflection geometry setup. The application of high-accuracy experimental techniques resulted in low uncertainty mass attenuation coefficients and L-subshell fluorescence yields that are directly compared to existing databases and with updated relativistic configuration mixing Dirac–Fock calculations including QED corrections.

DOI:10.1088/1681-7575/aad1d6  Keywords: fluorescence yield, L-shell 83Bi

Theoretical and experimental determination of K- and L-shell x-ray relaxation parameters in Ni

36,96,84,41,40,79,9,68,97M. Guerra, J.M. Sampaio, F. Parente, P. Indelicato, P. Hönicke, M. Müller, B. Beckhoff, J.P. Marques, J.P. Santos
Physical Review A 97(4), 042501, 2018

Fluorescence yields (FY) for the Ni K and L shells were determined by a theoretical and an experimental group within the framework of the International Initiative on X-ray Fundamental Parameters (FPs) collaboration. Coster-Kronig (CK) parameters were also measured for the L shell of Ni. Theoretical calculations of the same parameters were performed using the Dirac-Fock method, including relativistic and QED corrections. The experimental values for the FY and CK were determined at the PTB laboratory in the synchrotron radiation facility BESSY II, Berlin, Germany, and are compared to the corresponding calculated values.

DOI:10.1103/PhysRevA.97.042501  Keywords: fluorescence yield, K shell, L shell 28Ni

Measurement of K fluorescence yields of niobium and rhodium using monochromatic radiation

93,62,78,81J. Riffaud, M.-C. Lépy, Y. Ménesguen, A. Novikova
X-Ray Spectrometry 46(5), 341-346, 2017

Both reactions Nb‐93(n,n′)Nb‐93 m and Rh‐103(n,n′)Rh‐103 m are of particular importance for dosimetry in reactor, and the measurement of the activity of Nb and Rh dosimeters provides the basic data that can be traced back to the reactor operating information. These radionuclides emit only X‐rays of which emission intensities in recommended data are determined thanks to the γ‐ray transition probabilities and fluorescence yield values. In general, the knowledge of fluorescence yields is rather poor and based on old measurements. Nowadays, the use of tunable monochromatic X‐ray sources allows performing optimized measurements. In a first step, accurate values of the attenuation coefficients are measured at the metrology beam line of the SOLEIL synchrotron, using procedures such as optimized for similar measurements. In a second step, the fluorescence yields are determined using experimental approaches in a traditional experimental configuration. For both materials, several incident energies are used to get experimental spectra with energy‐dispersive spectrometer. The peaks of interest are processed using the COLEGRAM software, which allows detailed fitting of the peak shape. The K fluorescence yields are derived with about 2% relative uncertainty.

Copyright © 2017 John Wiley & Sons, Ltd.

DOI:10.1002/xrs.2757  Keywords: K fluorescence yields, synchrotron radiation 41Nb 45Rh

Experimental determination of the x-ray atomic fundamental parameters of nickel

78,62,40,79,130,9,38,23,12,42,137,34Y. Ménesguen, M.-C. Lépy, P. Hönicke, M. Müller, R. Unterumsberger, B. Beckhoff, J. Hoszowska, J.-C. Dousse, W. Błachucki, Y. Ito, M. Yamashita, S. Fukushima
Metrologia 55(1), 56-66, 2017

The x-ray atomic properties of nickel (Ni) were investigated in a unique approach combining different experimental techniques to obtain new, useful and reliable values of atomic fundamental parameters for x-ray spectrometric purposes and for comparison with theoretical predictions. We determined the mass attenuation coefficients in an energy range covering the L- and K-absorption edges, the K-shell fluorescence yield and the and transition probability ratios. The obtained line profiles and linewidths of the and transitions in Ni can be considered as the contribution of the satellite lines arising from the [KM] shake processes suggested by Deutsch et al (1995 Phys. Rev. A 51 283) and Ito et al (2016 Phys. Rev. A 94 042506). Comparison of the new data with several databases showed good agreement, but also discrepancies were found with existing tabulated values.

DOI:10.1088/1681-7575/aa9b12  Keywords: fluorescence yield, MAC 28Ni

What are the correct L-subshell photoionization cross sections for quantitative X-ray spectroscopy?

40,1,9P. Hönicke, M. Kolbe, B. Beckhoff
X-Ray Spectrometry 45, 207-211, 2016

For fundamental parameter-based, quantitative X-ray fluorescence, X-ray photoelectron spectroscopy or Auger electron spectroscopy, it is crucial to accurately know the photoionization cross sections (PCS). This atomic probability to absorb the exciting photon and eject a photoelectron, in general, followed by a subsequent decay resulting in the emission of a fluorescence photon or an Auger electron, strongly depends on the electron configuration and photon energy. Two contrary models for the photon energy dependence of the L-subshell PCS, or the 2s, 2p ½ and 2p 3/2; energy levels, respectively, exist in the literature, and an experimental verification was not available until recently. In this work, the two models for calculating the PCS are discussed, and their influence on quantitative experiments is demonstrated by means of the fluorescence production cross sections for the three L shells. Depending on the excitation conditions, these fluorescence production cross sections and, thus, the derived quantitative results can differ significantly if the wrong PCS model is employed. Copyright © 2016 John Wiley & Sons, Ltd.

DOI:10.1002/xrs.2691  Keywords: Partial L-Shell Photoionization Cross Sections, Quantitative analysis

Measurement of partial L fluorescence yields of bismuth using synchrotron radiation

78,151,152,62Y. Ménesguen, B. Boyer, M. Rodrigues, M.-C. Lépy
Applied Radiation and Isotopes 109, 133-138, 2016

Tunable monochromatic photon radiation was used to measure transmission of a bismuth target in the energy range from 7keV to 20keV. Partial L fluorescence yields of bismuth were obtained by combining measurement of the fluorescence induced by photoionization of the bismuth target and X-rays from the radioactive decay of (210)Pb. Several photon energies have been used to successively ionize the L subshells, which allowed detailed analysis of the rearrangement spectra and determination of the X-ray relative intensities of the L1, L2 and L3 series.

DOI:10.1016/j.apradiso.2015.11.081  Keywords: fluorescence yield 83Bi

Experimental determination of the oxygen K-shell fluorescence yield using thin SiO2 and Al2O3 foils

40,1,54,130,9P. Hönicke, M. Kolbe, M. Krumrey, R. Unterumsberger, B. Beckhoff
Spectrochimica Acta Part B: Atomic Spectroscopy 124, 94-98, 2016

In this work, the K-shell fluorescence yield for oxygen ωO, K-shell is determined experimentally, employing the radiometrically calibrated X-ray fluorescence instrumentation of the Physikalisch-Technische Bundesanstalt (PTB), Germany's National Metrology institute. Four free-standing thin foils with two different thicknesses of both SiO2 and Al2O3 were used in order to derive an experimental value for this atomic fundamental parameter. Multiple excitation photon energies were applied to record fluorescence spectra of all four samples. The resulting value (ωO, K-shell = 0.00688 ± 0.00036) is almost 20% higher than the commonly used value from the Krause tables [M. Krause, Atomic Radiative and Radiationless Yields for K and L shells, J. Phys. Chem. Ref. Data 8(2), 307-327 (1979)]. In addition, the achieved total uncertainty budget for the new experimental value is reduced significantly in comparison to available literature data. For validation purposes, thin SiO2 layers on Si samples were used. Here, the layer thicknesses derived from X-ray reflectometry are well in line with our X-ray fluorescence quantification results based on the new experimental value for the O K-shell fluorescence yield.

DOI:10.1016/j.sab.2016.08.024  Keywords: Atomic fundamental parameters, fluorescence yield, Quantitative analysis, X-ray fluorescence spectroscopy, X-ray reflectometry 8O

High accuracy experimental determination of copper and zinc mass attenuation coefficients in the 100 eV to 30 keV photon energy range

78,149,86,130,150,9,62Y. Ménesguen, M. Gerlach, B. Pollakowski-Herrmann, R. Unterumsberger, M. Haschke, B. Beckhoff, M.-C. Lépy
Metrologia 53(1), 7, 2016

The knowledge of atomic fundamental parameters such as mass attenuation coefficients with low uncertainties, is of decisive importance in elemental quantification using x-ray fluorescence analysis techniques. Several databases are accessible and frequently used within a large community of users. These compilations are most often in good agreement for photon energies in the hard x-ray ranges. However, they significantly differ for low photon energies and around the absorption edges of any element. In a joint cooperation of the metrology institutes of France and Germany, mass attenuation coefficients of copper and zinc were determined experimentally in the photon energy range from 100 eV to 30 keV by independent approaches using monochromatized synchrotron radiation at SOLEIL (France) and BESSY II (Germany), respectively. The application of high-accuracy experimental techniques resulted in mass attenuation coefficient datasets determined with low uncertainties that are directly compared to existing databases. The novel datasets are expected to enhance the reliability of mass attenuation coefficients.

DOI:10.1088/0026-1394/53/1/7  Keywords: MAC 29Cu 30Zn

Fundamental parameters of Zr and Ti for a reliable quantitative X-ray fluorescence analysis

1,40M. Kolbe, P. Hönicke
X-Ray Spectrometry 44(4), 217-220, 2015

Employing characterized beamlines as well as radiometrically calibrated detection systems in the Physikalisch-Technische Bundesanstalt laboratory at the electron storage ring BESSY II in Berlin, fundamental parameters of the Zr (L subshells) and the Ti (K shell) have been experimentally determined and compared to available literature data. This study is mainly focused on the provision of a reliable uncertainty budget based on the calibrated instrumentation. Using a reference-free X-ray fluorescence approach and an advanced evaluation procedure without any input from databases, fundamental parameters, such as Coster–Kronig probabilities as well as fluorescence yields, are determined with both decreased and reliable uncertainties. Copyright © 2015 John Wiley & Sons, Ltd.

DOI:10.1002/xrs.2603  Keywords: fluorescence yield 22Ti 40Zr

Theoretical and experimental determination of L-shell decay rates, line widths, and fluorescence yields in Ge

36,96,63,84,41,68,97,38,23,61,140,79,130,9M. Guerra, J.M. Sampaio, T.I. Madeira, F. Parente, P. Indelicato, J.P. Marques, J.P. Santos, J. Hoszowska, J.-C. Dousse, L. Loperetti, F. Zeeshan, M. Müller, R. Unterumsberger, B. Beckhoff
Physical Review A 92(2), 022507, 2015

Fluorescence yields (FYs) for the Ge L shell were determined by a theoretical and two experimental groups within the framework of the International Initiative on X-Ray Fundamental Parameters Collaboration. Calculations were performed using the Dirac-Fock method, including relativistic and QED corrections. The experimental value of the ω L3 was determined at the Physikalisch-Technische Bundesanstalt undulator beamline of the synchrotron radiation facility BESSY II in Berlin, Germany, and the L α 1,2 and L β 1 line widths were measured at the Swiss Light Source, Paul Scherrer Institute, Switzerland, using monochromatized synchrotron radiation and a von Hamos x-ray crystal spectrometer. The measured fluorescence yields and line widths are compared to the corresponding calculated values.

DOI:10.1103/PhysRevA.92.022507  Keywords: fluorescence yield 32Ge

Approaches for theoretical and experimental determinations of K-shell decay rates and fluorescence yields in Ge

96,63,68,84,154,41,97,62,78J.M. Sampaio, T.I. Madeira, J.P. Marques, F. Parente, A. M. Costa, P. Indelicato, J.P. Santos, M.-C. Lépy, Y. Ménesguen
Physical Review A 89, 012512, 2014

Fluorescence yields are one of the fundamental parameters in atomic physics and related areas. Despite the increase of experimental work in the last decade, to obtain values of K-shell fluorescence yields available data are scarce or outdated for many elements. The available theoretical results cannot fill the gap since quite often they are derived from semi-empirical calculations based on old models. This is the case of Ge that has many applications in science. In this work, we present the results of a collaboration between an experimental and a theoretical group to obtain the decay rates and fluorescence yields for Ge. The calculations were performed within the Dirac-Fock method, including relativistic and QED corrections, using a state-of-the-art approach. The experimental work was carried out at the SOLEIL synchrotron and the fluorescence yields were measured by two distinct methods: the reflection geometry method and the escape peak method. The results show a very good agreement between the experiment and theory (1.1%), well within the experimental uncertainty (2.4%).

DOI:10.1103/PhysRevA.89.012512  Keywords: Dirack-Fock, experiment, fluorescence yield 32Ge

Experimental Verification of the Individual Energy Dependencies of the Partial L-Shell Photoionization Cross Sections of Pd and Mo

40,1,79,66,55,9P. Hönicke, M. Kolbe, M. Müller, M. Mantler, M. Krämer, B. Beckhoff
Physical Review Letters 113(16), 163001, 2014

An experimental method for the verification of the individually different energy dependencies of L1-, L2-, and L3- subshell photoionization cross sections is described. The results obtained for Pd and Mo are well in line with theory regarding both energy dependency and absolute values, and confirm the theoretically calculated cross sections by Scofield from the early 1970 s and, partially, more recent data by Trzhaskovskaya, Nefedov, and Yarzhemsky. The data also demonstrate the questionability of quantitative x-ray spectroscopical results based on the widely used fixed jump ratio approximated cross sections with energy independent ratios. The experiments are carried out by employing the radiometrically calibrated instrumentation of the Physikalisch-Technische Bundesanstalt at the electron storage ring BESSY II in Berlin; the obtained fluorescent intensities are thereby calibrated at an absolute level in reference to the International System of Units. Experimentally determined fixed fluorescence line ratios for each subshell are used for a reliable deconvolution of overlapping fluorescence lines. The relevant fundamental parameters of Mo and Pd are also determined experimentally in order to calculate the subshell photoionization cross sections independently of any database.

DOI:10.1103/PhysRevLett.113.163001  Keywords: Partial L-Shell Photoionization Cross Sections 42Mo 46Pd

A critical analysis of the experimental L-shell Coster–Kronig and fluorescence yields data

83T. Papp
X-ray Spectrometry 41(3), 128-132, 2012

A critical analysis of the methods used to determine the L-shell Coster–Kronig and fluorescence yield data are given. The collected data sets have a large scatter, indicating methodological issues. The Kα-L coincidence technique and the synchrotron ionization methods are analyzed in detail, and it is demonstrated that both methods have unrecognized systematic errors. It is emphasized that the synchrotron measurements clearly show deviations from the exclusively used exponential form of the energy dependence of the photoionization cross-section. Thus, the far-range extrapolation introduces an error, which magnitude is difficult to assess. Comment on the use of polarization-sensitive devices to detect polarized X-ray is offered. New strategies are recommended for the measurement of these parameters. Copyright © 2012 John Wiley & Sons, Ltd.

DOI:10.1002/xrs.2367  Keywords: Coster-Kronig, fluorescence yield, L shell

L-subshell fluorescence yields and Coster-Kronig transition probabilities with a reliable uncertainty budget for selected high- and medium-Z elements

1,40,79,9M. Kolbe, P. Hönicke, M. Müller, B. Beckhoff
Physical Review A 86(4), 042512, 2012

Photon-in/photon-out experiments at thin specimens have been carried out to determine L-subshell fluorescence yields as well as Coster-Kronig transition probabilities of Au, Pb, Mo, and Pd using radiometrically calibrated instrumentation in the Physikalisch-Technische Bundesanstalt (PTB) laboratory at the electron storage ring BESSY II in Berlin. An advanced approach was developed in order to derive the fluorescence line intensities by means of line sets of each subshell that were corrected for self-absorption and broadened with experimentally determined detector response functions. The respective photoelectric cross sections for each subshell were determined by means of transmission measurements of the same samples without any change in the experimental operating condition. All values derived were compared to those of earlier works. A completely traceable uncertainty budget is provided for the determined values.

DOI:10.1103/PhysRevA.86.042512  Keywords: Coster-Kronig transition probability, fluorescence yield, L-shell 42Mo 46Pd 79Au 82Pb

Characterization of the Metrology beamline at the SOLEIL synchrotron and application to the determination of mass attenuation coefficients of Ag and Sn in the range 3.5 keV≤E≤28 keV

78,62Y. Ménesguen, M.-C. Lépy
X-Ray Spectrometry 40, 411-416, 2011

This work presents the new Metrology beamline at the SOLEIL synchrotron facility and a first attempt to quantitative measurements of mass attenuation coefficients for Ag and Sn performed on the hard X‐ray branch. We first describe the beamline itself and the characterization performed of the unfocused monochromatic beam running mode. We performed a first experimental measurement of mass attenuation coefficients in the range 3.5 ≤ E  ≤ 28 keV and we also derived the K‐absorption and L‐absorption jump ratios. The results are compared with theoretical values as well as with other experimental data and agree well with previous published values. Copyright © 2011 John Wiley & Sons, Ltd.

DOI:10.1002/xrs.1366  Keywords: MAC 47Ag 50Sn

Cascade L-shell soft-x-ray emission as incident x-ray photons are tuned across the 1s ionization threshold

116,53,79,1,9,66,139,4,59,47D. Sokaras, A. Kochur, M. Müller, M. Kolbe, B. Beckhoff, M. Mantler, C. Zarkadas, M. Andrianis, A. Lagoyannis, A.G. Karydas
Physical Review A 83(5), 052511, 2011

The cascade L-shell x-ray emission as an incident polarized and unpolarized monochromatic radiation overpass the 1s ionization threshold is investigated for the metallic Fe by means of moderate resolution, quantitative x-ray spectrometry. A full ab initio theoretical investigation of the L-shell x-ray emission processes is performed based on a detailed straightforward construction of the cascade decay trees within the Pauli-Fock approximation. The agreement obtained between experiments and the presented theory is indicated and discussed with respect to the accuracy of advanced atomic models as well as its significance for the characterization capabilities of x-ray fluorescence (XRF) analysis.

DOI:10.1103/PhysRevA.83.052511  Keywords: cascade effect, L shell, soft x-rays 26Fe

Mass attenuation coefficients in the range 3.8 ≤ E ≤ 11 keV, K fluorescence yield and Kα/Kβ relative X-ray emission rate for Ti, V, Fe, Co, Ni, Cu and Zn measured with a tunable monochromatic X-ray source

78,62Y. Ménesguen, M.-C. Lépy
Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 268(16), 2477-2486, 2010

This work presents new measurements of mass attenuation coefficients in the range 3.8 E 11 keV , K-absorption jump-ratios, K [alpha] and K [beta] fluorescence yields for Ti, V, Fe, Co, Ni, Cu and Zn. We use the experimental facility SOLEX, a tunable monochromatic X-ray source combined with an energy-dispersive high-purity germanium detector. The results are compared with theoretical values as well as with other experimental data and show a relatively good agreement. However, the derived K-jump-ratios appear larger than those widely used in the XCOM database. The K [alpha] and K [beta] fluorescence yields and the corresponding relative emission rates K [beta] / K [alpha] are also derived, which was made possible by the use of energy-dispersive detectors with good spectral resolution.

DOI:10.1016/j.nimb.2010.05.044  Keywords: K [beta] / K [alpha] relative X-ray emission rate, K-absorption jump-ratio, K-fluorescence yield, Mass absorption coefficient 22Ti 23V 26Fe 27Co 28Ni 29Cu 30Zn

Synchrotron-radiation-based determination of Xe L-subshell Coster-Kronig yields: A reexamination via high-resolution x-ray spectroscopy

16,23,38,141,49,13W. Cao, J.-C. Dousse, J. Hoszowska, M. Žitnik, M. Kavčič, K. Bucar
Physical Review A 81(1), 012501, 2010

The xenon L-subshell Coster-Kronig (CK) transition yields were revisited via high-resolution measurements of the Lα1,2 (L3−M4,5) and Lβ1 (L2−M4) x-ray emission lines. The L x-ray spectra were measured employing a Johansson-type curved crystal spectrometer and energy-tunable synchrotron radiation. The CK yields were derived from the relative L x-ray intensity jumps at the L edges by fitting the fluorescence intensities as a function of the photon energy to the L-subshell photoionization cross sections. The latter were obtained from the measured L-edge photoabsorption spectrum. Values of 0.118±0.029, 0.383±0.037, and 0.096±0.016 were found for the f23, f13, and f12 CK yields, respectively. Thanks to high resolution, the L1 fluorescence yield of 0.059±0.002 was also determined from intensity ratios of the well-resolved Lβ4 (L1−M2) and Lβ1 (L2−M4) lines.

DOI:10.1103/PhysRevA.81.012501  Keywords: Coster-Kronig, L-shell, synchrotron radiation 54Xe

Resonant Raman scattering of polarized and unpolarized x-ray radiation from Mg, Al, and Si

116,79,1,9,139,47D. Sokaras, M. Müller, M. Kolbe, B. Beckhoff, C. Zarkadas, A.G. Karydas
Physical Review A 81, 012703, 2010

The x-ray resonant Raman scattering (RRS) effect of polarized and unpolarized radiation in the vicinity of the 1s absorption threshold of low-Z elements such as magnesium, aluminum, and silicon is investigated. For the polarized and tunable exciting x-ray radiation the plane grating monochromator (PGM) beam line at the PTB

laboratory in the BESSY II synchrotron radiation facility was employed, while unpolarized x-ray beams were induced by 1-MeV proton beam irradiation on various pure thick targets. For the latter case, a novel proton-induced x-ray fluorescence scattering chamber was designed and installed at the Tandem accelerator laboratory of the Institute of Nuclear Physics at N.C.S.R. “Demokritos.” The total RRS cross sections deduced from both independent excitation modes were found to be in a good agreement, within the experimental uncertainties. The predictions of the existing theory with respect to the dependence of the RRS to the incident beam polarization state is calculated and discussed with respect to the experimental results.

DOI:10.1103/PhysRevA.81.012703  Keywords: polarized radiation, Resonant Raman cross section, unpolarized radiation 12Mg 13Al 14Si

Energies and widths of atomic core-levels in liquid mercury

64,23,38Y.-P. Maillard, J.-C. Dousse, J. Hoszowska
The European Physical Journal D 57(2), 155-170, 2010

High-resolution measurements of the photoinduced X-ray emission of liquid mercury were performed, using a transmission DuMond-type crystal spectrometer for transitions above 11 keV and a reflection von Hamos-type crystal spectrometer for transitions below 11 keV. The target X-ray fluorescence was produced by irradiating the sample with the Bremsstrahlung from X-ray tubes. The energies and natural linewidths of 6 K-shell, 26 L-shell and 2 M-shell X-ray transitions were determined. Using a least-squares-fit method to solve the two sets of equations derived from the observed transition energies and transition widths the binding energies of the subshells K to M5 and O1 and the level widths of the subshells K to N5 and O1 could also be determined.

DOI:10.1140/epjd/e2010-00023-x  Keywords: line width 80Hg

The necessity of maximum information utilization in x-ray analysis

83,70,82T. Papp, J.A. Maxwell, A.T. Papp
X-Ray Spectrometry 38(3), 210-215, 2009

There are significant discrepancies in the experimental data needed in the analysis of x‐ray spectra. Examination of the data in detail shows that they often contradict simple logic, elemental arithmetic, even parity and angular momentum conservation laws. We have identified that the main source of the problems, other than the human factor, is rooted in the signal processing electronics. We have developed a line of fully digital signal processors that not only have excellent resolution and line shape but also allow proper accounting. We achieve this by processing all events and separating them into two or more spectra where the first spectrum is the accepted or good spectrum and the second spectrum is the rejected spectrum. It is not enough to know that an event was rejected, and increment the input counter—it is necessary to know what happened and why, whether it was pure noise, a noisy or disturbed event, a true event, or any pile up combination of the above in order to account properly for true event input rate and processor dead time. The data processing methodology cannot be reliably established on the partial and fractional information offered by other approaches. The availability of all the events allows one to see the other part of the spectrum. To our surprise the total information explains many of the shortcomings and contradictions of the x‐ray database. We call this a maximum information utilization approach in signal processing. Also a fundamental parameter x‐ray fluorescence analysis program (CSX‐XRF) has been developed to utilize all the information offered by the signal processor. The fundamental parameter method is only as good as the database it uses and the description of the x‐ray fluorescence analysis system. This latter poses significant difficulties, and to ease the demand we have developed an inverse fundamental parameter program package for x‐ray tube based equipment characterization. Copyright © 2009 John Wiley & Sons, Ltd.

DOI:10.1002/xrs.1150  Keywords: X-ray fluorescence analysis

Fluorescence yields and Coster-Kronig probabilities for the atomic L subshells. Part II: The L1 subshell revisited

14J.L. Campbell
Atomic Data and Nuclear Data Tables 95(1), 115-124, 2009

Our recently recommended values for the L1 subshell fluorescence yield [omega]1 and Coster-Kronig probabilities f13 and f12 in the atomic number range 64 Z 92 are re-assessed in the light of new experimental data. Special attention is paid to the regions of atomic number in which discontinuities arise due to the onset of L1L2N1, L1L3M4, and L1L3M5 transitions. Attention is drawn to large scatter and to systematic differences in the data from different experimental techniques, both of which result in large uncertainties being attached to the recommended values. The urgent need for additional refined measurements is emphasized.

DOI:10.1016/j.adt.2008.08.002  Keywords: Coster-Kronig, fluorescence yield, L-shell

Evaluation of High-Resolution X-ray Absorption and Emission Spectroscopy for the Chemical Speciation of Binary Titanium Compounds

92,9,26,45,1,76,79,86,94,129F. Reinhardt, B. Beckhoff, H. Eba, B. Kanngießer, M. Kolbe, M. Mizusawa, M. Müller, B. Pollakowski-Herrmann, K. Sakurai, G. Ulm
Analytical Chemistry 81, 1770-1776, 2009

For the chemical speciation of binary compounds of tri- and tetravalent titanium, high-resolution X-ray absorption and emission spectra were recorded in different energy regimes in order to evaluate and to qualify both near-edge X-ray absorption fine structure (NEXAFS or XANES)spectroscopy and wavelength-dispersive X-ray emission spectroscopy (WDXES) as spectroscopic methods for this analytical task. A high resolving power in the excitation channel was ensured by use of monochromatic synchrotron radiation provided by BESSY II, where the soft X-ray emission spectra were recorded as well. In the hard X-ray range, emission measurements were performed at SPring-8. For a comparison of the information gained from the various methods, the titanium compounds were classified according to the bonded titanium's oxidation state. Thus, it was possible to distinguish between inner atomic effects due to different oxidation states and external effects related to the respective ligand and the surrounding structure. It becomes evident, that certain compounds, while hardly distinguishable in their Ti-K XANES spectra, still show significant differences in their emission characteristics. On the other hand, some compounds with little difference in their emission spectra are easily distinguished by their NEXAFS structures. Only the combined use of the complementary methods both in the soft and the hard X-ray range allows for a reliable speciation of tri- and tetravalent titanium compounds.

DOI:10.1021/ac8018069  Keywords: chemical effect, diagram lines, K shell, L shell, satellite lines, tri- and tetravalent titanium 22Ti

Investigation of L X-ray production from Au with protons in low energy region

153H. Mohan
Journal of Physics: Conference Series 194(8), 082011-082011, 2009

The Coulomb ionization of an inner shell electron by an energetic proton is a fundamental problem in ion-atomic collision physics. The experimental measurements of L X-ray intensity ratios for Au with protons in the energy range 260 – 400 keV at the interval of 20 keV are reported. These are compared with theoretical calculations obtained on the basis of recently prevailing UAECPSSR theory using transition rates of Scofield and also that of Campbell and Wang, respectively. Their importance in understanding this phenomenon and existing arguments in this regard will be highlighted.

DOI:10.1088/1742-6596/194/8/082011  Keywords: L-shell 79Au

Nickel LIII fluorescence and satellite transition probabilities determined with an alternative methodology for soft-x-ray emission spectrometry

79,9,31,45M. Müller, B. Beckhoff, R. Fliegauf, B. Kanngießer
Physical Review A 79(1), 032503, 2009

An accurate determination of the nickel LIII x-ray transition probabilities was performed employing a wavelength-dispersive spectrometer (WDS) at the plane grating monochromator beamline for undulator radiation of the Physikalisch-Technische Bundesanstalt, Germany’s national metrology institute, at the electron storage ring BESSY II. An absolute calibration method developed for this spectrometer improves the reliability of the determination significantly because the calibration method does not require measurements of reference samples and provides a traceable uncertainty budget. The device was calibrated with respect to both its absolute detection efficiency and its response behavior. Therefore, a method to obtain the detection efficiency of a WDS in comparison to an absolutely calibrated energy-dispersive detector was successfully applied. In addition, response functions were developed and experimentally validated. The present results for the Ni LIII transition probabilities differ clearly from theoretical calculations and tabulated data found in the literature. Perspectives of a quantitative study of the interactions causing the satellite transitions are outlined and discussed in view of shake-off and Coster-Kronig processes.

DOI:10.1103/PhysRevA.79.032503  Keywords: L-shell, transition probability 28Ni

L-subshell Coster-Kronig yields of palladium determined via synchrotron-radiation-based high-resolution x-ray spectroscopy

16,38,23,52,49,141,13,73,124,115W. Cao, J. Hoszowska, J.-C. Dousse, Y. Kayser, M. Kavčič, M. Žitnik, K. Bucar, A. Mihelic, J. Szlachetko, K. Slabkowska
Physical Review A 80(1), 2009

We report on the experimental determination of the palladium L-subshell Coster-Kronig (CK) transition yields via high-resolution measurements of the Lα1,2 (L3−M4,5) and Lβ1 (L2−M4) x-ray emission lines. The L x-ray spectra were recorded by means of curved crystal spectrometers employing energy-tunable synchrotron radiation for fluorescence production. The CK yields were derived from the relative L x-ray intensity jumps at the L edges by fitting the fluorescence intensities as a function of the photon energy to the photoionization cross sections. The L x-ray intensities were corrected for solid-state effects which were estimated from the comparison of the measured and theoretical Pd L-edge x-ray-absorption spectra. Thanks to high resolution, the partial CK yield fL1L3M13 could be extracted from the intensities of the resolved LαM satellite transitions. For f23, f12, and f13 CK rates, values of 0.164±0.033, 0.047±0.001, and 0.730±0.039 were found, respectively. For the partial CK yields fL1L3M13 and fL1L3N13, results of 0.406±0.023 and 0.324±0.032, respectively, were obtained.

©2009 American Physical Society

DOI:10.1103/PhysRevA.80.012512  Keywords: Coster-Kronig, synchrotron radiation 46Pd

Reference-free X-ray spectrometry based on metrology using synchrotron radiation

9B. Beckhoff
Journal of Analytical Atomic Spectrometry 23, 845-853, 2008

X-ray spectrometry is a wide spread technique for revealing reliable information concerning the elemental composition and binding state in various materials. Reference-free quantitation in X-ray spectrometry is based on the knowledge of both the instrumental and fundamental atomic parameters. Instrumental or experimental parameters involve the radiant power and spectral purity of the excitation radiation, the beam geometry, the solid angle of detection, and the response behavior and efficiency of the detector. The reliability of the quantitation equally depends on the relative uncertainty of the atomic fundamental parameters involved. Both the values and estimated uncertainty of atomic fundamental parameters given in the literature can be improved by dedicated experiments: By means of transmission and fluorescence experiments with tunable synchrotron radiation, the mass absorption coefficient and fluorescence yield of Al was determined. Furthermore, the transition probabilities of the fluorescence lines belonging to the Cu-Liii and Lii subshells were determined using a superconducting tunnel junction detector offering an energy resolution of about 10 eV in the soft X-ray range. Selected techniques and applications of reference-free X-ray spectrometry are presented. A particular advantage of reference-free quantitation modes is their capability to directly probe new materials without the need to wait for appropriate standard reference materials.

DOI:10.1039/B718355K  Keywords: K fluorescence yield, L-shell, mass absorption coefficient, transition probability 13Al 29Cu

L-subshell vacancy decay processes for elements with 52≤Z≤57 following ionization using Mn Kα x rays

110,58,72,113V. Sharma, S. Kumar, D. Mehta, N. Singh
Physical Review A 78(1), 2008

The Li- (i=1–3) subshell x-ray spectra for the 52Te, 53I, 55Cs, 56Ba, and 57La elements excited by Mn Kα (EKα2=5.888 keV and EKα1=5.899 keV) x rays have been investigated using the 55Fe radioisotope in conjunction with a Cr absorber. A low-energy Ge detector was used to measure the L x rays at an emission angle ψ=126°, where the second-order Legendre polynomial term P2 (cos ψ) associated with the angular distribution is annulled. In the case of the 56Ba and 57La elements, alignment of the L3-subshell vacancy states was investigated through angular distribution measurements of the emitted L3-subshell x rays. The Lα1,2 and Lβ2,15 x-ray groups are observed to be nearly isotropic, while the data for the pure Ll (L3−M1) x-ray emission are indicative of a small anisotropic trend, though within experimental error. The integral x-ray fluorescence cross sections are deduced and interpreted in terms of Li-subshell photoionization cross sections, fluorescence and Coster-Kronig yields, and x-ray emission rates. The L2-subshell x-ray cross sections for 57La measured using targets of lanthanum (III) fluoride and dilanthanum (III) trioxide are found to be unusually higher. The enhancement is observed due to the contribution of the L2-subshell radiative resonant Raman scattering (RRS) of Mn Kα x rays having energy around the L2-subshell binding energy of 57La in these compounds. Also, the observed enhancement of the L3-subshell x-ray cross sections in 57La is suggestive of intrashell vacancy transfer via L2−L3 Coster-Kronig RRS transitions. The L2-subshell total RRS cross sections in 57La have been deduced from the present measured attenuation coefficients for Mn Kα x rays in La2O3
and LaF3. The L2-subshell radiative and total RRS cross sections in 57La using LaF3 are higher by ∼30% than those using La2O3. The contribution of processes predicted in the framework of Mozouchi’s four-band model involving inner subshells along with the valence and conduction bands of these wide-band-gap insulator compounds is likely to account for the observed results. The L2-subshell radiative and L2−L3 Coster-Kronig yields and the ratio of the L2−M4 and L2−N4 radiative RRS intensities in both La compounds are found to be same and are consistent with values from photoexcited vacancy decay. The L2-subshell radiative RRS was also observed to be isotropic.

DOI:10.1103/PhysRevA.78.012507  Keywords: L-shell 52Te 53I 55Cs 56Ba 57La

Azimuthal-angle dependence of L x-ray intensity following photoionization of Pb, Au, and W atoms by a linearly polarized photon

80,7,37Y. Namito, S. Ban, H. Hirayama
Physical Review A 78(3), 2008

We measured the L x-ray intensities of Pb, Au, and W for several different azimuthal angles and partially polarized photon beams by using high-purity low-energy Ge detectors. We utilized a monochromatized synchrotron beam as the source. It had an energy of 10.88–40keV, and its degree of linear polarization P ranged from 0.84 to 0.89. The scattering polar angle (θ) was 90°, and the azimuthal angle (ϕ1) was 0° or 90°, relative to the polarization direction. We obtained the x-ray intensity ratio R[=I(ϕ1=0°)∕I(ϕ1=90°)]. We observed that the Ll intensities depended on the azimuthal scattering angle ϕ1, i.e., R=0.92–0.94, 0.91–0.94, and 0.90–0.93 for Pb, Au, and W, respectively. On the other hand, the dependence of Lα on the azimuthal scattering angle was not clear due to experimental uncertainty. The anisotropy of Lγ was not observed. These results agreed with the theoretical calculations based on Scofield’s theory.

DOI:10.1103/PhysRevA.78.033419  Keywords: L-shell, synchrotron radiation 74W 79Au 82Pb

Detector Calibration and Measurement of Fundamental Parameters for X-Ray Spectrometry

104,9,1,54,79,129F. Scholze, B. Beckhoff, M. Kolbe, M. Krumrey, M. Müller, G. Ulm
Microchimica Acta 155, 275–278, 2006

Energy-dispersive X-ray spectrometry offers the opportunity for a fast and reliable determination of the composition of a specimen. For fundamental parameter based quantification, detailed knowledge of the X-ray generation cross sections and of the detection system’s efficiency is required. The detection efficiency is determined comparing the measured and calculated spectrum of undispersed synchrotron radiation (SR) from the electron storage ring BESSY II in the spectral range from 0.1 keV to 100 keV. Alternatively, monochromatized SR in the spectral range from 0.1 keV to 60 keV is used to determine the detection efficiency with a typical relative uncertainty of 1% to 2% by direct comparison with a reference detector. Employing well-calibrated detectors and monochromatized SR of well-known radiant power and high spectral purity, fluorescence yields have been investigated and resonant Raman scattering was studied as an example of a basic effect creating spectral background.

DOI:10.1007/s00604-006-0555-4  Keywords: L-shell, resonant Raman cross section 23V 78Pt

X-ray resonant Raman scattering on Ni employing polarized and unpolarized exciting radiation

139,47,79,9C. Zarkadas, A.G. Karydas, M. Müller, B. Beckhoff
Spectrochimica Acta Part B 61, 189–195, 2006

The X-ray resonant Raman scattering effect on nickel was studied by means of monochromatic polarized and unpolarized exciting radiation, respectively. Experiments involving polarized exciting radiation were carried out at the four crystal monochromator beamline of the Physikalisch-Technische Bundesanstalt for synchrotron radiation from 4 to 10 keV at the electron storage ring BESSY II. Resonant Raman spectra of thin Ni foils were recorded at the Cu-Kα (8041 eV) exciting beam energy. In the Institute of Nuclear Physics of the N.C.S.R. Demokritos, the resonant Raman spectrum of a thick nickel target was also recorded for an unpolarized Cu-Kα (8041 eV) exciting beam produced after the ionization of a



thick Cu target by 1.7 MeV protons in a triaxial, orthogonal geometry. In the present work, the individual spectral characteristics and the methodological approaches adopted for the extraction of the Ni-RRS cross sections, with respect to each mode of excitation, are presented, compared and discussed. An excellent agreement was found between the Ni KLRRS cross sections determined for polarized and unpolarized exciting radiation confirming the theoretical predictions within the experimental uncertainties achieved.

DOI:10.1016/j.sab.2006.01.002  Keywords: resonant Raman cross section 28Ni

Absolute determination of cross sections for resonant Raman scattering on silicon

79,9,129,45M. Müller, B. Beckhoff, G. Ulm, B. Kanngießer
Physical Review A 74(1), 012702, 2006

We studied the resonant Raman scattering of x rays in the vicinity of the K absorption edge of silicon. The investigation was carried out at the plane grating monochromator beamline for undulator radiation of the PTB laboratory at BESSY II in Berlin. Cross sections were determined absolutely for a wide energy range of incident photons with small relative uncertainties employing calibrated instrumentation avoiding any reference samples. The experimentally determined values differ clearly from the theoretical ones found in the literature.

DOI:10.1103/PhysRevA.74.012702  Keywords: resonant Raman cross section 14Si

Coster-Kronig transition probability f23 in gold atoms

25,46,56,119,138,77,120,19,53,85R. Dunford, E. Kanter, B. Krässig, S. Southworth, L. Young, P. Mokler, T. Stöhlker, S. Cheng, A. Kochur, I. Petrov
Physical Review A 74(6), 2006

We have investigated the Coster-Kronig transition probability f23 in gold atoms (nuclear charge Z=79) using the L x-ray versus K x-ray coincidence method. K vacancies were created using synchrotron radiation and the cascade decays were measured using germanium x-ray detectors. We find f23=0.112±0.004 which is somewhat lower than the recent coincidence measurement of Santra et al. which yielded f23=0.119±0.003. Our result is smaller than the values calculated by McGuire (f23=0.132) and Puri et al. (f23=0.129) but agrees with our own single-configuration Pauli-Fock calculation, which gives f23=0.114, as well as the global set of prior experimental data.

DOI:10.1103/PhysRevA.74.062502  Keywords: Coster-Kronig 79Au

Li (i = 1, 2, 3) sub-shell fluorescence yields for 79Au, 80Hg and 81Tl

109,114,106,72,113M. Sharma, P. Singh, J.S. Shahi, D. Mehta, N. Singh
X-Ray Spectrometry 34(1), 35-41, 2005

The Li (i = 1, 2, 3) sub-shell x-ray fluorescence yields (ωi ) for 79Au, 80Hg and 81Tl were deduced from the measured cross-sections for the Li (i = 1, 2, 3) sub-shell x-rays following ionization by 59.54 keV γ-rays (B L1 < E inc < B K) and for the L3 sub-shell x-rays following ionization by Rb K x-rays (B L3 < E Kα < B L2, B L1/L2 < E Kβ < B K), where B K/L is the K shell/Li sub-shell ionization threshold of the target element. An energy-dispersive x-ray fluorescence setup, involving photon sources consisting of a 241Am annular source in the direct and secondary excitation modes along with RbCl secondary exciter and an Si(Li) detector, was used for the measurements. The measured ω2 and ω3 values exhibit good agreement with those based on the relativistic Dirac–Hartree–Slater (RDHS) calculations, while the ω1 values are found to be higher by ∼25%. The present data indicate that the L1–L3 Coster–Kronig yield f 13 based on the RDHS calculations are overestimated.

Copyright © 2004 John Wiley & Sons, Ltd.

DOI:10.1002/xrs.784  Keywords: fluorescence yield, L-shell 79Au 80Hg 81Tl

Thickness determination for Cu and Ni nanolayers: Comparison of completely reference-free fundamental parameter-based X-ray fluorescence analysis and X-ray reflectometry

1,9,54,129M. Kolbe, B. Beckhoff, M. Krumrey, G. Ulm
Spectrochimica Acta Part B: Atomic Spectroscopy 60(4), 505-510, 2005

Monochromatized synchrotron radiation of the electron storage ring BESSY II has been used for the non-destructive thickness determination of nanolayered materials by two different methods. The aim of these investigations was the comparison of completely reference-free fundamental parameter-based X-ray fluorescence analysis with X-ray reflectometry to validate the quantification of X-ray fluorescence analysis as an absolute method. For this purpose, Cu and Ni layers with a thickness varying between 5 nm and 50 nm as well as double layers of both metals deposited on Si have been studied. In X-ray reflectometry characterization experiments, the tunability of the photon energy allows the determination of not only the total layer thickness but also the individual layer thicknesses of the Cu/Ni double-layer systems. Reference-free X-ray fluorescence analysis involves both the fundamental parameter approach and the knowledge of all relevant experimental parameters obtained by instrumentation calibrated absolutely. The layer thickness determined by both methods agreed within their combined uncertainties. In view of the limits of X-ray reflectometry for very thin layers, laterally inhomogeneous samples, and multi-elemental layer compositions, reference-free X-ray fluorescence analysis offers the potential for the thickness determination of such samples.

DOI:10.1016/j.sab.2005.03.018  Keywords: Atomic fundamental parameters, Nanolayer thickness determination, Synchrotron radiation, X-ray fluorescence analysis, X-ray reflectometry 28Ni 29Cu

Measurement of the x-ray mass attenuation coefficient of silver using the x-ray extended range technique

163,164,165,166,167,168,169,170C.Q. Tran, C.T. Chantler, Z. Barnea, M.D. de Jonge, B.B. Dhal, C.T.Y. Chung, D. Paterson, J. Wang
Journal of Physics B 38(1), 89–107, 2005

We used the x-ray-extended range technique to measure the x-ray mass attenuation coefficients of silver in the 15–50 keV energy range with a level of uncertainty between 0.27% and 0.4% away from the K-edge. The imaginary part of the atomic form factor of silver was derived by subtracting the scattering component from the measured total mass attenuation coefficients. Discrepancies between the measured mass attenuation coefficients and alternative theoretical predictions are discussed.

DOI:10.1088/0953-4075/38/1/009  Keywords: MAC 47Ag

Measurement of the x-ray mass attenuation coefficient and determination of the imaginary component of the atomic form factor of molybdenum over the 13.5–41.5 kev energy range

166,163,164,165,167,171,172,173M.D. de Jonge, C.Q. Tran, C.T. Chantler, Z. Barnea, B.B. Dhal, D.J. Cookson, W.K. Lee, A. Mashayekhi
Physical Review A 71(3), 032702, 2005

We use the x-ray extended-range technique (XERT) [ Chantler et al. Phys. Rev. A 64 062506 (2001)] to measure the mass attenuation coefficients of molybdenum in the x-ray energy range of 13.5–41.5 keV to 0.02–0.15 % accuracy. Measurements made over an extended range of the measurement parameter space are critically examined to identify, quantify, and correct where necessary a number of experimental systematic errors. These results represent the most extensive experimental data set for molybdenum and include absolute mass attenuation coefficients in the regions of the x-ray absorption fine structure (XAFS) and x-ray-absorption near-edge structure (XANES). The imaginary component of the atomic form-factor f2 is derived from the photoelectric absorption after subtracting calculated Rayleigh and Compton scattering cross sections from the total attenuation. Comparison of the result with tabulations of calculated photoelectric absorption coefficients indicates that differences of 1–15 % persist between the calculated and observed values.

DOI:10.1103/PhysRevA.71.032702  Keywords: MAC 42Mo

Barium L subshells Coster-Kronig and fluorescence yields by the subshell selective photoionization method

8,89,125R.A. Barrea, C.A. Pérez, H.J. Sánchez
Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 215(3), 308-316, 2004

The method of selective photoionization of individual subshells by monochromatized synchrotron radiation has been employed to measure independently all Coster–Kronig and fluorescence yields of the Ba L subshells. The energy of the primary radiation was set at about 50 energy points in the range of the L edges. At each setting, the induced L fluorescence radiation was recorded by a Si(Li) detector. A pure Ti foil was used for normalization purposes and the Ti K fluorescence lines were also recorded under the same geometrical conditions as the Ba sample. Fitting the measured fluorescence intensities versus primary energy with the photoelectric cross-sections derived the Coster–Kronig coefficients and fluorescence yields. The obtained yields were compared with tabulated data.

DOI:10.1016/j.nimb.2003.09.017  Keywords: Coster-Kronig, fluorescence yield, L shell, synchrotron radiation, Photoionization 56Ba

Method of determining the value of the Coster-Kronig parameter (f23)

98,74,99,11,105,65S. Santra, D. Mitra, M. Sarkar , D. Bhattacharya, P. Sen, A. Mandal
Physical Review A 69(2), 024701, 2004

The present work demonstrates the utility and efficacy of a technique to measure the Coster-Kronig parameter (f23) of elemental targets. For this purpose a pure gold foil was irradiated in a beam of 88-keV γ rays from a radioactive 109Cd source. The photoinduced K and L x rays emitted from the gold foil were then measured in coincidence, with the data collected in the list mode. On analysis, the f23 value of gold was found to be 0.119±0.003. The technique demonstrated here is different in the sense that, in contrast to the earlier coincidence methods, where the x rays emitted directly from a radioactive source are detected in coincidence, in the present method the x rays of the elements under investigation are obtained by photoionization.

DOI:10.1103/PhysRevA.69.024701  Keywords: Coster-Kronig 79Au

L1-L3 Coster-Kronig yield for elements with 70 ≤ Z ≤ 81

109,114,88,72,113M. Sharma, P. Singh, S. Puri, D. Mehta, N. Singh
Physical Review A 69(3), 2004

The L1−L3 Coster-Kronig (CK) yield f13 for the 70Yb, 71Lu, 74W, 75Re, 79Au, 80Hg, and 81Tlelements was deduced using measured intensities of the Lα x rays emitted following decay of the Li-subshell (i=1,2,3) vacancies produced in widely different proportions by the 59.54keV γ rays (BL1<Einc<BK) and the Ge/Se/Rb K x rays (BL3<EKα<BL2,BL1∕L2<EKβ<BK); where BK∕Li is the K-shell∕Li-subshell binding energy of the target element. An energy-dispersive x-ray fluorescence set up, involving photon sources consisting of a 241Am annular source in the direct and secondary excitation modes along with the Ge/Se/RbCl secondary exciter and a Si(Li) detector, was used for the measurements. The measured f13 yields for 70Yb, 71Lu, and 74W are found to agree with the values based on the relativistic Dirac-Hartree-Slater (RDHS) calculations, while those for 79Au, 80Hg, and 81Tl are lower by ∼20%. The measured f13 yields exhibit a jump from 0.354(24) for 74W to 0.450(27) for 75Re compared to that from 0.352 to 0.640 as predicted by the RDHS calculations due to onset of the intense L1−L3M5 CK transition.

DOI:10.1103/PhysRevA.69.032501  Keywords: Coster-Kronig, L-shell 70Yb 71Lu 72Hf 73Ta 74W 75Re 76Os 77Ir 78Pt 79Au 80Hg 81Tl

Numerical description of photoelectric absorption coefficients for fundamental parameter programs

27,122,28,107,39H. Ebel, R. Svagera, M.F. Ebel, A. Shaltout, J.H. Hubbell
X-Ray Spectrometry 32(6), 442–451, 2003

After a systematic analysis of different databases and a comparison with empirical data, we decided to describe photoelectric absorption coefficients, coherent and incoherent scattering coefficients and mass attenuation coefficients in the energy range from 1 to 300 keV for elements from Z = 1 to 94 by a modified version of Scofield's tables in combination with scattering coefficients from Elam et al. Modifications include check and correction of edge positions, description of M4- and M5-ranges of elements from promethium upwards by sawtooth responses and reduction of data by introduction of least-squares fits of fifth order to Scofield's and Elam et al.'s numerical data. Our database was developed especially for application in fundamental parameter programs for quantitative x-ray analysis (XRFA, EPMA, XPS and TEY).

DOI:10.1002/xrs.667  Keywords: mass attenuation coefficients, photoelectric absorption coefficients, scattering coefficients

Fluorescence yields and Coster-Kronig probabilities for the atomic L subshells

14J.L. Campbell
Atomic Data and Nuclear Data Tables 85(2), 291-315, 2003

L subshell fluorescence yields ωi and Coster–Kronig probabilities fij (i,j=1,2,3) obtained from experimental measurements are collected. A critical examination of these data is undertaken, including recalculation of some results. A subset of the data is selected for presentation in graphs, which also show the interpolated predictions of the Dirac–Hartree–Slater version of the independent-particle model. Tables provide recommended values for ωi and fij, respectively, and include for comparison the Dirac–Hartree–Slater predictions and the values recommended in the widely referenced 1979 review of Krause.

DOI:10.1016/S0092-640X(03)00059-7  Keywords: Coster-Kronig, fluorescence yield, L-shell

Fundamental parameter method for the low energy region including cascade effect and photoelectron excitation

50,111,136,48,9,129,66N. Kawahara, T. Shoji, T. Yamada, Y. Kataoka, B. Beckhoff, G. Ulm, M. Mantler
Advances in X-ray Analysis 45, 511-516, 2002

We have demonstrated the cascade effect and the secondary photoelectron excitation effect by means of Cr-L line measurements by using monochromatic radiation of high spectral purity and well-known flux provided by two beamlines of the Physikalisch-Technische Bundesanstalt (PTB), Germany's national institute of metrology at the electron storage ring BESSY II. The plane grating monochromator beamline for undulator radiation covers the energy range from 30 eV to 1.9 keV, and the four-crystal monochromator beamline for synchrotron radiation from 1.75 keV to 10.5 keV. The Cr-L fluorescence intensities show a considerable jump at Cr-K edge energy as the source photon energy rises, indicating the magnitude of the cascade effect. The fundamental parameter method including the cascade effect and the secondary photoelectron excitation effect shows good agreement with the measurement. The evaluation of this computation method for the measurement carried out with a conventional XRF spectrometer also shows good performance of the calculation.

https://www.icdd.com/axa-login/?article=ad8644339f53f2  Keywords: cascade effect, L shell, secondary photoelectron excitation 24Cr

L-shell Coster-Kronig yields for Pb

57,88,72,5,113A. Kumar, S. Puri, D. Mehta, B.K. Arora, N. Singh
X-Ray Spectrometry 31(4), 310-313, 2002

DOI:10.1002/xrs.570  Keywords: Coster-Kronig, L-shell 82Pb

A new atomic database for X-ray spectroscopic calculations

29,91,112W.T. Elam, B.D. Ravel, J.R. Sieber
Radiation Physics and Chemistry 63, 121-128, 2002

The authors undertook to compile a database of recent values of the atomic parameters required for fundamental parameters (FP) calculation of X-ray fluorescence (XRF) spectra, calculation of X-ray absorption in crystals and other samples, and correction of X-ray absorption spectra for self-absorption effects. All values were obtained from published sources and include the elements hydrogen (atomic number 1) through californium (atomic number 98). The data were collected into a single unstructured ASCII text file.

DOI:10.1016/S0969-806X(01)00227-4  Keywords: absorption cross sections, Coster-Kronig transition probability, fluorescence yield, photon cross sections

Erbium L-subshell Coster-Kronig and fluorescence yields determination by synchrotron radiation photoionization

8,89,125R.A. Barrea, C.A. Pérez, H.J. Sánchez
Journal of Physics B: Atomic, Molecular and Optical Physics 35(14), 3167-3178, 2002

The method of selective photoionization of individual subshells by monochromatized synchrotron radiation has been employed to measure independently all Coster-Kronig and fluorescence yields of Er L subshells. Fitting the measured fluorescence intensities versus primary energy with the photoelectric cross sections derived the Coster-Kronig coefficients and fluorescence yields. The obtained yields were compared with tabulated data and a very good agreement among them was found.

DOI:10.1088/0953-4075/35/14/312  Keywords: Coster-Kronig, fluorescence yield, L shell, synchrotron radiation 68Er

L1 atomic-level width of elements 62 <~Z<~83

90,10,23,64P.-A. Raboud, M. Berset, J.-C. Dousse, Y.-P. Maillard
Physical Review A 65(2), 2002

High-resolution measurements of the photoinduced dipole-forbidden L 1 − M 4 , 5 x-ray emission lines were performed with a reflection-type and a transmission-type bent-crystal spectrometer for 62 Sm , 67 Ho , 70 Yb , 74 W , 78 Pt , 80 Hg , and 83 Bi . From the observed linewidths of the L 1 − M 4 , 5 x-ray transitions, the level widths of the subshell L 1 were determined assuming for the M 4 , 5 level widths the values reported recently by Campbell and Papp [X-ray Spectrom. 24, 307 (1995); At. Data Nucl. Data Tables 77, 1 (2001)].

DOI:10.1103/PhysRevA.65.022512  Keywords: x-ray transition 62Sm 67Ho 70Yb 74W 78Pt 80Hg 83Bi

Measurements of L-shell x-ray production cross sections of W, Pt, and Au by 10-30-keV electrons

15,131,60,95C. Campos, M. Vasconcellos, X. Llovet, F. Salvat
Physical Review A 66(1), 2002

We present results from measurements of Lα x-ray production cross sections of the elements W, Pt, and Au by impact of electrons with energies in the range 10–30 keV. The cross sections were obtained by measuring Lα x-ray intensities emitted from very thin films of the studied elements deposited on thick carbon substrates. The directional and energy spreading of the electron beam within the active film and the x-ray enhancement due to electron backscattering from the substrate were accounted for by means of Monte Carlo simulation. Recorded x-ray intensities were converted to absolute x-ray production cross sections by using two different methods; the first employs measured values of the sample thickness and the number of incident electrons and estimated detector efficiencies; the second is based on a comparison between measured and calculated bremsstrahlung intensities. Experimental data are compared with the results of simple analytical formulas of common use in practical electron probe microanalysis, with calculated cross sections obtained from the distorted-wave Born approximation and with other experimental data available in the literature.

DOI:10.1103/PhysRevA.66.012719  Keywords: L-shell 74W 78Pt 79Au

Determination of fluorescence yields using monochromatized undulator radiation of high spectral purity and well-known flux

9,129B. Beckhoff, G. Ulm
Advances in X-ray Analysis 44, 349-354, 2001

Along with the increasing importance of material and surface analysis by means of X-ray fluorescence analysis (XRF) in the soft X-ray range, the need for standard-free quantification modes has grown. Here, improving the knowledge of accurate values of the fluorescence yields for photon energies below 2 keV becomes a major task. For this purpose, an irradiation chamber was built by the Physikalisch-Technische Bundesanstalt (PTB), Germany's national metrology institute. This UHV chamber allows an accurate positioning of up to 6 specimens with respect to a set of high purity Al diaphragms defining exactly the excitation beam size and the solid angles of radiation detection. The scattered and fluorescence radiation was registered by a calibrated semiconductor detector. The monitoring of the monochromatized excitation radiation by means of calibrated photodiodes was ensured. For the specimen excitation, the plane grating monochromator beamline of the PTB for undulator radiation at the electron storage ring BESSY II, involving a high spectral purity, was used. In the present investigation, the fluorescence yields associated with the K-edge of boron and of carbon were determined for different mass depositions of the respective elements. The results of the initial experiments, including the achieved accuracy, are given.

https://www.icdd.com/axa-login/?article=fc1dd424647f7a  Keywords: fluorescence yield 5B 6C

Widths Of The Atomic K-N7 Levels

14,83J.L. Campbell, T. Papp
Atomic Data and Nuclear Data Tables 77(1), 1-56, 2001

Atomic level widths obtained from experimental measurements are collected in Table I, along with the corresponding theoretical widths derived from the Evaluated Atomic Data Library (EADL) of Lawrence Livermore National Laboratory; these EADL values are based upon the Dirac–Hartree–Slater version of the independent-particle model. In a minority of cases, many-body theory predictions are also provided. A brief discussion of the manner in which the experimental widths were deduced from spectroscopic data is included. The bulk of the data are for elements in the solid state, but a few data for gases and simple compounds are included.

For the K, L2, L3, and M5 levels, where Coster–Kronig contributions do not contribute or contribute only to a small extent to the overall widths, the EADL predictions appear satisfactory for elements in the solid state. For other levels, where Coster–Kronig and super-Coster–Kronig transitions have large probabilities within the independent-particle model, this model is not satisfactory. Table II provides a complete set of recommended elemental values based upon consideration of the available experimental data.

DOI:10.1006/adnd.2000.0848  Keywords: Coster-Kronig

X-ray extended range technique for precision measurement of the x-ray mass attenuation coefficient and Im(f) for copper using synchrotron radiation

164,163,169,171,165C.T. Chantler, C.Q. Tran, D. Paterson, D.J. Cookson, Z. Barnea
Physics Letters A 286(5), 338-346, 2001

We reconsider the long-standing problem of accurate measurement of atomic form factors for fundamental and applied problems. We discuss the X-ray extended-range technique for accurate measurement of the mass attenuation coefficient and the imaginary component of the atomic form factor. Novelties of this approach include the use of a synchrotron with detector normalisation, the direct calibration of dominant systematics using multiple thicknesses, and measurement over wide energy ranges with a resulting improvement of accuracies by an order of magnitude. This new technique achieves accuracies of 0.27-0.5% and reproducibility of 0.02% for attenuation of copper from 8.84 to 20 keV, compared to accuracies of 10% using atomic vapours. This precision challenges available theoretical calculations. Discrepancies of 10% between current theory and experiments can now be addressed.

DOI:10.1016/S0375-9601(01)00444-3  Keywords: MAC 29Cu

Measurement of the x-ray mass attenuation coefficient of copper using 8.85– 20 keV synchrotron radiation

164,163,165,169,171,176C.T. Chantler, C.Q. Tran, Z. Barnea, D. Paterson, D.J. Cookson, D.X. Balaic
Physical Review A 64, 062506, 2001

This work presents the x-ray extended range technique for measuring x-ray mass attenuation coefficients. This technique includes the use of multiple foil attenuators at each energy investigated, allowing independent tests of detector linearity and of the harmonic contributions to the monochromated synchrotron beam. Measurements over a wide energy range allow the uncertainty of local foil thickness to be minimized by the calibration of thin sample measurements to those of thick samples. The use of an extended criterion for sample thickness selection allows direct determination of dominant systematics, with an improvement of accuracies compared to previous measurements by up to factors of 20. Resulting accuracies for attenuation coefficients of copper (8.84 to 20 keV) are 0.27-0.5 %, with reproducibility of 0.02%. We also extract the imaginary component of the form factor from the data with the same accuracy. Results are compared to theoretical calculations near and away from the absorption edge. The accuracy challenges available theoretical calculations, and observed discrepancies of 10% between current theory and experiments can now be addressed.

DOI:10.1103/PhysRevA.64.062506  Keywords: MAC 29Cu

Coster-Kronig, fluorescence, and Auger yields of the 47AgL subshells measured through synchrotron photoionization

44,121,83,99W. Jitschin, R. Stötzel, T. Papp, M. Sarkar
Physical Review A 59, 3408–3414, 1999

The decay of individual L subshell vacancies in 47Ag has been investigated through selective photoionization by monochromatized synchrotron radiation. By tuning the radiation energy over the L edges, the ionization of particular subshells can be turned off and on. The corresponding subshell ionization cross sections including the subtle structure caused by electron correlations are known from our previous studies. The x-ray fluorescence emitted in the vacancy decay was recorded by a Si (Li) detector. Advanced fitting techniques were employed to extract the intensities of lines originating from different subshells. The extracted line intensities were plotted versus energy of the primary radiation. The relative jumps of the line intensities occurring at the edges directly correspond to the Coster-Kronig yields, whereas the absolute values of the total subshell fluorescence give the fluorescence yields. The following Coster-Kronig yields were obtained: f12=0.14(3), f13=0.58(5), and f23=0.18(3). Adopting the value ω3=0.056(7) from literature, the following fluorescence yields are obtained: ω1=0.013(2) and ω2=0.067(9). The results agree reasonably with theoretical calculations. In particular, the rather large value of f13 indicates that the L1-L3M4,5 Coster-Kronig channel is well allowed.

DOI:10.1103/PhysRevA.59.3408  Keywords: Coster-Kronig transition probability, fluorescence yield, L shell 47Ag

Coster-Kronig, fluorescence, and Auger yields of the 47Ag L subshells measured through synchrotron photoionization

Jitschin, W.
Physical Review A 59(5), 3408-3414, 1999

DOI:10.1103/PhysRevA.59.3408 47Ag

Investigation of the Effect of Coster-Kronig Transitions and Incident Photon Energy on Average L Shell Fluorescence Yields

3,117,75,113,108K.L. Allawadhi, B.S. Sood, R. Mittal, N. Singh, J.K. Sharma
X-Ray Spectrometry 25(5), 233-238, 1996

In order to investigate the dependence of average L shell fluorescence yields on incident photon energy and the role of Coster-Kronig transitions therein, the values of average L shell fluorescence yields were calculated and experimentally determined in elements 40Z92 for incident photons with energies lying just above the L1 edge and just below the K edge energies of the target element without and with Coster-Kronig transitions. In the absence of Coster-Kronig transitions the fluorescence yields are found to be strongly energy dependent but the extent of compensation provided by the Coster-Kronig transitions at different incident photon energies is adjusted in such a way as to make the average L shell fluorescence yields independent of the incident photon energies. Thus, the Coster-Kronig transitions are seen to play a major role in making average L shell fluorescence yields independent of incident photon energy.

DOI:10.1002/(SICI)1097-4539(199609)25:5<233::AID-XRS171>3.0.CO;2-D  Keywords: Coster-Kronig, fluorescence yield, L-shell

Atomic level widths for x-ray spectrometry

14,83J.L. Campbell, T. Papp
X-Ray Spectrometry 24(6), 307-319, 1995

A self-consistent set of level widths for the K-N7 subshells is assembled using literature experimental data from a variety of spectroscopic methods. In cases where Coster-Kronig processes contribute significantly, the widths differ from the predictions of the atomic single-particle model; in the restricted regions where atomic many-body predictions are available, the agreement is much better. The assembled widths will be useful to Si(Li) spectroscopists who wish to include natural width in the description of spectrometer lineshape; such inclusion will improve accuracy in both fundamental and analytical work. The present database is also of value in identifying where improvements to the currently incomplete knowledge of natural widths are most critical.

DOI:10.1002/xrs.1300240606  Keywords: Coster-Kronig

Theoretical form factor, attenuation and scattering tabulation for Z=1–92 from E=1–10 eV to E=0.4–1.0 MeV

164C.T. Chantler
Journal of Physical and Chemical Reference Data 24(1), 71–85, 1995

Tables for form factors and anomalous dispersion are widely used in the UV, x‐ray, and y‐ray communities, and have existed for a considerable period of time. Much of the recent theoretical basis for these was contributed by Cromer, Mann, and Liberman while much of the experimental data were synthesized by Henke et al. More recent developments in both areas have led to new and revised tables. These works have employed numerous simplifications compared to detailed relativistic S‐matrix calculations; the latter do not lend themselves to convenient tabular application for the range of Z and energy of general interest. Conversely, the former tables appear to have large regions of limited validity throughout the range of Z and energies, and in particular have important limitations with regard to extrapolation to energies outside tabulated ranges. In the present study, the primary interactions of x‐rays with isolated atoms from Z=1 (hydrogen) to Z=92 (uranium) are described and computed within a self‐consistent Dirac–Hartree–Fock framework. This has general application across the range of energy from 1–10 eV to 400–1000 keV, with limitations (described below) as the low‐ and high‐energy extremes are approached.
Tabulations are provided for the f1 and f2 components of the form factors, together with the photoelectric attenuation coefficient for the atom, μ, and the value for the K‐shell, μK, as functions of energy and wavelength. Also provided are estimated correction factors as described in the text, conversion factors, and a simple estimate for the sum of the scattering contributions (from an isolated atom). The method used herein is primarily theoretical and considers intermediate assumptions which limit the precision and applicability of previous theoretical tabulations. Particular concern involves the application of the dispersion relation to derive Re(f) from photoelectric absorption cross‐sections. The revised formulation presented here explicitly avoids most of the limitations of previous works. Revised formulae can lead to significant qualitative and quantitative improvement, particularly above 30–60 keV energies, near absorption edges, and at 0.03 keV to 3 keV energies. Recent experimental syntheses are often complementary to this approach. Examples are given where the revised theoretical tables are in better agreement with experiment than are those based on experimental syntheses.

DOI:10.1063/1.555974  Keywords: form factor, MAC, scattering

Coster-Kronig yields of the 54Xe L subshells measured through synchrotron photoionization

44,121,83,99,22W. Jitschin, R. Stötzel, T. Papp, M. Sarkar , G.D. Doolen
Physical Review A 52(2), 977-983, 1995

The method of selective photoionization of individual subshells by monochromatized synchrotron radiation has been employed to measure all Coster-Kronig yields of the 54Xe L subshells. The energy of the primary radiation was set at about 50 energy points in the range of the L edges. At each setting, the induced Xe L fluorescence and the induced Ar K fluorescence (used for normalization purposes) were recorded simultaneously by a Si(Li) detector. Both Xe and Ar were in the gaseous state. The recorded fluorescence spectra were carefully analyzed with proper modeling of the line tailing due to the intrinsic line profile and the detector line shape. The Coster-Kronig yields were derived by fitting the measured fluorescence intensities versus primary energy with the photoelectric cross sections. The derived yields are sensitive to the precise dependence of the cross sections on primary energy. Evaluations have been performed assuming a smooth power-law dependence and employing corrections for electron-correlation effects, which were estimated from comparative calculations in the independent-particle approximation and linear-response approximation models. Still, the uncertainties of the correlation effects constitute the main contribution to the uncertainties of the derived Coster-Kronig yields. The finally adopted values are f12=0.12±0.03, f13=0.23±0.04, and f23=0.14±0.02.

DOI:10.1103/PhysRevA.52.977  Keywords: Coster-Kronig, L shell 54Xe

L shell fluorescence yields and coster-kronig transition probabilities for the elements with 25 ≤ Z ≤ 96

88,72,18,113,127S. Puri, D. Mehta, B. Chand, N. Singh, P.N. Trehan
X-Ray Spectrometry 22(5), 358-361, 1993

The values of Li sub-shell fluorescence yields ([omega]i) and Coster-Kronig transition probabilities (fij) were evaluated using radiative and non-radiative transition rates based on the relativistic Dirac-Hartree-Slater (RDHS) model for all the elements in the atomic number range 25 ≤ Z ≤ 96. The values of the Coster-Kronig-corrected fluorescence (vi) and average L shell fluorescence (L) yields were also evaluated and least-squares fitted to obtain the polynomials representing them as a function of atomic number.

DOI:10.1002/xrs.1300220507  Keywords: Coster-Kronig, fluorescence yield, L-shell

Fluorescence, Coster-Kronig and Auger yields of the 62Sm L subshells measured with the synchrotron photoionization method

121,134,99,44R. Stötzel, U. Werner, M. Sarkar , W. Jitschin
Journal of Physics B: Atomic, Molecular and Optical Physics 25(10), 2295, 1992

Using monochromatized synchrotron radiation a sample of thin samarium and titanium foils was excited, and the induced Sm L X-rays and Ti K X-rays were detected by a Si(Li) detector. When the primary photon energy is tuned across the Sm L2 and L1 edges, the intensities of the Sm L X-ray lines normalized to the Ti K alpha intensity exhibit abrupt changes. From these intensity changes the Coster-Kronig factors were determined: f23=0.14+or-0.03, f13=0.18+or-0.03 and f12=0.19+or-0.03. The value of f13 is substantially smaller than predicted by theory and extrapolated from heavier elements. Furthermore, from the total intensities of all lines originating from the same Sm L subshell the ratios of the fluorescence yields omega 1/ omega 3=0.48+or-0.07 and omega 2/3=1.05+or-0.05 were obtained.

DOI:10.1088/0953-4075/25/10/011  Keywords: Auger yield, Coster-Kronig yield, Fluorescence yield 62Sm

L-shell Coster-Kronig transition probabilities in Ni, Cu, and Mo measured with synchrotron radiation

118,102,135,21,17S.L. Sorensen, S.J. Schaphorst, S.B. Whitfield, B. Crasemann, R. Carr
Physical Review A 44(1), 350, 1991

A recent technique, based on differential subshell ionization by tuned synchrotron radiation, has been applied to measurements of L-subshell Coster-Kronig yields of Ni, Cu, and Mo from L2 and L3 Auger spectra. Results for Ni are f23=0.6+0.2, f12=0.4+0.2, and f13=0.5+0.2; for Cu, f23=0.8+0.1, f12=0.44+0.06, and f13=0.3+0.2; for Mo, f23=0.15+0.

DOI:10.1103/PhysRevA.44.350  Keywords: Coster-Kronig, L-shell, synchrotron radiation 28Ni 29Cu 42Mo

Au L x-ray relative intensities induced by proton impact

161J.Q. Xu
Physical Review A 44(1), 373-376, 1991

Theoretical intensity ratios of the L[beta], L[gamma], L[eta], L[gamma]1, and L[gamma]2,3,6 to the L[alpha] line induced by proton impact on gold have been calculated from various L-subshell databases in the proton energy range 0.18-10 MeV. Good agreements are obtained between the measurements and the ratios computed by using the decay yields we present and the ionization cross sections by Cohen and Harrigan [At. Data Nucl. Data. Tables 33, 255 (1985)]. The latter were calculated in the plane-wave Born approximation with corrections for energy loss, Coulomb deflection, perturbed stationary state, and relativistic effects. The L-subshell coupling effects are not found.

DOI:10.1103/PhysRevA.44.373  Keywords: L-shell 79Au

Multiplet structure in Ni Kβ x-ray fluorescence spectra of nickel compounds

51,126,101J. Kawai, M. Takami, C. Satoko
Phys. Rev. Lett. 65, 2193–2196, 1990

We show that the profiles of the Ni Kβ1,3,β’ x-ray fluorescence spectra of NiF2 and NiO, which were long believed to originate from the multiplet splittings due to an exchange interaction between the x-ray hole and valence unpaired electrons, are clearly interpreted by a charge-transfer effect during the photoionization of one of the 1s electrons. The profiles of the Kβ x-ray fluorescence spectra of NiCl2, NiBr2, and NiI2 are also predicted from the charge-transfer effect. The range of validity of the present theory and its relation to the shakeoff satellites are also discussed.

DOI:10.1103/PhysRevLett.65.2193  Keywords: chemical effect, compounds, K shell 28Ni

Coster-Kronig factor f13 of 39Y measured with the synchrotron photoionization method

44,174,175W. Jitschin, G. Grosse, P. Röhl
Physical Review A 39(1), 103-109, 1989

The intensity of the L3-M4,5M4,5 Auger line of 39Y excited by photons with energies in the range of the L1 edge has been measured. It exhibits a jump at the edge due to the onset of the Coster-Kronig vacancy transfer from the L1 to the L3 subshell. From the measured jump ratio 1.13±0.02 the Coster-Kronig yield f13=0.49±0.09 is derived. This value agrees with a currently recommended value; however, it is significantly smaller than the prediction of recent relativistic calculations.

DOI:10.1103/PhysRevA.39.103  Keywords: Coster-Kronig, L shell 39Y

Coster-Kronig yields in silver measured with synchrotron radiation

118,17,102,135,21S.L. Sorensen, R. Carr, S.J. Schaphorst, S.B. Whitfield, B. Crasemann
Physical Review A 39(12), 6241-6246, 1989

The Coster-Kronig transition probabilities fij for shifting a vacancy from the Li to the Lj subshell of Ag have been measured by differential photoionization of the subshells with synchrotron radiation by observing the intensity of the ensuing Lj-M4,5M4,5 Auger transitions. In the course of the analysis, spectator satellites in these Auger spectra were identified. The following Ag Coster-Kronig yields were determined: f23=0.16±0.03, f12=0.044±0.004, and f13=0.61±0.05. While f23 agrees very well with relativistic independent-particle calculations by Chen et al. [Phys. Rev. A 24, 117 (1981)], f12 and f13 fall below predictions by 35% and 18%, respectively, in qualitative accord with expected many-body effects.

DOI:10.1103/PhysRevA.39.6241  Keywords: Coster-Kronig yield, synchrotron radiation 47Ag

X-ray attenuation coefficients of beryllium in the energy range 5 to 20 keV

162L. Gerward
Acta Crystallographica Sect. A 45, 1-3, 1989

Mass attenuation coefficients for beryllium have been determined by an X-ray energy-dispersive method with a relative experimental error of 1-2%. Results are given for Cr, Fe, Co, Cu and Mo Kα lines and compared with recent experimental and theoretical results.

DOI:10.1107/S0108767388008347  Keywords: MAC 4Be

Coster-Kronig and fluorescence yields of Au L subshells derived from photoionisation measurements

44,69,134,35W. Jitschin, G. Materlik, U. Werner, P. Funke
Journal of Physics B: Atomic and Molecular Physics 18(6), 1139-1153, 1985

Photoionisation studies provide a direct method for an accurate determination of vacancy decay parameters. The authors report on such measurements performed for the Au L shell. Thin Au foils were irradiated by photons with energies ranging from 11.5 to 15.2 keV. The mass absorption coefficient as well as the induced L X-radiation were measured. From the absorption coefficient the ionisation cross sections of the individual L subshells were derived. Comparison of the cross sections and the induced X-ray fluorescence gives Coster-Kronig factors, fluorescence yields and branching ratios for different X-ray lines. For the Coster-Kronig factors and fluorescence yields significant deviations from previously adopted values were found.

DOI:10.1088/0022-3700/18/6/015  Keywords: Coster-Kronig, fluorescence yield, L shell 79Au

X-ray attenuation coefficients of carbon in the energy range 5 to 20 keV

L. Gerward
Acta Cryst. A39, 322-325, 1983

Mass attenuation coefficients for pyrolytic graphite have been determined by an X-ray energy-dispersive method with a relative experimental error of about 0.5%. Results are given for the Fe, Co, Cu and Mo K[alpha]1 and K[beta]1 lines.

DOI:10.1107/S0108767383000744

X-ray attenuation coefficients of carbon in the energy range 5 to 20 keV

162L. Gerward
Acta Crystallographica Section A 39(3), 322--325, 1983

Mass attenuation coefficients for pyrolytic graphite have been determined by an X-ray energy-dispersive method with a relative experimental error of about 0.5%. Results are given for the Fe, Co, Cu and Mo Kα1 and Kβ1 lines.

DOI:10.1107/S0108767383000744  Keywords: MAC 6C

Behaviour of Raman resonance scattering across the K X-ray absorption edge

128,2J. Tulkki, T. Aberg
Journal of Physics B: Atomic and Molecular Physics 15(13), L435-L440, 1982

A generalisation of the Kramers-Heisenberg formula is used to demonstrate the evolution of inelastic X-ray scattering into fluorescence across the K absorption edge. As an illustration the results of a recent synchrotron radiation study of the inelastic scattering in the vicinity of the Mn K absorption edge in KMnO4 by Briand et al. (1981) are analysed and found to be in qualitative agreement with the theory.

DOI:10.1088/0022-3700/15/13/004  Keywords: resonant Raman scattering 25Mn

Widths and fluorescence yields of atomic L-shell vacancy states

160,21,67M.H. Chen, B. Crasemann, H. Mark
Physical Review A 24, 177-182, 1981

A comprehensive set of theoretical L-shell Auger and total widths, and Coster-Kronig and fluorescence yields is presented for atomic numbers 18≤Z≤100. These quantities are based on ab initio relativistic calculations. Agreement with experimental values is fair for ?1 and generally good for ?2, ?3 (Z≥54), f23 (Z≥60), ?(L2), ?(L3), and for ?(L1) in the range 49≤Z≤75. Discrepancies in ?(L1) for Z<49 point toward the need for a many-body calculation of low-energy L1-L2,3M4,5 Coster-Kronig transitions. There is a pronounced need for measurements of ?3 and f23 of elements lighter than Xe.

DOI:10.1103/PhysRevA.24.177  Keywords: Auger yield, Coster-Kronig transition probability, fluorescence yield, L shell

Average L-shell fluorescence, Auger, and electron yields

159M.O. Krause
Physical Review A 22, 1958–1961, 1980

The dependence of the average L-shell fluorescence and Auger yields on the initial vacancy distribution is shown to be small. By contrast, the average electron yield pertaining to both Auger and Coster-Kronig transitions is shown to display a strong dependence. Numerical examples are given on the basis of Krause's evaluation of subshell radiative and radiationless yields. Average yields are calculated for widely differing vacancy distributions and are intercompared graphically for 40<=Z<=100 in the case of the fluorescence and Auger yields, and 12<=Z<=100 in the case of the electron yield. Average fluorescence and Auger yields are found to differ by less than 7% from the respective L3 subshell yields in most cases of inner-shell ionization.

DOI:10.1103/PhysRevA.22.1958  Keywords: Auger yield, electron yield, fluorescence yield, L-shell

Angular dependence of fluorescent x rays

158J.H. Scofield
Physical Review A 14(4), 1418-1420, 1976

The angular correlation between ionizing and fluorescent x rays is calculated including the dependence on the linear polarization of either x ray. The calculation is done relativistically including all the radiation multipoles using single-particle wave functions calculated in the Hartree-Slater model. The results are given for the ionization of a 2 p32 electron with the subsequent filling by a n=3 electron for Z=30,79 and 92.

DOI:10.1103/PhysRevA.14.1418  Keywords: Hartree-Slater

Angular Distribution of Auger Electrons Following Photoionization

32,71,103S. Flügge, W. Mehlhorn, V. Schmidt
Physical Review Letters 29(1), 7-9, 1972

It is shown that the photoionization process of inner-shell electrons by unpolarized radiation leads to an alignment of the ionized atoms. From the nonisotropic angular distribution of the following Auger electrons the relative partial photoionization cross sections can be determined.

DOI:10.1103/PhysRevLett.29.7  Keywords: Auger electron

X-Ray Fluorescence Yields, Auger, and Coster-Kronig Transition Probabilities

6,21,30,33,67,123,87,132W. Bambynek, B. Crasemann, R.W. Fink, H.-U. Freund, H. Mark, C.D. Swift, R.E. Price, P. Venugopala Rao
Rev. Mod. Phys. 44, 716–813, 1972

The present status of the field of fluorescence yields, radiationless (Auger and Coster-Kronig) and radiative transition probabilities is summarized. Tables of experimental and theoretical results are included, and tables of "best values" of important quantities are presented.

DOI:10.1103/RevModPhys.44.716  Keywords: fluorescence yield, transition probability

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