Coster-Kronig Transition Probabilities Research Articles

L-shell x-ray fluorescence relative intensities for elements with 62 ≤ Z ≤ 83 at 18 keV and 23 keV by synchrotron radiation

The relative intensities of L-subshell x-ray fluorescence (XRF) for elements with atomic numbers 62 ≤ Z ≤ 83 were measured at two excitation energies, 18 keV and 23 keV, using a synchrotron radiation source at a beamline of the Synchrotron Light Center for Experimental Science and Applications in the Middle East (SESAME), Jordan. The experimentally measured results of the relative intensities were compared with the calculated results using the subshell fluorescence yield and the Coster–Kronig transition probabilities recommended by Campbell and the values based on the Dirac–Hartree–Slater model by Puri. The experimental and theoretical results are in agreement. In this work, L XRF relative intensities for the elements Sm, Gd, Tb, Er, Ta, W, Re, Hg, Pb and Bi at energies of 18 keV and 23 keV were measured.

Experimental determination of ruthenium L-shell fluorescence yields and Coster–Kronig transition probabilities

Fluorescence yields and Coster–Kronig factors of the ruthenium L-shell are determined experimentally for the first time with reliable uncertainty budgets.

Experimental determination of tantalum L-shell fluorescence yields and Coster–Kronig transition probabilities

In this work, fluorescence yields and Coster–Kronig transition probabilities of the tantalum L-shell are determined with a reliable uncertainty budget.

Measurements of K-shell ionization cross sections and L-shell X-ray production cross sections of Al, Ti, Cu, Ag, and Au thin films by low-energy electron impact

The K-shell ionization cross sections of Al, Ti, Cu and L-shell characteristic X-ray production cross sections of Cu, Ag and Au (Lα, Lβ and Lγ subshells for Au) by electron impact at incident energy of 5–27 keV are determined experimentally. Thin films of the studied elements, deposited on thin carbon substrates, are employed as targets in the experiments. The thickness of the thin carbon substrate is 7 μg/cm<sup>2</sup>, the targets are Al, Ti, Cu, Ag and Au and their thickness values are 5.5 μg/cm<sup>2</sup>, 28 μg/cm<sup>2</sup>, Cu 35.5 μg/cm<sup>2</sup>, 44 μg/cm<sup>2</sup> and 44 μg/cm<sup>2</sup>, respectively. The target thickness values are checked by using Rutherford Backscattering Spectrometry (RBS). The electron beam is provided by a scanning electron microscope (KYKY-2800B). The characteristic X-rays produced are recorded by a silicon drifted detector (XR-100SDD, Amptek), which has a C2 ultrathin window and can detect the low-energy X-rays down to boron Kα line (0.183 keV). The detector efficiency is calibrated by using the standard sources (<sup>55</sup>Fe, <sup>57</sup>Co, <sup>137</sup>Cs and <sup>241</sup>Am) for X-ray energy larger than 3.3 keV while using the characteristic peak method (i.e. by measuring characteristic X-ray spectra produced by 20 keV electron impacting various thick solid targets) for X-ray energy less than 3.3 keV. The experimental results are corrected by the Monte Carlo code PENELOPE for the effects of target structure and Faraday cup. Meanwhile, the electron escape rates obtained from the Faraday cup and the signal pile-up effect are also considered. The results show that when the incident electron energy is low, the influences of electron energy loss and target thickness are significant. The thinner the target , the smaller the correction is. Experimental uncertainties for K-shell ionization cross sections of Al, Ti and Cu are about 5.0%, 5.6% and 5.1%, respectively; experimental uncertainties for L-shell X-ray production cross sections for Cu and Ag are about 5.3% and 4.0%, and for Lα,Lβ,and Lγ of Au are about 6.1%, 8.9% and 11.0%, respectively. The experimental L-shell characteristic X-ray production cross sections of Cu are given for the first time. Compared with the theoretical values of the semi-relativistic distorted-wave Born approximation (DWBA), most of the experimental values in this work are in good agreement within 7% deviation. The best agreement between the experimental results and the theoretical values is obtained for the K shell ionization cross section of Al, and the deviation is less than 1.7% for the data where the incident energy is above 10 keV. The least consistency with the theoretical values is the experimental L shell characteristic X-ray production cross sections of Cu, with a deviation being about 5–22%. The comparison of the experimental L shell characteristic X-ray production cross sections of Cu (including Ga and As elements) with those from the DWBA theory indicates that the theoretical calculations of L shell ionization cross sections of medium heavy elements and the corresponding atomic parameters (such as fluorescence yields and Coster-Kronig transition probabilities) need to be more accurately determined. According to the present results, the ionization cross sections or characteristic X-ray production cross sections measured by the thin target thin substrate, the thin target thick substrate and the thick target methods are equivalent to each other within the uncertainties.

How do Uncertainties in Atomic Parameters Influence Theoretical Predictions of X-Ray Production Cross Sections By Proton Impact?

The emission of characteristic X-rays induced by proton impact is a phenomenon known since the first half of the 20th century. Its more widely known application is the analytical technique Particle Induced X-ray Emission (PIXE). Several models have been developed to calculate, first, ionization cross sections and then the subsequent X-ray production cross sections. However, to carry out the comparisons of these predictions with experimental data it is necessary to use atomic parameters databases (fluorescence yields, Coster-Kronig transition probabilities, emission rates) that also have experimental uncertainties. In this work it is demonstrated how these values do not allow to decide which model describes more accurately the cross sections, due to a final “theoretical uncertainty” obtained through the propagation of the original uncertainties.

L- and M-shell X-ray production cross section measurements in 73Ta and 78Pt using B3+,4+-ions of energies below and above the potential barrier

In this paper, we report the L- and M-shell X-ray production cross sections in 73Ta and 78Pt caused by the bombardment of 35 to 60 MeV B3+,4+-ions. The energies of B-ions, below and above the potential barrier, were selected to study the effect on inner- and outer-shell ionization i.e. absolute X-ray production cross sections for various L- and M X-ray lines/group of lines (namely Lℓ, Lα2, Lα1, Lη, Lβ4,6, Lβ1, Lβ3, Lβ2,15, Lβ5,7,9,10, Lγ5, Lγ1, Lγ2,3,6, Lγ4,4′, Mξ2,1, Mδ + M3N1, Mα1,2 + M2N1, Mβ + Mη, Mγ, Mm11 (M3O1 + M3O4,5), Mm12 (M2N4 + M1N3), Mm21 (M2O1), Mm22 (M2O4 + M1O2,3) and the change in the intensity ratios due to multiple ionization of M- and higher-shells. The present measurements were carried out at 16UD Pelletron Accelerator at Inter-University Accelerator Centre (IUAC) Delhi. The ion beams were bombarded on thin targets evaporated on an ultrapure carbon backing of 10 μg/cm2. The targets fixed on a steel ladder were placed in an evacuated (<10−6 Torr) scattering chamber at 45° each to the beam direction and to the Si(Li) detector. The recorded L and M X-ray spectra were separately deconvoluted into various components of the L and M X-ray lines using the computer code after subtracting suitable background. The experimental results have been compared with the theoretical values by converting the L and M-subshell ionization cross sections based on the PWBA and ECPSSR direct-ionization theories taking into effect the sub-shell fluorescence yields, Coster-Kronig transition probabilities and transition rates based on Dirac-Fock and Dirac-Hartree-Slater models. In the present measurements (0.0641 ≤ Z1/Z2 ≤ 0.0685), the velocity ratios v1/v2pi and the reduced ion velocity ξpi = 2v1/(θpi.v2pi) for p = L- or M-shell are in the range of 0.309 ≤ v1/v2Li ≤ 0.435 and 0.913 ≤ ξLi ≤ 1.316 and the ratios v1/v2Mi and ξMi for M-shell are in the range of 0.555 ≤ v1/v2Mi ≤ 0.790 and 2.575 ≤ ξMi ≤ 3.779 respectively. To the best of our information, this study of B-ion impact on 73Ta and 78Pt, near the potential barrier of the system which falls in the fast (ξLi ≈ 1, ξMi > 1) collision regime, is being reported for the first time.

Relative total L‐subshell X‐ray emission intensities and their impact on the fitting of complex X‐ray fluorescence spectra

Relative total L‐subshellX‐ray emission intensities, IL2/IL3 and IL1/IL3, are reported for the elements Er, Tm, Yb, Hf, Ta, W, Pt and Au, measured using approximately monoenergetic X‐rays at 17.4 keV. X‐ray spectra were recorded using a filtered X‐ray tube source and a silicon drift detector. Careful fitting was used to determine the intensities of the individual line transitions, accounting for line broadening and detector artefacts. The line intensities were summed to obtain the L1, L2 and L3 total X‐ray emission rates. Relative total L‐subshell emission intensities were also calculated using recommended values of subshell photoionization cross sections, fluorescence yields and Coster–Kronig transition probabilities. We find poor agreement between these accepted literature values and our experimental results. A simple modelling exercise was conducted to explore the impact on fitting complex L‐shellX‐ray fluorescence spectra using inaccurate literature values for line intensities and total subshell X‐ray emission rates. We find that large errors can be introduced when fitting with incorrect values for the total relative X‐ray emission from different L‐subshells. Copyright © 2017 John Wiley &amp; Sons, Ltd.

Calculation of Coster-Kronig energies and transition probabilities by linear interpolation method

The X-ray emission spectrum consists of two types of spectral lines heaving different origins. The diagram lines originate because of transitions in singly ionized atom, while the nondiagram lines or satellites originate due to transitions in doubly or multiply ionized atom. The X- ray satellite energy is the difference between the energies of initial and final states which are both doubly or multiply ionized. Thus, the satellite has a different energy than the energy of the X-ray diagram line. Once the singly ionized state has been created, it is the probability of a particular subsequent process that will lead to the formation of two-hole state. The single hole may get converted through a Coster-Kronig transition to a double hole state. The probability of formation of double hole state via this process is written as σ.σ', where σ is the probability of creation of single hole state and σ' is the probability of the Coster-Kronig transition. The value of σ' can be taken from the tables of Chen et al. [1], who have presented the calculated values of σ' for almost all possible Coster-Kronig transitions in some elements. The energies of the satellites can be calculated by using the tables of Parente et al. [2]. Both of these tables do not give values for all the elements. The aim of the present work is to show that the values for other elements, for which values are not listed by Chen et al. and Parente et al., can be calculated by linear interpolation method.

L X-ray intensity ratios for high Z elements induced with X-ray tube

Abstract We have studied the intensity ratios I(Lα1,2)/I(Lβ1,2), I(Lα1,2)/I(Lγ) and I(Lβ1,2)/I(Lγ) for elements Ta, W, Au and Pb by 13.1 keV bremsstrahlung radiation. In this work, experimental values were compared with the theoretical results and other experimental results. Theoretical results of the intensity ratios were calculated with theoretical subshell photoionization cross sections, fractional X-ray emission rates, fluorescence yields, and Coster–Kronig transition probabilities. Good agreement can be observed between experimental values and theoretical results. Comparing with L1 and L2 subshells, the ionization cross section of L3 subshell shows a large increase for Ta and W with the variation of excitation energy from 59.5 keV to 13.1 keV.

Empirical and semi-empirical interpolation of L X-ray fluorescence parameters for elements in the atomic range 50≤Z≤92

In this study, interpolations (empirical and semi-empirical) of L sub-shell fluorescence yield and L shell Coster–Kronig transition probability values and the measured L X-ray production cross-sections, intensity ratios and L sub-shell fluorescence yield values of elements have been performed in the range of 50≤Z≤92. In this experimental setup, two sources (50mCi 55Fe and 50mCi 241Am) were used. L X-rays emitted by samples were counted by an Ultra-LEGe detector with a resolution of 150eV at 5.9keV.

Measurement of Photon-Induced &amp;lt;i&amp;gt;L&amp;lt;/i&amp;gt; X-Ray Fluorescence Cross Sections for Ho and Yb in the 16.04 - 24.68 keV Energy Range

Lα, Lβ, and Lγ X-ray fluorescence cross sections for Ho and Yb have been measured at various incident photon energies in the energy range 16.04 ≤ E ≤ 24.68 keV. The measurements have been done using an X-ray tube with a secondary-excitor system of Zr, Nb, Mo, Cd, and In. The experimental values of the cross-sections were determined by measuring the absolute yield of L subshell X-rays emitted from a standard target of a given energy. Theoretical tabulated values of subshell photoionization cross-sections, fluorescence yields, Coster-Kronig transition probabilities and radioactive decay rates have been used to calculate the theoretical values of the cross-sections. The experimental results of the cross-sections at various excitation energies have been compared with theoretically calculated values. Fairly good agreement is obtained between the present experimental results and the calculated values.

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

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.

F-64 L Shell X-ray Fluorescence Cross-Sections for Elements with 33 ≤ Z ≤ 50

Accurate experimental data regarding the X-ray fluorescence (XRF) cross sections and fluorescence yields are important in basic studies of nuclear and atomic processes leading to the emission of X-ray and Auger electrons. The data is also required for many practical applications like elemental analysis by x-ray emission technique, dosimetric computation for medical physics and irradiation processes [1]. A systematic study of the Li (i =1-3) subshell x-ray fluorescence cross sections at the 5.89 keV photon energy has been undertaken for the elements in the atomic region 33  Z  50. The measurements have been performed under vacuum ~10 -2 torr using energy-dispersive spectrometer involving an LEGe (FWHM 150 eV at 5.895 keV) detector. The cross sections for the possible resolved L x-ray components were deduced and compared with those evaluated using the most reliable theoretical values of Li (i = 1, 2, 3) subshell photoionization cross sections, fluorescence yields, x-ray emission rates and Coster-Kronig transition probabilities [2]. For the L, L and L1,5 groups of x rays, the measured cross sections for all the elements are in agreement with theoretical cross sections. The measured L2,3 cross sections in the atomic region 39  Z  46 are in general agreement within ~10% except for 39Y, where the difference ~25% was observed. The comparison provides the insight regarding the cutoff energy of the L1-L2M4,5 and L1-L3M4,5 CK transitions at Z~39, and L1-L3M4,5 and L2-L3M4,5 CK transitions at Z ~50 as predicted by the RDHS model [2].

The polarization of X-rays and magnetic photoionization cross-sections for L3 sub-shell

The alignment of atoms with inner-shell vacancies resulting from ionization by photons was investigated by measuring the anisotropic emission of L shell X-ray lines. The X-ray line intensities were measured using an Si(Li) detector and radioisotope photon source in various emission angles. It was observed from measured intensities that Lα and Ll X-ray intensities for the L 3 sub-state depended on the emission angle, meaning that Lα and Ll X-rays had an anisotropic spatial distribution. Thus, the Lα to Ll intensity ratios for a set of elements were determined and alignment parameters for each element were obtained using these ratios. Also, the empirical values of the L 3 magnetic sub-state photoionization cross-sections for m j = 3 2 and 1 2 were evaluated using the determined alignment parameters, sub-state photoionization cross-sections and the Coster–Kronig transition probabilities.

Investigation of Coster–Kronig Transition Probabilities (L1→L2, L1→L3, and L2→L3) for Hf and Hf Compounds

In this study, the L 1 →L 2 , L 1 →L 3 , and L 2 →L 3 Coster–Kronig (CK) transition probabilities ( f 12 , f 13 , and f 23 ) for Hf compounds were investigated. The samples were excited by 59.5 keV γ-rays from a 241 Am annular radiative source. L X-rays emitted by samples were counted by an Ultra-LEGe detector with a resolution of 150 eV at 5.9 keV. In addition, it was observed a chemical effect on the CK transition probabilities for Hf compounds. The semi-empirical values of f 12 , f 13 , and f 23 CK transition probabilities have been compared with the semi-empirical, theoretical and experimental data for pure Hf, respectively.

Measurement of relative L X-ray intensity ratio following radioactive decay and photoionization

The measurements of the L X-ray intensity ratio I(Lα)/I(Lβ), I(Lα)/I(Lγ), I(Lα)/I(Lι), I(Lβ)/I(Lγ) and I(Lι)/I(Lγ) for elements Dy, Ho, Yb, W, Hg, Tl and Pb were experimentally determined both by photon excitation, in which 59.5 keV γ-rays from a filtered radioisotope 241Am was used, and by the radioactive decay of 160Tb, 160Er, 173Lu, 182Re, 201Tl, 203Pb and 207Bi. L X-rays emitted by samples were counted by a Si(Li) detector with resolution 160 eV at 5.9 keV. Obtained values were compared with the calculated theoretical values. Theoretical values of the I(Lα/Lβ), I(Lα/Lγ), I(Lα/Lι), I(Lβ/Lγ) and I(Lι/Lγ) intensity ratios were calculated using theoretically tabulated values of subshell photoionization cross-section, fluorescence yield, fractional X-ray emission rates, Coster–Kronig transition probabilities. It was observed that present values agree with previous theoretical and other available experimental results.

The effect of an external magnetic field on the L subshell X-ray fluorescence cross sections and L subshell fluorescence yields in elements 73 ≤ Z ≤ 92 by 59.54 keV photons

L i ( i = 1, 2 and 3) X-ray fluorescence cross sections for Ta, W, Au, Hg, Tl, Pb, Bi, Th and U have been measured using the 59.54 keV incident photons energy in the external magnetic field of intensity +0.60 T. The values of L i subshell fluorescence yields ( w 1 , w 2 and w 3 ) have been measured for the same elements using the previously measured cross section values and the theoretical L i subshell photoionisation cross sections, Coster–Kronig transition probabilities and emission rates. It is observed that the measured L i subshell X-ray fluorescence cross section and L i subshell fluorescence yield values for B = 0 are in good agreement with the theoretical ones evaluated using L i subshell fluorescence yield and L i subshell photoionization cross section. Furthermore, the results show that the atomic parameters such as spectral linewidth, radiation rates, photoionization cross section and fluorescence yield can change when the irradiation is conducted in a magnetic field.

Measurements of L X-ray production cross sections, L subshell fluorescence yields and K to L shell vacancy transfer probabilities

L i X-ray production cross sections have been measured for Sm, Eu, Gd, Dy, Ho, Er, Pt, Au, Tl, Pb and Bi at 59.54 keV incident photon energy. The values of L i subshell fluorescence yields ( ω 1, ω 2 and ω 3) have been determined using the presently measured X-ray production cross sections and the theoretical L i subshell photoionization cross sections values, Coster–Kronig transition probabilities and radiative emission rates. Furthermore, K to L shell vacancy transfer probabilities η KL i ( i=1, 2, 3) for Sm, Eu, Gd, Dy, Ho, Er were determined by measuring the L X-ray production cross section and L subshell fluorescence yields. The measurements were performed using an Am-241 radioisotope as the photon source and a Si(Li) detector. The measured X-ray production cross sections, fluorescence yields and vacancy transfer probabilities were compared with the theoretical values. The results in the present paper are found to be in good agreement with the calculated values.

Coster-Kronig transition probabilityf23in gold atoms

We have investigated the Coster-Kronig transition probability ${f}_{23}$ 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 ${f}_{23}=0.112\ifmmode\pm\else\textpm\fi{}0.004$ which is somewhat lower than the recent coincidence measurement of Santra et al. which yielded ${f}_{23}=0.119\ifmmode\pm\else\textpm\fi{}0.003$. Our result is smaller than the values calculated by McGuire $({f}_{23}=0.132)$ and Puri et al. $({f}_{23}=0.129)$ but agrees with our own single-configuration Pauli-Fock calculation, which gives ${f}_{23}=0.114$, as well as the global set of prior experimental data.

L i ( i=1–3) subshell fluorescence and Coster-Kronig yields for elements with 70⩽ Z⩽92

The atomic inner-shell vacancy decay processes comprised of radiative and nonradiative transitions are characterized by the fluorescence, Auger and Coster-Kronig yields. We present a review of our recent measurements of the L i ( i=1, 2, 3) sub-shell fluorescence yields ( ω i ) and the L 1–L 3 Coster-Kronig transition probabilities ( f 13) for elements with 70⩽ Z⩽92 following photoionization. The comparison of the measured ω i and f 13 values with the theoretical ones, based on the relativistic Dirac–Hartree–Slater (RDHS) model calculations, indicated the need for more refined calculations of transition probabilities for different Coster-Kronig transitions.