Coster-Kronig Yields Research Articles

Energy and Z dependence of low velocity Nq+ ion induced M X-ray relative intensities for some heavy elements

The intensity ratios, IMk/IMn (exp)(k = ξ, γ, m1; n = total, αβ), for some heavy elements, 70Yb, 79Au, 81Tl, 82Pb and 83Bi induced by 1000 keV−1750 keV Nq+ (q = 4, 5) ions have been measured in order to investigate their dependence on the projectile energy and atomic number of the respective target elements. The measured intensity ratios have been compared with two sets of values calculated using the Mj (j = 1–5) sub-shell ionization cross sections based on the ECPSSR-UA model, the X-ray emission rates based on the Dirac-Hartree Slater (DHS) model, two sets of the fluorescence and Coster-Kronig yields based on the DHS model and those evaluated by McGuire employing non-relativistic Hartree-Slater model. Significant differences have been observed between the present measured IMk/IMαβ (exp) (k = ξ, γ, m1) intensity ratios and those calculated using independent particle approximation (IPA) models based single atomic vacancy state physical parameters.

Lisbon Atomic Database (LISA): a compilation of calculated fundamental atomic parameters

The Lisbon Atomic Database (LISA) has a dedicated mission of compiling and providing a comprehensive collection of atomic parameters for the study of the interaction of X-rays with matter. This encompassing array of parameters spans a broad spectrum, extending from the calculation of electron impact ionization cross sections (EIICS) using the Modified Relativistic Binary Encounter Bethe model (MRBEB) , to pivotal data such as fluorescence and Coster–Kronig yields of atomic subshells, binding energies, and the full suite of radiative and non-radiative atomic transition parameters. Except for the EIICS values, all these parameters are obtained through ab initio calculations. These calculations are carried out using a self-consistent ab initio Multi-Configuration Dirac–Fock approach, supported by a specialized code developed by Desclaux, Indelicato, and others (MCDFGME).Graphical abstract

Understanding the mechanisms of L-shell x-ray emission from Os atoms bombarded by 4–6 MeV/u fluorine ion

The L-subshell ionization mechanism is studied in an ultra-thin Os target bombarded by 4–6 MeV/u fluorine ions. Multiple ionization effects are considered through the change of fluorescence and Coster-Kronig yields while determining L-subshell ionization cross sections from L x-ray production cross sections. The present experimental values are compared with various theoretical approximations: (i) the relativistic semi-classical approximation (RSCA), (ii) the shellwise local plasma approximation (SLPA), and (iii) the ECUSAR theory. We also take into account the vacancy sharing among the subshells by the coupled-states model (CSM) and the electron capture (EC) by a standard formalism. We find that the ECUSAR-CSM-EC describes the measured excitation function curves the best. However, the theoretical calculations are still about a factor of two smaller than the measured values even though the recent fluorescence and Coster-Kronig yields are considered. Hence, a re-evaluation of these parameters is a challenge for the theoretical works. Whatsoever, this work leads to demonstrate that in the present energy range the heavy-ion induced inner-shell ionization of the heavy atoms can be understood by combining the direct Coulomb ionization, the electron capture, and the vacancy sharing among subshells, together with optimizing the atomic parameters. Optimization of the atomic parameters shows that our experimental results agree with theoretical vacancy production theories if the L1 fluorescence yield is nearly doubled. Such a optimization is validated by the proton induced L-shell ionization data of uranium atoms.

A Review, Tabulation, and Parameterization of M-Series X-Ray Production Cross Sections for Proton and Helium Ion Impact

In the present work, the experimental total and line resolved M-series x-ray production cross sections (XRPCSs) for different elements with Z = 59–92 for 0.05–39.34 MeV proton and 0.2–6.0 MeV He ion (3He/4He) impact reported by different research groups until December 2020 have been compiled in tabular form. A status of different physical parameters, namely, the ionization cross sections, x-ray emission rates, fluorescence yields, and Coster–Kronig and super Coster–Kronig yields, required to calculate the theoretical M-series XRPCSs have been reviewed. The tabulated experimental total M-series XRPCSs for different elements are found to exhibit universal scaling similar to that shown by the theoretical cross sections. These tabulated experimental cross sections for different elements have been parameterized in order to provide empirical cross sections for use in different applications.

Influence of chemical effects on the Li (i = 1–3) subshell X-ray spectra for 79Au compounds

The influence of chemical effects on intensity ratios i.e. ILi/ILα (i = l, β1, β15,2,3 and β5/2), ILα2/ILα1, ILj/ILβ1 (j = η, γ1 and γ5), ILk/ILγ4 (k = β6,4, β10,9/1 and γ2,3,6) and ILβ1/ILγ1 and chemical shift of Ll and Lγ1 X-ray emission peaks for 79Au compound has been investigated using polychromatic high resolution wavelength dispersive X-ray fluorescence (WDXRF). The measured intensity ratios of L X-ray emission spectra were corrected for spectrometers detector efficiencies and self-absorption correction factors. The experimental values of intensity ratios have been compared with the theoretical values evaluated using different set of available fractional emission rates, fluorescence and Coster-Kronig yields. The measurements also report significant energy shift (∼1–7 eV) in Ll and Lγ1 X-ray peaks of 79Au compounds relative to pure elemental form. The discrepancies in measured intensity ratios and shift in L X-ray emission spectra of 79Au compounds from the theoretical predicated values can be attributed to chemical effects due to core-valence exchange interactions and crystal effects of different ligands attached to central 79Au atom.

Experimental production cross sections for synchrotron radiation induced L‐series X‐rays of Sn and Sb at energies across their Li (i = 1–3) absorption edges

We have measured the X‐ray production cross sections (XRPCS) for the Lp (p = l, α, η, β1,3,4,6, β2,15, γ1,5, γ2,3,4) emission lines of Sn and Sb using synchrotron induced mono‐chromatic radiation tuned across their respective Li (i = 1–3) sub‐shell absorption edges covering the range 4.0 keV–5.0 keV. These measured XRPCS have been compared with the corresponding values calculated using the non‐relativistic Hartree‐Fock‐Slater model based Li (i = 1–3) photoionization cross‐sections, the Dirac‐Fock model based X‐ray emission rates and three sets of fluorescence and Coster‐Kronig (CK) yields based on the Dirac‐Hartree‐Slater model, the semi‐empirical values tabulated by Krause and recently reported experimental values. The present measured Lp XRPCS for both Sn and Sb at different investigated photon energies are found to be in good agreement with those calculated using the experimental photoionization cross sections, fluorescence and CK yields. Further, a good agreement observed between the present measured and calculated branching ratios for both Sn and Sb indicates the reliability of the Dirac‐Fock model based X‐ray emission rates. The Lp XRPCS and intensity ratios for Sn and Sb calculated using the experimental photoionization cross sections, the DF model based X‐ray emission rates and the experimental fluorescence and CK yields are recommended for use in different applications.

Experimental L-series x ray production cross sections for Re by tuning synchrotron radiation across its Li (i=1–3) sub-shell ionization thresholds

In the present work, the Lk (k = l, α, η, β1, β3, β6, β4, β2,15, β5,7, β9,10, γ1,5, γ2,3,6,8, γ4) x ray production (XRP) cross sections have been measured for Re at energies across its Li (i = 1–3) sub-shell ionization threshold energies covering the region 10.5 keV–14.0 keV using synchrotron radiation. The measured values have been compared with the three sets of XRP cross sections calculated using the Dirac-Fock model based x ray emission rates, the non-relativistic Hartree-Fock-Slater model based Li (i = 1–3) sub-shell photoionization cross-sections and three sets of the fluorescence (ωi) and Coster-Kronig (fij) yields based on the Dirac-Hartree-Slater model based values, the semi-empirical values and the experimental values reported earlier by us. The present measured XRP cross sections are found to be in a good agreement with those calculated using the experimental ωi/fij values; whereas these are found to be significantly lower (~30%) than those calculated using the theoretical and the semi-empirical ωi/fij values. In view of the observed good agreement of the present measured Lk XRP cross sections with those calculated using the experimental fluorescence and Coster-Kronig yields and that of the measured branching ratios (ILl/ILα,; ILβ2,15/ILα,; ILη/ILβ1; ILγ1,5/ILβ1 and ILγ2,3/ILβ3) with the theoretical values calculated using the Dirac-Fock model based x ray emission rates, the use of these parameters is recommended for different analytical applications.

Experimental validation of theoretically predicted cut-off of L1–L3M4,5 transitions at Z = 50 through measurements of fluorescence and Coster–Kronig yields for Sn and Sb

In the present work, we have deduced the fluorescence (ω 1, ω 2, ω 3) and Coster–Kronig (CK)(f 12, f 13, f 23) yields for Sn (Z = 50) and Sb (Z = 51) from the L i (i = 1–3) sub-shell x-ray intensities measured using the energy tunable synchrotron radiation employing the selective photoionization method. For both the elements, yields have been obtained using two sets of theoretical photoionization cross sections based on the non-relativistic Hartree–Fock–Slater (HFS) model and the self-consistent Dirac–Hartree–Fock (DHF) model. In case of Sb, we have obtained a third set of measured yields also by using the experimental photoionization cross sections evaluated from independent measurements of the mass-attenuation coefficients. The experimental yields for Sb are reported for the first time by us. We have compared the present deduced fluorescence and CK yields with the Dirac–Hartree–Slater model based values, the semi-empirical values tabulated by Krause and the earlier reported values. In case of Sn, using the DHF and the HFS model based photoionization cross sections, two sets of present measured L1 sub-shell fluorescence yields (ω 1) are found to be 0.039 ± 0.007 and 0.036 ± 0.003, and the CK yields (f 13) are found to be 0.428 ± 0.107 and 0.405 ± 0.028, respectively. In case of Sb, using three sets of the photoionization cross sections (DHF, HFS and recent experimental values), the ω 1 values are measured to be 0.042 ± 0.007, 0.040 ± 0.004 and 0.047 ± 0.005, and the CK yields are measured to be 0.343 ± 0.085, 0.297 ± 0.021 and 0.247 ± 0.022, respectively. The comparison of these present measured yields with the theoretical values provided a reliable experimental evidence indicating cut-off of the intense L1–L3M4,5 CK transitions at Z = 50.

L-shell x ray production cross sections of Sm and Yb induced by carbon ions between 2 MeV and 5 MeV

We have measured L-shell x rays for Sm and Yb induced by carbon ions with energies between 2 and 5 MeV. The measured spectra have been used to extract the individual Li (Lα, Lβ, Lγ and Lℓ) and total L-shell x ray production cross sections. Related ionizations cross sections for Li sub-shells have been determined from individual measured L-shell x ray production cross sections, L-shell fluorescence and Coster-Kronig yields corrected by the multiple ionization effects. The results have been compared with the available experimental data from the literature as well as with the predictions of the PWBA and ECUSAR theories. The analysis of data shows that the ECUSAR predictions agree well with our experimental data.

Experimental and theoretical L-shell ionization cross sections of heavy atoms by impact of Si ions

We present a theoretical and experimental study of the subshell resolved L-shell ionization of relativistic targets such as 73Ta, 78Pt, 90Th, and 92U. The measurements of x-ray production cross sections by (84–140 MeV) Si+q ions (q = 8; 12), were held at the Inter-University Accelerator Centre of New Delhi. Multiple-hole fluorescence and Coster-Kronig yields were used to obtain the Li(i = 1–3) ionization cross sections from the measured x-ray production cross sections of Lℓ, Lα, and Lβ, Lη, and Lγ lines. The experimental results are compared with ab initio theoretical calculations by means of the shell-wise local plasma approximation (SLPA). This model uses the quantum dielectric formalism to obtain the total ionization cross sections from an initial ground state. The wave functions and binding energies of the different targets were obtained by solving the fully relativistic Dirac equation using the HULLAC code package. These calculations are based on first order perturbation theory with a central field, including Breit interaction and quantum electrodynamics corrections. The present SLPA ionization cross sections of the L-shell are found to be independent of the charge state of the Si ions. The experimental observations display also quite similar character if the correct mean projectile charge state inside the target is used for including the multiple ionization effect during ion-solid collisions. A general good agreement between the experimental measurements and full theoretical calculations supports the reliability of present results. The comparison also includes the well-known ECPSSR and ECUSAR semi empirical approximations. We noted that the ECUSAR results agree well with the SLPA, while the ECPSSR cross sections are rather low.

Low energy carbon ion induced M X-ray relative intensities for 70Yb, 82Pb and 83Bi

In the present work, the intensity ratios, IMk/IMn (exp) (k = ξ, β, γ, m1; n = αβ, α), for 70Yb, 82Pb and 83Bi induced by the Cq+ (q = 4, 5) ions having energies in the range 800–1500 keV have been measured. These intensity ratios have been compared with those calculated using the ECPSSR model based carbon ion induced Mj (j = 1–5) sub-shell ionization cross sections, the X-ray emission rates based on the Dirac-Fock (DF) model, two sets of the fluorescence and Coster-Kronig yields based on the non-relativistic Hermann-Skillman potential calculations and those based on the relativistic Dirac-Hartree-Slater model. Significant differences observed between the present measured and calculated ratios could be due to multiple-ionization induced in the investigated elements by the incident carbon ions.

Measurement of L XRF cross sections for elements with 33 ≤ Z ≤ 51 and their interpretation in terms of L (i = 1–3) subshell vacancy decay parameters

Abstract The Li (i = 1–3) subshell integral X-ray fluorescence (XRF) cross sections have been measured for 17 elements with 33 ≤ Z ≤ 51 following photoionization by the Mn K X-rays (EKαβ = 5.96 keV). The Li (i = 1–3) subshell X-rays were measured using a low-energy Ge (LEGe) detector at an emission angle, ψ = 125°, where angle-dependent emission effects, if any, are nullified as P2(cos ψ) ∼ 0. The XRF cross sections were interpreted in terms of available sets of theoretical Li (i = 1–3) subshell photoionization cross sections, radiative transition probabilities, and the atomic vacancy decay parameters, namely, fluorescence (ωi) and Coster-Kronig (fij) yields. A set of L1 subshell fluorescence (ω1) yields was deduced for the elements with 37 ≤ Z ≤ 51 from the present measured Lγ2,3,(4) [L1-N2,3(O2,3)] XRF cross sections. The ω1 values exhibit jumps at Z = 40 and 49, which are identified to be due to cut-off of the L1L2M4,5 and L1L3M4,5 Coster-Kronig (CK) transitions predicted by calculations based on relativistic Dirac-Hartree-Slater (RDHS) model. However, the measured ω1 values are found to differ considerably from those based on the RDHS model calculations for the elements below Z = 50. The pronounced discrepancies between measured and theoretical ω1 values are likely to be due to overestimation of the L1-L2,3M4,5 CK transition rates by a factor of ∼2–3. Our experiential results demand consideration of extra-atomic relaxation from the solid-state effects and exchange splitting in many-body theoretical calculations of the low-energy CK transitions.

Low-energy proton induced M X-ray production cross sections for 70 Yb, 81 Tl and 82 Pb

Abstract The cross sections for production of Mk (k = Mξ, Mαβ, Mγ, Mm1) X-rays of 70Yb, 81Tl and 82Pb induced by 50–250 keV protons have been measured in the present work. The experimental cross sections have been compared with the earlier reported values and those calculated using the ionization cross sections based on the ECPSSR (Perturbed (P) stationary(S) state(S), incident ion energy (E) loss, Coulomb (C) deflection and relativistic (R) correction) model, the X-ray emission rates based on the Dirac-Fock model, the fluorescence and Coster-Kronig yields based on the Dirac-Hartree-Slater (DHS) model. In addition, the present measured proton induced X-ray production cross sections have also been compared with those calculated using the Dirac-Hartree-Slater (DHS) model based ionization cross sections and those based on the Plane wave Born Approximation (PWBA). The measured M X-ray production cross sections are, in general, found to be higher than the ECPSSR and DHS model based values and lower than the PWBA model based cross sections.

Cascade Mi (i = 1–5) subshell X‐ray emission at incident photon energies across the Lj (j = 1–3) subshell absorption edges of 66Dy

The total M shell and the Mk (k = ξ, αβ, γ, m) X‐ray production cross sections for 66Dy have been measured at incident photon energies across its Lj (j = 1–3) subshell absorption edge energies, ranging 7.8–9.2 keV. This study aims to investigate the evolution of the probability for cascade decay of Lj subshell vacancies as the tunable incident energy ionizes progressively different 66Dy Lj subshells. The experimental X‐ray production cross sections have been compared with theoretical ones calculated using the nonrelativistic Hartree–Fock–Slater (HFS) model‐based photoionization cross sections; three sets of the X‐ray emission rates, fluorescence and Coster–Kronig yield based on the nonrelativistic Hartree–Slater (NRHS) model, Dirac–Hartree–Slater (DHS) model and Dirac–Fock (DF) model; the Lj (j = 1–3) subshell to the Mi (i = 1–5) subshell vacancy transfer probabilities evaluated in the present work. Presently measured total M shell and the Mαβ X‐ray production cross sections are found to be significantly lower than the theoretical ones evaluated using physical parameters based on the relativistic Dirac–Fock/Dirac–Hartree–Slater model calculations, whereas a much better agreement is observed with respect to the NRHS model‐based calculations; however, the measured X‐ray production cross sections are still systematically lower than the NRHS values.

L x-ray production cross sections in high-Z atoms by 3–5 MeV/u silicon ions

Abstract Total L x-ray production cross sections have been measured in 74W, 79Au, 82Pb, and 83Bi by impact of 3–5 MeV/u 28Si ions, with different charge states q = 8+ up to 12+. We find that the measured cross sections do not differ with the charge state of the projectile ions, but they vary with the beam energies. The experimental data has been compared with three theoretical results, ECUSAR, ECPSSR and SLPA by using the multiple-hole fluorescence and Coster-Kronig yields. The comparison has showed the best agreement with the ECUSAR. The SLPA results also describe the experiments quite well for 74W, 79Au and 83Bi, but certain differences are observed for 82Pb, while the ECPSSR values underestimate by up to a factor two. Surprisingly, the theoretical-experimental agreement is better at low beam energies than in the high beam energy side.

Measurements of fluorescence and Coster-Kronig yields for 66Dy using synchrotron radiation induced selective photoionization method

The L shell fluorescence (ω1, ω2, ω3) and Coster-Kronig (f12, f13, f23) yields for 66Dy have been deduced from the Li (i=1–3) sub-shell X-ray intensities measured at different incident photon energies across its Li absorption edge energies. Three sets of photoionization cross sections used for determination of these yields include two sets of theoretical values based on the non-relativistic Hartree-Fock-Slater model and the self-consistent Dirac-Hartree-Fock model, and the third one is that deduced from independently measured mass attenuation coefficients of 66Dy. The present experimental fluorescence and Coster-Kronig yields deduced using the self-consistent Dirac-Hartree-Fock model based photoionization cross sections have been found to be in good agreement with the semi-empirical values tabulated by Krause [1] and the Dirac-Hartree-Slater model based values.

L sub-shell fluorescence cross-section measurements for elements, Z = 62–67, at tuned photon energies

L sub-shell X-ray fluorescence (XRF) cross-sections for 6 elements with Z= 62-67 have been measured at tuned photon energies on synchrotron Beamline-16, Indus-2, RRCAT, India. Three incident photon energies at the intervals of 0.1keV were tuned in each region; > EL1, < EL1 & >EL2 and <EL2 & >EL3 where ELi are Li (i= 1-3) absorption edge energies of element. No single measurement is available in literature for present incident photon energies and elements, therefore, certainty and reliability of the measurements have been judged from three different aspects. One, from comparison of measured cross-sections with calculated theoretical values. Second, evaluation of Coster-Kronig yield (fij’s) and fluorescence yield (ωi’s) fine parameters from measured XRF cross-sections with formulations derived from total intensity of X-rays originating from individual sub-shells that generated a data set for fij’s and ωi’s of six elements for comparison with available theoretical/empirical/experimental values. Third, from trends of total measured L XRF cross-sections with photon energy for the elements. The results were found affected by the 4f electron filling in the elements.

Measurements of the line resolved M-shell X-ray production cross sections for 79Au, 82Pb and 83Bi by 100 keV/u proton, C, N, O ions

The cross sections for production of the Mk (k=ξ, αβ, γ, m1) X-rays of 79Au, 82Pb and 83Bi induced by the 100keV/u proton, C4+, N5+ and O6+ ions have been measured in the present work. The experimental cross sections have been compared with the earlier reported values and those calculated using the ionization cross sections based on the ECPSSR model, the X-ray emission rates based on the Dirac-Fock model, the fluorescence and Coster-Kronig yields based on the Dirac-Hartree-Slater model. In addition, the present measured proton induced X-ray production cross sections have also been compared with those calculated using the Dirac-Hartree-Slater model based ionization cross sections. The intensity ratios among the Mk X-rays have been deduced and compared with the theoretical values. The present measured Mk (k=ξ, αβ, γ, m1) X-ray production cross sections are found to be very high as compared to the theoretical values. The total M X-ray production cross sections for the targets under investigation exhibited Zp2 dependence; Zp denotes the projectile atomic number.

L shell x ray production in high-Z elements using 4–6 MeV/u fluorine ions

L shell line and total x ray production cross sections in 78Pt, 79Au, 82Pb, 83Bi, 90Th, and 92U targets ionized by 4–6MeV/u fluorine ions were measured. These cross sections are compared with available theories for L shell ionization using single- and multiple-hole fluorescence and the Coster-Kronig yields. The ECPSSR and the ECUSAR theories exhibit good agreement with the measured data, whereas, the FBA theory overestimates them by a factor of two. Although for the F ion charge states q=6–8 the multiple-hole atomic parameters do not significantly differ from the single-hole values, after an account for the multiple-holes, our data are better in agreement with the ECUSAR than the ECPSSR theory.

Relativistic calculations of atomic parameters in Ununoctium

SynopsisK shell, and L and M subshells fluorescence and Coster-Kronig yields for the super-heavy element Uuo are calculated for the first time using the Dirac-Fock approach.