Subshell Fluorescence Yields Research Articles

Semi-Empirical and Theoretical Calculation of L1, L2, and L3 Subshell Fluorescence Yields

In this study, semi-empirical Li subshells fluorescence yields (ωLi) were calculated from the available experimental data covering the period from 1955 to 2022 for elements with 28 ≤ Z ≤ 96 for L1 subshell, and 23 ≤ Z ≤ 96 for L2 and L3 subshells. First, we critically examine these data and obtain weighted average values (ωL1W,ωL2W,andωL3W) using a formula based on experimental (ωEXP) values and measurement errors. New recommended values ωWR are obtained by calculating the ratio S = ωEXP/ωW and removing out-of-range values (less than 0.8 or greater than 1.2). Semi-empirical values were derived for the three subshells using two interpolations: the analytical function [ωWR/(1 − ωWR)]1/4 and the fitting ratio S = ωEXP/ωWR, both as function of the atomic number Z. Furthermore, new theoretical calculations based on the Multiconfiguration Dirac-Fock Method have been performed for some elements and are presented in this work. Finally, our semi-empirically and theorical calculated Li subshell fluorescence yields were compared with other theoretical, experimental, and empirical values from the literature.

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.

Measurement of M subshell X-ray fluorescence parameters of gold, lead and bismuth using 7 keV synchrotron radiation

The Mα and Mβ X-ray fluorescence cross sections, IMα/IMβ intensity ratio, M5 subshell fluorescence yield and M5 subshell Auger yield for gold, lead and bismuth elements were determined using Indus-2 synchrotron radiation available at the Raja Ramanna Center for Advanced Technology, India. A 7 keV synchrotron radiation was used to generate the characteristic M X-ray photons in gold, lead and bismuth and consequent X-ray photons were detected with Amptek silicon drift detector which has energy resolution of 129 eV at 5.9 keV. By measuring the area under Mα and Mβ X-ray peaks, Mα and Mβ X-ray fluorescence cross sections, IMα/IMβ intensity ratio, M5 subshell fluorescence yield and M5 subshell Auger yield were determined for gold, lead and bismuth. Experimentally determined values were compared with the theoretical and other experimental values available in the literature.

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.

Measurement of L subshell fluorescence yield ratios of some high Z elements by selective excitation method

The L1, L2 and L3 subshells of Hf, Ta and Re atoms have been excited selectively by using microprobe XRF beam line, Indus‐2, RRCAT, India. The consequent characteristic L X‐ray photons, emitted from the targets due to creations of vacancies in L subshells, are measured using silicon drift detector (X‐123) spectrometer. As the energy of synchrotron radiation increases, the contribution of characteristic L X‐ray intensity increases. The advantage of the increase in the intensity of the characteristic L X‐ray photons with an increase in the energy of synchrotron radiation has been used to determine the L subshell fluorescence yield ratios of Hf, Ta and Re atoms by adopting the selective excitation method. The measured ratios of L subshell fluorescence yield have been compared with theoretical and other experimental values.

Study of the solid-state effect on L3 subshell fluorescence yield for high Z targets using Indus-2 synchrotron radiation

L3 subshell fluorescence yields (ω3) have been determined experimentally for the compounds of Hg, Pb, and Bi and Pb element using Indus-2 synchrotron radiation available at RRCAT, India. Compounds with the same chemical bonding and oxidation state but different crystal structure have been selected in the present investigation to understand the effect of solid-state environment on ω3. The characteristic L X-ray spectra of the element and compounds were generated by synchrotron radiation and then recorded with a Vortex-90EX silicon drift detector. By measuring intensities of the characteristic Lα X-ray photons, the ω3 have been determined and compared with theoretical values and other available experimental values. Comparison between the experimental and the theoretical values indicates that the solid-state environment plays a significant role on the ω3 for the selected compounds.

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.

Measurement of Coster-Kronig vacancy transfer factor of some lanthanides using monoenergetic X-ray photons

Using monoenergetic X-ray photons from Indus-2 synchrotron Centre, the Coster-Kronig vacancy factor(κ) for L3 subshell X-rays of some lanthanide elements such as Gd, Tb, Ho and compounds such as Pr2O3, Pr2(CO3)3·8H2O, Nd2O3, Sm2O3, Sm2(CO3)3.2.85H2O, Sm2(SO4)3·8H2O, Gd2(CO3)3, Tb2O3, Dy2(SO4)3, Ho2O3 and HoF3 have been determined experimentally. By measuring Lα X-ray production cross-section, the L3 subshell fluorescence yield and theoretical values of the L3 subshell photoionization cross-section and level widths, the κ values have been determined. Comparison of the measured experimental κ values with theoretical values indicates that the influence of the chemical environment on κ values in the selected lanthanide targets is not noticeable.

L 1 , L 2 , and L 3 subshell fluorescence yields: Updated database and new empirical values

Abstract In this paper, a summary of experimental data published in the period of time between 1955 to february-2016 was presented in a tabular form for Li subshell fluorescence yields ( ω L1 , ω L2 and ω L3 ) taken from different sources. First, a critical examination of these data using the weighted average values ω Li - W was presented. Then, an interpolation using the famous analytical function ( ω Li - W / ( 1 − ω Li - W ) ) 1 / 4 vs the atomic number Z was proformed to deduce a new empirical Li subshell fluorescence yields for elements in the range 40≤Z≤96 for ω L1 and ω L2 and 23≤Z≤96 for ω L3 . At last, our calculated empirical Li subshell fluorescence yields have been compared with other theoretical and empirical values reported in the literature.

Calculations of photo-induced X-ray production cross-sections in the energy range 1–150 keV and average fluorescence yields for Zn, Cd and Hg

In this paper, we calculate the K-, L- and M-shells X-ray production, and X-ray fluorescence cross-sections after photo-induced ionization, for Zn, Cd, and Hg, and for incident photon energy range from 1 to 150 keV. For this purpose, the corresponding average fluorescence yields for Zn, Cd, and Hg as well as the photoionization cross-sections were calculated using the Dirac–Fock method. Subshell fluorescence, intrashell and intershell yields are obtained consistently from radiative and radiationless transitions calculated in the exact same method. A comprehensive account of the relations between the X-ray production, X-ray fluorescence cross-sections and the photoionization cross-sections and these yields is presented. Comparisons are made with results from other authors. The obtained values for the photoionization cross-sections are in good agreement with the widely used data of Scofield in the studied energy range. However our results for the X-ray fluorescence cross sections seem to favor some data relatively to others. The energy dependence of the average fluorescence yields is discussed, in particular, the reliability of extrapolated data for lighter elements from measurements and calculations in heavier elements above the inner shell absorption edges is questioned. Tabulated data on photoionization and X-ray production cross-sections are presented for the incident photon energy range 1–150 keV in steps of 1 keV.

Effect of chemical environment on L subshell fluorescence yields using synchrotron radiation

The L1, L2 and L3 subshell fluorescence yields have been measured for some rare earth elements such as Gd, Tb, Ho and compounds such as Gd2(CO3)3, Tb2O3 and Ho2O3 using Indus-2 synchrotron radiation. By adopting reflection geometry, the elemental and compound targets are excited with 10 keV and 11 keV synchrotron radiations in order to generate the characteristic L X-ray photons. These energies of the characteristic L X-ray photons have been measured with a silicon drift detector, which has a high energy resolution of 130 eV at 5.9 keV. By measuring the intensities of L X-rays photons, the L subshell fluorescence yields have been determined for some rare earth elements and compounds and found to be dependent on chemical environment.

Measurement of L subshell fluorescence yields of some rare earth elements using synchrotron radiation

The L subshell fluorescence yields ω1, ω2 and ω3 of Gd, Tb and Ho have been measured using Indus‐2 synchrotron radiation. The L X‐ray photons generated in the elemental targets by 10 and 11 keV synchrotron radiation have been measured using silicon drift detector that has an energy resolution of 130 eV at 5.9 keV. The measured values of ω1, ω2 and ω3 have been compared with theoretical values, semi‐empirical fitted values and other experimental values. Copyright © 2015 John Wiley &amp; Sons, Ltd.

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 L3 subshell absorption jump ratios and jump factors for high Z elements using EDXRF technique

Energy dispersive X-ray fluorescence technique (EDXRF) has been employed for measuring L3-subshell absorption jump ratios, rL3 and jump factors, JL3 for high Z elements. Jump factors and jump ratios for these elements have been determined by measuring L3 subshell fluorescence parameters such as L3 subshell X-ray production cross section σL3, L3 subshell fluorescence yield, ωL3, total L3 subshell and higher subshells photoionization cross section σLT. Measurements were performed using a Cd-109 radioactive point source and an Si(Li) detector in direct excitation experimental geometry. Measured values for jump factors and jump ratios have been compared with theoretically calculated and other experimental values.

M sub-shell fluorescence and Coster–Kronig yield data generation for elements, 57≤Z≤90 (computer code ‘MFCKYLD’)

M subshell fluorescence yield (ωMi, i=1−5) and Coster-Kronig yield (fMij, i=1−4, j=2−5) values have been generated for elements with Z, 57≤Z≤90. Keeping in view the importance of ωMi and fMij for M X-ray productions in the region Z>56, the interpolation of non-relativistic data of McGuire [Phys. Rev. A 1972;5:1043–7] in the region Z=57–90 as well as relativistic data of Chen et al. [Phys. Rev. A 1980;21:449–53 and 1983;27:2989–94] in the region Z=67–90 was attempted. The agreement between the generated data and the actual ones supported the adopted procedure. Subsequently, a computer software code MFCKYLD was developed to generate the yield values on computer terminal or in file for both non-relativistic and relativistic data just by entering the atomic number Z of the element through keyboard or file. The precision of present procedure that relies on the deviation of fitted values from the actual ones was found far better than the earlier fitted data.

Investigation on L-shell X-ray fluorescence parameters for heavy elements and compounds

The L-shell X-ray intensity ratios, the production cross-sections, the average L-shell fluorescence yields, the L 3 sub-shell fluorescence yields and the radiative vacancy transfer probabilities from the L 3 sub-shell to the M, N and O sub-shells for heavy elements and their compounds from Ta to Pt were measured. The samples were excited by 59.5 keV γ-rays from a 241Am annular radioactive source. The L X-rays emitted by the samples were counted by an Ultra-LEGe detector with a resolution of 150 eV at 5.9 keV. The experimental values were compared with the theoretical and other experimental values for pure elements.

L1 and L2 sub-shell fluorescence yields for elements with 64⩽Z⩽70

Abstract The L 1 and L 2 sub-shell fluorescence yields have been deduced for elements with 64 ⩽ Z ⩽ 70 from the L k ( k = l , α , β 1,4 , β 3,6 , β 2,15,9,10,7 , γ 1,5 and γ 2,3,4 ) X-ray production cross sections measured at 22.6 keV incident photon energy using a spectrometer involving a disc type radioisotope of Cd 109 as a photon source and a Peltier cooled X-ray detector. The incident photon intensity, detector efficiency and geometrical factor have been determined from the K X-ray yields emitted from elemental targets with 20 ⩽ Z ⩽ 42 in the same geometrical setup and from knowledge of the K shell cross sections. The present deduced ω 1 (exp) values, for elements with 64 ⩽ Z ⩽ 70, are found to be in good agreement with those tabulated by Campbell (J.L. Campbell, Atom. Data Nucl. Data Tables 95 (2009) 115), where as these are, on an average, higher by 19% and 24% than those based on the Dirac–Hartree–Slater model (S. Puri et al., X-ray Spectrometry 22 (1993) 358) and the semi-empirical values compiled by Krause (M.O. Krause, J. Phys. Chem. Ref. Data 8 (1979) 307), respectively. The present deduced ω 2 (exp) values are found to be in good agreement with those based on the Dirac–Hartree–Slater model and are higher by up to ∼13% than the semi-empirical values for the elements under investigation.

Measurement of L subshell fluorescence yields of some elements in the atomic range 75⩽ Z⩽92 using photoionization

L subshell fluorescence yields ( ω 1, ω 2 and ω 3) for the elements Re, Os, Ir, Pt, Au, Hg, Tl, Pb, Bi, Th and U have been measured at the 123.6 keV γ-ray emission excitation energy from a 57Co annular radioactive source (925 MBq) using a Si(Li) detector. The measured L subshell fluorescence yields were compared with the theoretical and semi-empirical values.

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

Our recently recommended values for the L1 subshell fluorescence yield ω 1 and Coster–Kronig probabilities f 13 and f 12 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.

L i ( i = 1–3) subshell X-ray production cross sections and fluorescence yields for some elements with 56 ⩽ Z ⩽ 68 at 22.6 keV

The L k ( k = l, α, β 1,4, β 3,6, β 2,15,9,10,7, γ 1,5 and γ 2,3,4) X-ray production (XRP) cross sections have been measured for six elements with 56 ⩽ Z ⩽ 68 at 22.6 keV incident photon energy using the EDXRF spectrometer. The incident photon intensity, detector efficiency and geometrical factors have been determined from the K X-ray yields emitted from elemental targets with 22 ⩽ Z ⩽ 42 in the same geometrical setup and from knowledge of the K XRP cross sections. The L 1 and L 2 subshell fluorescence yields have been deduced from the present measured L k XRP cross sections using the relativistic Hartree-Fock-Slater (HFS) model based photoionization cross sections. The present deduced ω 1 (exp) values have been found to be, on an average, higher by 15% and 20% than those based on the Dirac–Hartree–Slater (DHS) model and the semi-empirical values compiled by Krause, respectively, for elements with 60 ⩽ Z ⩽ 68.