Relativistic Dirac-Hartree-Slater Research Articles

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.

M ξ, M αβ, M γ and M m X-ray production cross-sections for elements with 71⩽ z⩽92 at 5.96 keV photon energy

The M ξ, M αβ, M γ and M m X-ray production (XRP) cross-sections have been measured for the elements with 71⩽ Z⩽92 at 5.96 keV incident photon energy satisfying E M1< E inc< E L3, where E M1(L3) is the M 1(L 3) subshell binding energy. These XRP cross-sections have been calculated using photoionization cross-sections based on the relativistic Dirac–Hartree–Slater (RDHS) model with three sets of X-ray emission rates, fluorescence, Coster–Kronig and super Coster–Kronig yields based on (i) the non-relativistic Hartree–Slater (NRHS) potential model, (ii) the RDHS model and (iii) the relativistic Dirac–Fock (RDF) model. For the third set, the M i ( i=1–5) subshell fluorescence yields have been calculated using the RDF model-based X-ray emission rates and total widths reevaluated to incorporate the RDF model-based radiative widths. The measured cross-sections have been compared with the calculated values to check the applicability of the physical parameters based on different models.

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.

Measurement of the radiative vacancy transfer probabilities from the L 3 to M and to N shells for W, Re and Pb using synchrotron radiation

The radiative vacancy transfer probabilities from L 3 to M shell, η L 3 M ( R ) and L 3 to N shell, η L 3 N ( R ) , have been determined for W, Re and Pb. The pure elements samples were excited by monochromatic synchrotron radiation. The X-rays were generated by excitation of L 3 edge and measured using a high resolution Si(Li) detector. The experimentally determined radiative vacancy transfer probabilities were compared with the theoretical values deduced using radiative X-ray emission rates based on the relativistic Dirac–Hartree–Slater (RDHS) model. In the case of Pb, the experimental data were compared as well with experimental values of Simsek. In both cases, a good agreement was found between the datasets.

Probabilities for radiative vacancy transfer from Li (i=1, 2, 3) sub-shells to the M, N and higher shells for elements with 77≤Z≤92

Abstract The probabilities for transfer of the Li (i=1, 2, 3) subshell vacancy to the M, N and higher shells through radiative decay, η L i J ( R ) , have been deduced for the elements with 77≤Z≤92 using the measured L X-ray production cross-sections at (i) the 59.54 keV γ-rays such that B L 1 E inc B K and (ii) the K X-rays of a suitable secondary target chosen such that B L 3 E K α B L 2 and B L 1 / L 2 E K β B K ; where B K / L i is the K shell/Li subshell ionisation threshold of the target element. The deduced probabilities are compared with those calculated using the radiative and nonradiative transition rates based on the Dirac–Fock (DF) and the relativistic Dirac–Hartree–Slater (RDHS) calculations, respectively.

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

AbstractThe 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 &lt; Einc &lt; BK) and for the L3 sub‐shell x‐rays following ionization by Rb K x‐rays (B &lt; EKα &lt; B, B &lt; EKβ &lt; BK), where B 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 f13 based on the RDHS calculations are overestimated. Copyright © 2004 John Wiley &amp; Sons, Ltd.

L1−L3Coster-Kronig yield for elements with70⩽Z⩽81

The ${L}_{1}\text{\ensuremath{-}}{L}_{3}$ Coster-Kronig (CK) yield ${f}_{13}$ for the $_{70}\mathrm{Yb}$, $_{71}\mathrm{Lu}$, $_{74}\mathrm{W}$, $_{75}\mathrm{Re}$, $_{79}\mathrm{Au}$, $_{80}\mathrm{Hg}$, and $_{81}\mathrm{Tl}$ elements was deduced using measured intensities of the $L\ensuremath{\alpha}$ x rays emitted following decay of the ${L}_{i}$-subshell $(i=1,2,3)$ vacancies produced in widely different proportions by the $59.54\phantom{\rule{0.3em}{0ex}}\text{keV}$ $\ensuremath{\gamma}$ rays $({B}_{{L}_{1}}l{E}_{inc}l{B}_{K})$ and the $\text{Ge}∕\text{Se}∕\text{Rb}$ $K$ x rays $({B}_{{L}_{3}}l{E}_{K\ensuremath{\alpha}}l{B}_{{L}_{2}},{B}_{{L}_{1}∕{L}_{2}}l{E}_{K\ensuremath{\beta}}l{B}_{K})$; where ${\mathrm{B}}_{K∕Li}$ is the $K$-shell∕${L}_{i}$-subshell binding energy of the target element. An energy-dispersive x-ray fluorescence set up, involving photon sources consisting of a $^{241}\mathrm{Am}$ annular source in the direct and secondary excitation modes along with the $\text{Ge}∕\text{Se}∕\text{RbCl}$ secondary exciter and a $\text{Si}(\text{Li})$ detector, was used for the measurements. The measured ${f}_{13}$ yields for $_{70}\mathrm{Yb}$, $_{71}\mathrm{Lu}$, and $_{74}\mathrm{W}$ are found to agree with the values based on the relativistic Dirac-Hartree-Slater (RDHS) calculations, while those for $_{79}\mathrm{Au}$, $_{80}\mathrm{Hg}$, and $_{81}\mathrm{Tl}$ are lower by $\ensuremath{\sim}20%$. The measured ${f}_{13}$ yields exhibit a jump from 0.354(24) for $_{74}\mathrm{W}$ to 0.450(27) for $_{75}\mathrm{Re}$ compared to that from 0.352 to 0.640 as predicted by the RDHS calculations due to onset of the intense ${L}_{1}\text{\ensuremath{-}}{L}_{3}{M}_{5}$ CK transition.

L i ( i=1,2,3) subshell X-ray production cross-sections and fluorescence yields for Ir, Pt, Pb and Bi

The L i ( i=1,2,3) subshell X-ray production (XRP) cross-sections were measured for 77Ir, 78Pt, 82Pb and 83Bi following direct ionization in the L i ( i=1,2,3) subshells by the 59.54 keV γ-rays and the L 3 subshell by the Br/Rb/Sr/Y K X-rays. The photon sources consisting of an 241Am source in (i) the direct excitation mode and (ii) the secondary excitation mode together with the KBr/RbNO 3/SrCO 3 /Y secondary exciter and an Si(Li) detector were used. The L i ( i=1,2,3) subshell fluorescence yields ( ω i ) for these elements were deduced using the measured XRP cross-sections and the L i subshell photoionization cross-sections based on the Hartree–Fock–Slater model. The measured ω 1 values are found to be higher upto 50% than those based on the relativistic Dirac–Hartree–Slater (RDHS) calculations, while the ω 2 and ω 3 values exhibit good agreement. The predicted jump in the RDHS based ω 1 values from 77Ir to 78Pt due to onset of intense L 1–L 3M 4 CK transition is not observed.

L X-ray fluorescence cross sections in the atomic region 46⩽ Z⩽51 excited by 6.47, 7.57 and 8.12 keV photons

Total L X-ray fluorescence cross sections have been measured for the elements Sb, Sn, In, Cd, Ag and Pd excited by 6.47, 7.57 and 8.12 keV photons. The measurements have been performed using an X-ray tube with a modified secondary exciter system as the excitation source. In order to improve the efficiency of the detection system, the excitation source, detector and the target assembly were placed in a vacuum chamber. The measurements were made at a pressure of 10 −2 mbar. The present system considerably reduces the scattering and background effects and improves the monochromaticity. The experimental results have been compared with the theoretical values evaluated using L-subshell fluorescence yields ( ω i ) and Coster-Kronig transition probabilities ( ƒ ij ) based on relativistic Dirac-Hartree-Slater (RDHS) theory. It is observed that the L X-ray cross-section values for the elements in the region are in good agreement with the theoretical values based on RDHS theory. The average L-shell fluorescence yields have also been computed using the experimentally measured cross-section values and the theoretical photoionization cross sections. The average fluorescence yields have been compared with the available results in the literature.

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

AbstractThe values of Li sub‐shell fluorescence yields (ωi) 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 (ϖL) yields were also evaluated and least‐squares fitted to obtain the polynomials representing them as a function of atomic number.

Measurements of L to M shell vacancy transfer probabilities for the elements in the atomic region 70 ≤ Z ≤ 92

The probabilities for vacancy transfer from L to M shell, \\ ̄ gh LM, are deduced for 15 elements in the atomic region 70 ≤ Z ≤ 92 by measuring the M X-ray yields from the targets excited by 5.96 and 22.6 keV incident photons, i.e. below and above the L-edge of the elements and using the theoretical L and M shell photoionisation cross-sections. These results are compared with the theoretical values based on the relativistic Dirac-Hartree-Slater (RDHS) and the nonrelativistic approximate Herman-Skillman (AHS) calculations. From the comparison, it is concluded that the onset of L 1−L 3M 5 Coster-Kronig transition occurs at Z = 75 as predicted by the RDHS model based Coster-Kronig transition energy calculations.

Measurements of K to L shell vacancy transfer probability for the elements 37 ≤ Z ≤ 42

The probabilities for vacancy transfer from K shell to L shell, η kl , are deduced for six elements in the atomic region 37 ≤ Z ≤ 42 by measuring the L X-ray yields from targets excited by 5.96 and 22.6 keV incident photons, i.e. below and above the K edge of the elements and using the theoretical K shell and L shell photoionisation cross-sections. The measured results are found to be in good agreement with those based on relativistic Dirac Hartree Slater (RDHS) calculations and the available semi-empirical values. The theoretical η KL values for the elements with 18 ≤ Z ≤ 96 are least-squares fitted to the fifth-order polynomial in atomic number ( Z).

Physical parameters for L x‐ray production cross‐sections

AbstractPhoton‐induced L x‐ray production cross‐sections for the elements with 56 ≤ Z ≤ 92 were calculated at different energies in the range 11–60 keV using the photoionization cross‐sections based on the relativistic Dirac–Hartree–Slater (RDHS) model, fluorescence yields and Coster–Kronig transition probabilities based on the RDHS model and two sets of emission rates based on the Dirac–Fock (DF) model and the Dirac–Hartree–Slater (DHS) model. These calculated results were compared with the experimentally measured cross‐sections to check the applicability of emission rates based on the DF and DHS models.