Relativistic Hartree-Slater Research Articles

Contribution of near-edge processes to the L X-ray emission lines for various lanthanum (III) compounds

The present measurement illustrates the study of near-edge processes and the intensity ratios [ILl/ILα, ILβ1/ILα and ILl/ILβ1] for Mn Kα1,2 X-rays across the L2 edge of lanthanum in its various chemical forms viz., lanthanum oxide (La2O3), lanthanum oxalate (C6La2O12) and lanthanum acetate (C6H9LaO6) at four different scattering angles i.e. 90°, 105°, 115° and 125° with a lab-scale X-ray fluorescence (XRF) spectrometer. The current observation reveals that the Lβ1 X-ray emission lines exhibit a variance of ∼ (21–40) % between measured and calculated fluorescence cross-sections. Apart from this, the measured values of intensity ratios have been compared with the three data sets of calculated values using L shell emission rates based on the Dirac-Fock (DF) model, total X-ray emission rates and photoionization cross-section values based on the relativistic Hartree-Slater (RHS) model and three sets of Coster-Kronig (CK) and fluorescence yields. The correlation between crystal structure, bond distance and intensity ratio are also discussed in this work.

Experimental measurements of K X-ray production cross-sections and yields for the elements with 58 $\leqslant$ Z $\leqslant$ 64 at 123.6 keV photon energy

Considering the importance of the K X-ray production cross-sections $(\sigma_{K_{i}}^{\rm x})$ as well as the K shell fluorescence yields (ωK) for the determination of element concentrations in a given material, we have measured them experimentally for the elements Ce, Pr, Nd, Sm, Eu and Gd using photons at 123.6 keV from a 57Co radioisotope source. Furthermore, the K X-rays intensity ratios (Kβ/Kα) for these elements have been investigated. The characteristic K X-rays emitted by the target were detected by a high-resolution with an energy resolution of 160 eV full with at half-maximum (FWHM) at 5.96 keV. The experimental results of K X-ray production cross-sections were compared with theoretically predicted values based on relativistic Hartree-Slater and Hartree-Fock theories. Similarly, the measured K shell fluorescence yields/cross-sections and the K X-rays intensity ratios were compared with the theoretical values. In most cases, there is an agreement between the experimental and theoretical data within the experimental uncertainties.

Measurement of total, radiative and radiationless (Auger) vacancy transfer probabilities from K to Li subshell of Sm and Tb

The vacancy transfer probabilities of K to L1, L2 and L3 shell were measured with a new method. The L X-ray yields of targets excited by 59.5 keV incident photons, i.e., above the K edge of elements, were detected with a high-resolution Si(Li) detector. For comparison with the experimental results, theoretical calculations were made using data available on radiative and radiationless transitions. The radiative transition values of these elements were taken from the relativistic Hartree-Slater model, those of the radiationless transitions from the Dirac-Hartree-Slater model. The measured values were found to be in good agreement with theoretical ones. The hKLi (i = 1, 2, 3) values were calculated by measuring the L1x, L2x and L3x X-ray production cross-sections.

Measurement of probabilities for vacancy transfer from the K to L shell of the elements 73⩽Z⩽92

K- to L-shell vacancy transfer probabilities were measured for ten elements in the atomic range 73\ensuremath{\leqslant}Z\ensuremath{\leqslant}92. Those measuring L x-ray yields from targets excited by 59.5 and 122 keV incident photons, i.e., below and above the K edge of elements, were detected with a high-resolution Si(Li) detector. For comparison with experimental results, theoretical calculations were made by using available data on radiative and radiationless transitions. The radiative transitions of these elements were observed from the relativistic Hartree-Slater model which was proposed by Scofield [At. Data Nucl. Data Tables 14, 121 (1974)]. The radiationless transitions were observed from the Dirac-Hartree-Slater model which was proposed by Chen, Craseman, and Mark [At. Data Nucl. Data Tables 24, 13 (1979)]. The measured results were found to be in good agreement with theoretically calculated values. The experimental and theoretical values were fitted versus atomic number Z.

A Practical Method for the Analysis of Overlapped Peaks in Energy Dispersive X-Ray Spectra

ABSTRACT In this study a practical method for the spectral analysis of some overlapped characteristic X-ray peaks is presented. The overlapped characteristic K, and K, peaks and the artificially overlapped two K, peaks (peak doublet) of arsenic obtained by the radioisotope-excited, energy dispersive X-ray fluorescence (EDXRF) technique, are resolved. A total of 34 overlapped peak systems were investigated: the proposed method provided 18 reliable results, whereas the first and the second methods gave 15 and 1, respectively. The intensity ratios of Kβ/Kα, obtained by the novel method are also in good agreement with the theoretical relativistic Hartree-Slater values.

Angular distribution of photoelectrons from polarized X-rays

The general form of the angular distribution of the photoelectrons ejected by linearly polarized radiation is presented which includes the contributions of all multipoles of the ionizing radiation. Explicit results for photon energies less than 3 keV are presented calculated on the basis of the independent particle relativistic Hartree-Slater theory. It is found that for energies as low as 500 eV, ten percent asymmetries can be expected from the multipoles beyond the electric dipole approximation. In general, for photon energies less than 3 keV, three energy-dependent parameters are sufficient to describe the angular distribution. For some ranges of atomic numbers, a few subshells have 5 percent contributions from two additional parameters.

Quantum efficiency of gold photocathodes (2–8 keV) and EXAFS in its secondary electron yield and in the detection currents of a microchannel plate and a silicon surface barrier detector

The quantum efficiency of gold photocathodes has been investigated by using synchrotron radiation from 2–8 keV; in particular its detailed structure near the M absorption edge region is obtained. The secondary electron conversion efficiency of gold has been calculated by using the mass absorption coefficient given by a relativistic Hartree-Slater model and by the semiempirical values of Henke et al., respectively. These data are compared with the published data at some discrete energies, and we add several new data points, especially for the gold M edge region (2–4 keV). X-ray absorption fine structure (EXAFS) has been observed in the secondary electron current of the gold photocathode as well as in the detection current responses of a microchannel plate and a silicon surface barrier detector.

Relative intensity database of L-Shell lines of lanthanides and analysis of the PIXE spectra

The PIXE spectra resulting from proton beam bombardment in the energy range of 1 to 2.5 MeV of the thin targets of 14 lanthanides were measured using a Ge detector to obtain a relative intensity database of the L-shell lines. The database utilizes the relativistic Hartree-Slater (RHS) emission rates reported by Scofield. To correct the other quantities affecting the relative intensities such as L-subshell ionization cross sections etc., empirical factors are introduced and the values are determined by the least squares method. The reduced chi-squared value is 0.85 ± 0.4 for 90 spectra. The relative intensities of Nd, Dy and Yb obtained at 2 MeV are compared with the recent ECPSSR approach by Cohen and Harrigan, and it is found that these results are in fairly good agreement. The PIXE spectra of the mixtures of lanthanides and the crude rare-earth chlorides from monazite are analyzed by use of the database. The reasonable analytical results obtained confirm the practical utility of this approach. The performance of a program, PIXS, developed for doing the analysis on a personal computer is also reported.

Analytic perturbation theory for screened Coulomb potentials: Relativistic case

Analytic expressions for relativistic screened Coulomb radial wave functions, including bound-state energy eigenvalues as well as bound and continuum wave-function shapes and normalizations, are given explicitly as series in $\ensuremath{\lambda}\ensuremath{\simeq}\ensuremath{\alpha}{Z}^{\frac{1}{3}}$. The method employed is a direct generalization of an approach previously used for the nonrelativistic case. The analytic expansions which we obtain are compared with exact numerical solutions of the Dirac equation for relativistic Hartree-Slater potentials. Low-, intermediate-, and high-$Z$ cases are considered for a wide range of energies and angular momenta. In general, excellent agreement is found for both inner bound states and for relativistic continuum states.

UraniumMx-ray emission spectrum

The uranium $M$ x-ray spectrum from a thick metallic target excited by 12-keV electrons was measured by the PAX (photoelectron spectrometry for the analysis of x rays) technique. Energies of the strongest lines were obtained with an accuracy of 0.1 eV using Ag $L{\ensuremath{\beta}}_{1}$ and Ag $L{\ensuremath{\alpha}}_{1}$ as standards. Widths of the uranium lines were obtained by deconvoluting the measured Voigt profiles, and the experimental values were found to agree satisfactorily with McGuire's Hartree-Slater predictions. Natural widths of 4.0(3) and 3.8(3) eV were derived for the ${M}_{4}$ and ${M}_{5}$ levels, respectively, and the energies of the ${M}_{4}$, ${M}_{5}$, ${N}_{2}$, and ${N}_{3}$ levels in uranium metal were determined. Relative intensities of the $M$ lines were measured, and branching ratios were found to be in fair agreement with relativistic Hartree-Slater predictions. The satellite structures of the $M{\ensuremath{\alpha}}_{1}$ and $M\ensuremath{\beta}$ lines were interpreted in terms of the pertinent multiple-hole configurations. Finally, an approximate analytic expression for the Voigt half-width and its graphical representation are given.

Relativistic hartree-slater values for K and L X-ray emission rates

The x-ray emission rates for the filling of K - and L -shell vacancies, calculated with the relativistic Hartree-Slater theory, are given for elements with Z =5 to 104. Account was taken of the finite extent of nuclear-charge distributions. Presented are ratios of the major K -shell components, the total K - and L -shell radiative decay rates, and the rates of emission of individual x-ray lines.

Radiative Decay Rates of Vacancies in theKandLShells

A calculation is made of the rates of emission of x rays in the filling of vacancies in the $K$ and $L$ shells. The total radiative decay rates and the rates of emission of a number of x-ray lines are presented for a range of elements. The atomic electrons are taken to be in single-particle states in a central potential given by the relativistic Hartree-Slater theory. All multipoles of the radiation field and all transitions from occupied states of the atom are included. The electrons are treated relativistically and the effect of retardation is included.