Atomic Photoeffect Research Articles

Assessing the Accuracy of Mass Attenuation Coefficients for Soft X-ray EPMA.

The use of soft X-rays in electron probe microanalysis (EPMA) has gained renewed interest over the past decades due to the advent of new detector technologies. Because X-ray absorption is the dominant correction for soft X-rays, a reliable set of mass attenuation coefficients (MACs) is needed for accurate composition determination. Although several MAC tabulations cover the soft X-ray range, the accuracy of such tabulations below 1 keV is not firmly established. In this study, we assess the accuracy of MAC tabulations in the soft X-ray region by comparing tabulated values for Be, B, C, N, O, and F Kα X-rays with experimental data available in the literature. We find that the 1993 semi-empirical MAC compilation of Henke et al. [(1993). Low-energy X-ray interaction coefficients: Photoabsorption, scattering, transmission and reflection at E=50-30000 eV, Z=1-92. Atom Data Nucl Data Tables54, 181-342] and the more recent theoretical MAC calculations of Sabbatucci and Salvat [(2016). Theory and calculation of the atomic photoeffect. Rad Phys Chem121, 122-140] perform slightly better than the rest of the considered tabulations. The Sabbatucci-Salvat dataset also provides the best agreement with the few existing experimental measurements for Al L2,3M X-rays.

Determination of Mass Attenuation Coefficients of Th, U, Np, and Pu for Oxygen Kα X-Rays Using an Electron Microprobe.

Mass attenuation coefficients (MACs) of Th, U, Np, and Pu for oxygen X-rays have been experimentally determined using an electron microprobe. The MACs were obtained by measuring relative X-ray intensities emitted from ThO2, UO2, NpO2, and PuO2 targets, for incident electron energies from 5 to 30 keV, and processing them with the help of the computer program XMAC. The accuracy of the measured MACs is estimated to be better than 5%. Results are compared with MAC tabulations commonly used in electron probe microanalysis as well as with theoretical photoionization calculations. It is concluded that the MACs implemented in the Monte Carlo simulation program PENELOPE which are based on the photoionization cross-section calculations of Sabbatucci & Salvat [(2016). Theory and calculation of the atomic photoeffect. Rad Phys Chem121, 122-140], provide the best agreement with our measurements. The use of different MAC schemes for the analysis of mixed actinide oxide materials is discussed.

Dirac–Fock photoionization parameters for HAXPES applications

Presented here are the photoionization cross sections and parameters of the photoelectron angular distribution for atomic subshells with binding energies lower than 1.5 keV of all elements with 1≤Z≤100 in the photon energy range 1.5–10 keV. The calculations were performed in an effort to provide handy theoretical data for experimental studies by hard X-ray photoelectron spectroscopy (HAXPES). We used the relativistic treatment of atomic photoeffect and the Dirac–Fock method with proper consideration of the electron exchange for computing the electron wave functions. The photoionization cross sections were determined including all multipoles of the radiative field while the photoelectron angular distribution parameters were obtained within the quadrupole approximation. The effect of the hole resulting in the atomic subshell after photoionization was taken into account by the use of the frozen orbital model.

Theory and calculation of the atomic photoeffect

Abstract The so-called elementary theory of the atomic photoeffect is presented in a form that is suited for practical numerical calculation of subshell cross sections and angular distributions of emitted photoelectrons. Atomic states are described within the independent-electron approximation, with bound and free one-electron orbitals that are solutions of the Dirac equation with the Dirac–Hartree–Fock–Slater self-consistent potential of the ground-state configuration. Detailed derivations are given of subshell cross sections for both excitation to discrete bound levels and ionization. In the case of ionization, the cross section differential in the direction of the photoelectron is obtained for partially polarized photons, with the polarization specified by means of the Stokes parameters. The theoretical formulas have been implemented in a computer program named photacs that calculates tables of excitation and ionization cross sections for any element and subshell. Numerical calculations are practicable for excitations to final states with the principal quantum number up to about 20 and for ionization by photons with energy up to about 2 MeV. Elaborate extrapolation schemes for determining the subshell cross section for excitation to bound levels with larger principal quantum numbers and for ionization by photons with higher energies are described. The effect of the finite width of atomic energy levels is accounted for by convolving the calculated subshell cross-section with a Lorentzian profile.

On the Atomic Photoeffect in Non-relativistic QED

In this paper we present a mathematical analysis of the photoelectric effect for one-electron atoms in the framework of non-relativistic QED. We treat photo-ionization as a scattering process where in the remote past an atom in its ground state is targeted by one or several photons, while in the distant future the atom is ionized and the electron escapes to spacial infinity. Our main result shows that the ionization probability, to leading order in the fine-structure constant, α, is correctly given by formal time-dependent perturbation theory, and, moreover, that the dipole approximation produces an error of only sub-leading order in α. In this sense, the dipole approximation is rigorously justified.

Atomic photoeffect in the pulsed fields of a high-order harmonic and the fundamental wave

The atomic photoeffect is studied in the pulsed fields of two coherent waves: a high-order harmonic wave and the fundamental wave. Expressions are derived for the intensity of the main peak and satellites in the photoelectron energy spectrum for an arbitrary delay between the pulses. The role of inelastic Coulomb rescattering of photoelectrons from the residual ion in the fundamental wave field, in the production of satellites is analysed.

On discrepancies in atomic photoeffect cross sections in the low photon energy region

Studies on photon interaction with matter provide a wealth of data for various applied scientific fields. While large amounts of compiled data are available on photon cross sections, significant discrepancies have been observed at very low photon energies, especially in the region of absorption edges; the cross section in some elements shows approximately 10% variation with theory. In the present study, attenuation studies have been made for energies below 60 keV for the elements Zr, Pd, Cd, In, and Ta, these being situations in which discrepancies have been noted. Use has been made of a narrow beam, good geometry situation, coupled with a Freolectric cooled Si(Li) detector attached to a System 100 Canberra multichannel analyser. Total photon and total photoelectric cross sections have been deduced and compared with theory.

Double atomic photoeffect in the relativistic domain: Angular and energy distributions of photoelectrons

We study the double ionization of the atomic K-shell by a single photon in the relativistic energy domain. The differential and total cross sections of the process are calculated. It is shown that the ratio of the cross sections of double and single ionization increases with the photon energy, tending to the limit 0.34/Z2, where Z is the atomic number or the nuclear charge. The formulas are found to be valid for Z≫1 and αZ≪1, where α=1/137 is the fine-structure constant.

On the continuity in energy of the free-bound one-photon cross-sections

For a charged particle in a central field of force we discuss the continuity in energy of the cross-sections for the related processes of ground state photoeffect and radiative capture. This continuity follows from general arguments, while for a Coulomb potential, where exact analytic expressions are available, the continuity can also be traced explicitly through the calculation. Our analysis allows us to identify an error in papers on radiative muon capture in the ground state which claim the existence of a discontinuity in the cross-section, occurring in hydrogen for muon energies in the neighbourhood of 2.8 keV. As a discontinuity in radiative capture would imply a discontinuity in atomic photoeffect, we note that in the latter case there are extensive experimental results in good qualitative agreement with the usual continuous result (Stobbe formula) for the cross-section.

Atomic photoeffect below 100 keV: An overview and future scope

The atomic photoeffect is a very important mechanism of photon interaction with matter, especially below 100 keV, and most of the experimental data on photoelectric interaction is concentrated in this energy region. In spite of the availability of a huge amount of data, large discrepancies are observed in cross-sections close to the absorption edges and particularly on the high energy side. The K-absorption edges could be easily studied using transmission experiments by selecting the energies, in either of two ways. First, photon energies could be selected as close to the edge as possible so that the experimental cross-sections would give a possible clue to the extended X-ray absorption fine structure which is seen on the high energy side of the K-edge. Secondly, one can choose a wider photon energy region to cover at least three times the shell binding energy so that more distant cross-section values help to predict the trends of the cross-section curve with more certainty. In the present study, the advantages of such a method, methods of experimental procedures, and difficulties in experimentation are presented.

A new method to determine the atomic photo effect cross section in lead at 661.6 keV

A new method has been developed to determine the atomic photo effect cross section for lead at 661.6 keV. This method is simpler compared to all the direct methods in vogue to measure the total photo effect cross sections. The important attribute of this method is that one can measure the total photo effect cross sections of lead whether lead is in pure elemental (foil) form or in the form of its chemical compound. In the present study Pb, PbO, PbSO 4 and Pb(NO 3) 2 were used, and the photo effect cross section for lead was obtained. The salient features of the method are discussed. The mean value obtained from all the samples for lead is compared with Scofield's theoretical value and found to be in good agreement.

Direct radiative recombination and photoeffect cross sections for arbitrary atomic Coulomb bound states

Simple exact analytical cross sections for direct radiative recombination (DRR) and atomic photoeffect for arbitrary (n, l, m) states are obtained in the nonrelativistic Coulomb dipole approximation. These may also be used in the case of DRR or photoeffect on the Rydberg states of highly ionized atoms with N electrons by considering an effective ionic charge Z eff =Z-N. Asymptotic formulae in the energy of the incoming particle are derived. The numerical values of the DRR cross sections obtained with our formulae are in very good agreement with the existing numerical relativistic results. This is true for high Z values and large energies of the incoming electron

Atomic photoeffect cross sections for beryllium, carbon, silicon and copper from 5 to 20 keV

Atomic photoeffect cross sections for Be, C, Si, and Cu have been derived from experimental mass attenuation coefficients in the X-ray range. The data are compared with theoretical photoabsorption calculations by Scofield (1973) and others. Systematic trends suggest that the Scofield theoretical values with and without the Hartree-Slater to Hartree-Fock renormalisation can be used as lower and upper limits of the experimental photoeffect cross sections.

A study on atomic photo effect cross sections at the K-edge in high Z-elements

Abstract The various K-edge parameters have been evaluated for six elements, W, Hg, Pb, Bi, Th and U, from our previous total attenuation measurements. The results are compared with the latest data of Scofield and an agreement within the experimental uncertainty is observed. An extensive comparison with earlier experimental data and empirical relations is also made.

Incoherent scattering of gamma-rays in C, O, Al and S

The total atomic cross-sections are determined in carbon, oxygen, aluminium and sulphur at photon energies 52.0, 73.0, 84.2, 145.4, 279.2 and 661.6 keV by transmission method in a good geometry set-up. The incoherent-scattering cross-sections are obtained by subtracting the theoretical sum of atomic photoeffect and coherent scattering crosssections from the measured total cross-sections. The results obtained have been compared with theoretical values.

A relativistic program for optical response in atoms using a time-dependent local density approximation

The so-called elementary theory of the atomic photoeffect is presented in a form that is suited for practical numerical calculation of subshell cross sections and angular distributions of emitted photoelectrons. Atomic states are described within the independent-electron approximation, with bound and free one-electron orbitals that are solutions of the Dirac equation with the Dirac–Hartree–Fock–Slater self-consistent potential of the ground-state configuration. Detailed derivations are given of subshell cross sections for both excitation to discrete bound levels and ionization. In the case of ionization, the cross section differential in the direction of the photoelectron is obtained for partially polarized photons, with the polarization specified by means of the Stokes parameters. The theoretical formulas have been implemented in a computer program named photacs that calculates tables of excitation and ionization cross sections for any element and subshell. Numerical calculations are practicable for excitations to final states with the principal quantum number up to about 20 and for ionization by photons with energy up to about 2 MeV. Elaborate extrapolation schemes for determining the subshell cross section for excitation to bound levels with larger principal quantum numbers and for ionization by photons with higher energies are described. The effect of the finite width of atomic energy levels is accounted for by convolving the calculated subshell cross-section with a Lorentzian profile.

Photon cross section measurements in compounds and elements in the energy range 30–660 keV

Total photon attenuation coefficients have been measured at seven energies in the range 30–660 keV for 18 elements and 29 compounds. From the results obtained on compounds, the total photon cross sections for certain elements are obtained applying the mixture rule. Direct measurements could be obtained on 18 elements. Atomic photo effect cross sections in medium and high Z elements in the energy range 30–280 keV are derived from all data by subtracting the relatively small scattering (coherent+incoherent) cross sections from the total atomic cross sections. They are compared with theoretical values.

Photon mass attenuation and energy-absorption coefficients

Mass attenuation coefficients μ/ϱ and mass energy-absorption coefficients μ cn/ϱ are tabulated in units of m 2 kg −1 for photon energies 1 keV to 20 MeV for 40 elements ranging from hydrogen (Z= 1) to uranium (Z= 92). In addition, μ/ϱ and μ cn /ϱ values are tabulated over this same energy range for 45 mixtures and compounds of dosimetric interest, computed from the above data using fractions-by-weight of the constituent elements. Source data for these tables are primarily theoretical. The atomic photoeffect cross sections, with minor empirical modifications, are from the 1973 computations of Scofield. The incoherent (bound-electron Compton) and coherent scattering cross sections, also pair and triplet production cross sections, are from recently published (1975, 1979, 1980) compilations developed at NBS in collaboration with researchers from various laboratories including Kaman Sciences, Los Alamos Scientific Laboratory, Lawrence Livermore National Laboratory, Max-Planck-Institute (Mainz) and the University of Trondheim. Information is provided for estimating photonuclear contributions above 5 MeV. Differences for NSRDS-NBS 29 (1969) and Storm-Israel (1970) are of the order of 1% or less over most of the element-energy range, but in some cases are as much as 5%.

Radiative corrections to atomic photoeffect and tip bremsstrahlung. III

The radiative corrections to the photoeffect from the $K$ shell were evaluated recently by McEnnan and Gavrila assuming a hydrogenlike atomic model. The result was expressed in the form of a corrective factor [$1+(\frac{\ensuremath{\alpha}}{\ensuremath{\pi}})\ensuremath{\delta}$] multiplying the basic photoeffect differential cross section. An expression for $\ensuremath{\delta}$, correct to lowest order in $\ensuremath{\alpha}$ and $\ensuremath{\alpha}Z$, was derived in analytic form in terms of a large number of single and double integrals over Feynman parameters, requiring numerical integration. $\ensuremath{\delta}$ depends on the photon energy $\ensuremath{\omega}$, on the electron-ejection angle $\ensuremath{\theta}$, and on the energy threshold $\ensuremath{\Delta}E$ below which we allow the additional (soft) photon, emitted together with the ejected electron to go undetected. The $\ensuremath{\Delta}E$ dependence of $\ensuremath{\delta}$ reflects the inseparable connection between the $K$-shell photoeffect and the Compton effect from the $K$ shell with (soft) photons emitted in the range $\ensuremath{\Delta}E$. It was shown that the same expression for $\ensuremath{\delta}$ with an appropriate redefinition of the variables, also radiatively corrects the bremsstrahlung spectrum at its high-energy tip. In the present work we have carried out the computation of $\ensuremath{\delta}$. It covers the $\ensuremath{\omega}$ energy range from 0.5 keV to 50 MeV at all relevant angles. The relative error was kept below 0.001, except at high energies where it was only 0.01. We find that ($\ensuremath{-}\frac{\ensuremath{\alpha}\ensuremath{\delta}}{\ensuremath{\pi}}$) is always positive and increases with $\ensuremath{\theta}$ and $\ensuremath{\omega}$. At energies of about 500 keV, ($\frac{\ensuremath{\alpha}\ensuremath{\delta}}{\ensuremath{\pi}}$) becomes of the order of 1% and at 5 MeV it has grown to about 5%, when taking $\ensuremath{\Delta}E=0.01$${\mathit{mc}}^{2}$. By integrating over the angles we have derived the quantity $\ensuremath{\Delta}$ which radiatively corrects the total photoelectric cross section, in the form of a factor [$1+(\frac{\ensuremath{\alpha}}{\ensuremath{\pi}})\ensuremath{\Delta}$]. We also infer by exponentiation the correct form of $\ensuremath{\delta}$ and $\ensuremath{\Delta}$ in the limit $\ensuremath{\Delta}E\ensuremath{\rightarrow}0$. Finally, we derive the expression for the cross section describing the energy spectrum of the electrons emitted in the vicinity of the photoelectric peak, which is the basic information coming from coincidence experiments.

Pair, Triplet, and Total Atomic Cross Sections (and Mass Attenuation Coefficients) for 1 MeV-100 GeV Photons in Elements Z=1 to 100

Tables of photon cross sections and mass attenuation coefficients for all elements Z=1 to 100 are given for photo energies in the range 1 MeV to 100 GeV. The pair and triplet production cross sections take into account recent theoretical work, including atomic form factor and incoherent scattering function data, as well as extensive new total attenuation coefficient measurements at Mainz. Cross section values for the atomic photoeffect and coherent and incoherent (Compton) scattering are explicitly listed and are included in the total cross sections (excluding photonuclear) and mass attenuation coefficients.