Shell Photoionization Cross Section Research Articles

Energy variation of double K -shell photoionization of Ne

We report on an experimental and theoretical study of double $K$-shell photoionization of Ne over the 2.3--8.5 keV x-ray energy range. The ratio of double-to-single $K$-shell photoionization cross sections was determined experimentally by measuring the relative rates of the $KK\ensuremath{-}K{L}_{2,3}{L}_{2,3}$ ($^{2}D$) Auger hypersatellite and the $K\ensuremath{-}{L}_{2,3}{L}_{2,3}$ ($^{1}D$) diagram Auger transitions. By scaling the hypersatellite-diagram Auger-electron ratios to $KK/K$ cross-section ratios, comparison was made with theoretical cross-section ratios of He-like ${\mathrm{Ne}}^{8+}$ determined by the $R$ matrix with pseudostates method. The experimental Ne and theoretical ${\mathrm{Ne}}^{8+}$ cross-section ratios show similar variations with energy, but the experimental ratios systematically exceed the calculated ratios and also show a lower threshold energy for double $K$-shell photoionization onset compared to the computed ${\mathrm{Ne}}^{8+}$ threshold. The discrepancy is attributed to effects of $L$-shell electrons not included in the He-like ${\mathrm{Ne}}^{8+}$ calculations. Quantified scaling with nuclear charge $Z$ along the He-like isoelectronic sequence indicates that the measured 10-electron $Z=10$ double $K$-shell photoionization cross section behaves like the computed He-like $Z=8.9$ cross section, suggesting an effective nuclear screening parameter of ${s}_{L}=1.1$ by the additional eight outer $L$-shell electrons. Experimental results for the energy variations of Auger electron transitions from other multielectron hole states are also discussed.

A study of the valence shell absolute photoabsorption, photoionization and photodissociation cross sections, and the photoionization quantum efficiency of carbon monoxide

The spectroscopic characteristics and the decay mechanisms of the Rydberg states arising from valence shell excitations in carbon monoxide have been investigated by using a double ion chamber and synchrotron radiation to measure the absolute photoabsorption, photoionization and photodissociation cross sections, and the photoionization quantum efficiency, in the energy range between the ionization threshold and 36 eV. Guided by earlier theoretical predictions, the prominent absorption bands due to Rydberg states belonging to series converging onto the A 2Π state ionization threshold have been assigned, in accord with previous studies, to the ndδ and the [(n + 1)s + nd]σ transitions. Apart from the (4s + 3d)σ state which decays predominantly by predissociation into neutral fragments, most of the Rydberg states belonging to these series decay preferentially by autoionization. Another Rydberg series converging onto the A 2Π state limit has been tentatively assigned to the npσ transitions, even though these transitions are predicted to be weak. The v′ = 0 and v′ = 1 vibrational levels of the 4pσ state decay preferentially by predissociation into neutral fragments. The [(n + 1)s − nd]σ transitions are also calculated to be weak but may be associated with some previously unassigned absorption bands. Structure observed in the absorption spectrum between ∼19.5 and 23.5 eV may be due to Rydberg states associated with series converging onto the D 2Π or the 3 2Σ+ state limits. This structure is discussed in relation to dispersed fluorescence spectra and negative ion yields recorded over the same energy range.

Angular distribution of characteristic X-ray emission from Fe and V following photoionization

<sec> The de-excitation process of vacancy in the inner shell of the target atom caused by collision ionization produces the characteristic X-ray or Auger electrons. The precise measurement of ionization cross sections plays an important role in many basic research fields, as well as in practical fields, such as chemical analysis of Particle Induced X-ray Emission (PIXE), atomic and nuclear processes, and X-ray fluorescence (XRF) spectroscopy. As we know, when ionization cross sections are measured precisely, whether the emission of X-ray is isotropic in collision process must be considered. However, there have been few experimental results for angular dependence of <i>K</i><sub>β</sub>/<i>K</i><sub>α</sub> intensity ratios in the literature until now. Therefore, this study aims to verify that the <i>K</i><sub>α</sub> and <i>K</i><sub>β</sub> X-rays originated from filling of the <i>K</i> shell vacancies with total angular momentum quantum number 1/2 (<i>J</i> = 1/2) are isotropic.</sec><sec> In this work, the typical <i>K</i>-shell X-ray spectra for Fe and V, which induced by bremsstrahlung with central energy of 13.1 keV, have been measured at emission angles varied from 120° to 170° at intervals of 10°. The characteristic X-ray spectra obtained by the detector are fitted by Gauss function, where the absorption of incident X-rays by the detector, the absorption of emitted X-rays by the atmosphere and the self-absorption correction factor of incident and emitted X-rays by the target are all taken into account.</sec><sec> The experimental results of <i>K</i><sub>β</sub>/<i>K</i><sub>α</sub> intensity ratio in this experiment coincide with those of theoretical calculation, as well as the Ertuğral’s experimental result. The experimental results show that the intensity ratio of <i>K</i><sub>β</sub>/<i>K</i><sub>α</sub> is a constant at different detection angles. Therefore it can be concluded that the emission of <i>K</i><sub>α</sub> and <i>K</i><sub>β</sub> is isotropic in the detection range. Since the <i>K</i> shell has no sub-shell, there is no Coster-Kronig transition in the collision ionization process. In the process of photoionization, the vacancies in the <i>K</i> shell are produced by direct ionization. As a result, the cross section ratio of <i>K</i> shell X-ray generation is independent of the <i>K</i> shell photoionization cross section. In addition, the experimental results show that the <i>K</i><sub>β</sub>/<i>K</i><sub>α</sub> characteristic X-ray intensity ratio of target Fe is 8% higher than that of target V, which are consistent with the theoretical analysis results that the characteristic X-ray intensity ratio depends on the target atomic number <i>Z</i>.</sec>

A study of the valence shell absolute photoabsorption, photoionisation and photodissociation cross sections and the photoionisation quantum efficiency of carbonyl sulphide

The absolute photoabsorption, photoionisation and photodissociation cross sections and the photoionisation quantum efficiency of carbonyl sulphide have been measured using a double ion chamber and synchrotron radiation in the energy range from the ionisation threshold to 24eV. In addition to the absorption bands associated with well established Rydberg series, some previously unassigned features have been tentatively attributed to an f-type Rydberg series converging onto the B̃2Σ+ state ionisation threshold. Structure appearing in the photodissociation spectrum has been correlated with that observed in earlier fluorescence yields for emission, due mainly to the CS photofragment, occurring between 160 and 300nm. The photoionisation quantum efficiency reaches a plateau value close to unity for energies above ∼16eV. The predissociation of Rydberg states into neutral fragments does not appear to affect the photoionisation quantum efficiency of carbonyl sulphide to the extent that is commonly observed in other small molecules. A sum rule analysis has been carried out by combining the present absolute photoabsorption measurements with similar data covering the remaining energy regions.

Validation of Cross Sections for Monte Carlo Simulation of the Photoelectric Effect

Several total and partial photoionization cross section calculations, based on both theoretical and empirical approaches, are quantitatively evaluated with statistical analyses using a large collection of experimental data retrieved from the literature to identify the state of the art for modeling the photoelectric effect in Monte Carlo particle transport. Some of the examined cross section models are available in general purpose Monte Carlo systems, while others have been implemented and subjected to validation tests for the first time to estimate whether they could improve the accuracy of particle transport codes. The validation process identifies Scofield's 1973 non-relativistic calculations, tabulated in the Evaluated Photon Data Library(EPDL), as the one best reproducing experimental measurements of total cross sections. Specialized total cross section models, some of which derive from more recent calculations, do not provide significant improvements. Scofield's non-relativistic calculations are not surpassed regarding the compatibility with experiment of K and L shell photoionization cross sections either, although in a few test cases Ebel's parameterization produces more accurate results close to absorption edges. Modifications to Biggs and Lighthill's parameterization implemented in Geant4 significantly reduce the accuracy of total cross sections at low energies with respect to its original formulation. The scarcity of suitable experimental data hinders a similar extensive analysis for the simulation of the photoelectron angular distribution, which is limited to a qualitative appraisal.

Relativistic calculations of doubleK-shell-photoionization cross sections for neutral medium-Zatoms

Fully relativistic calculations are presented for the double $K$-shell photoionization cross section for several neutral medium-$Z$ atoms, from magnesium ($Z = 10$) up to silver ($Z = 47$). The calculations take into account all multipoles of the absorbed photon as well as the retardation of the electron-electron interaction. The approach is based on the partial-wave representation of the Dirac continuum states and uses the Green-function technique to represent the full Dirac spectrum of intermediate states. The method is strictly gauge invariant, which is used as an independent cross check of the computational procedure. The calculated ratios of the double-to-single $K$-shell ionization cross sections are compared with the experimental data and with previous computations.

On the strong influence of inner shell resonances upon the outer shell photoionization of endohedral atoms

It is demonstrated by the example of the Xe atom stuffed inside the C60 fullerene, i.e., the endohedral Xe@C60, that the so-called confinement resonances in 4d subshell strongly affect the photoionization cross section of outer 5p and subvalent 5s electrons near the 4d ionization threshold. It is a surprise that these narrow inner 4d shell resonances are not smeared out in the outer shell photoionization cross section. On the contrary; the inner shell resonances affect the outer cross section by enhancing them enormously. Close to its own photoionization thresholds, 5p and 5s photoionization cross sections of Xe@C60 are dominated by their own confinement resonances greatly affected by the amplification of the incoming radiation intensity due to polarization by it of the C60 electron shell. Between 4d and 5p thresholds, the effect of 4d is becoming stronger while own resonances of 5p and 5s are becoming much less important.

K-Shell X-Ray Spectroscopy of Atomic Nitrogen

Absolute K-shell photoionization cross sections for atomic nitrogen have been obtained from both experiment and state-of-the-art theoretical techniques. Because of the difficulty of creating a target of neutral atomic nitrogen, no high-resolution K-edge spectroscopy measurements have been reported for this important atom. Interplay between theory and experiment enabled identification and characterization of the strong 1s → np resonance features throughout the threshold region. An experimental value of 409.64±0.02 eV was determined for the K-shell binding energy.

Photoionization of the outer electrons in noble gas endohedral atoms

We suggest a prominent modification of the outer shell photoionization cross section in noble gas (NG) endohedral atoms NG@C n under the action of the electron shell of fullerene C n . This shell leads to two important effects: a strong enhancement of the cross section due to fullerene shell polarization under the action of the incoming electromagnetic wave and to prominent oscillation of this cross section due to the reflection of a photoelectron from the NG by the fullerene shell. Both factors lead to powerful maxima in the outer shell ionization cross sections of NG@C n , which we call giant endohedral resonances. The oscillator strength reaches a very large value in the atomic scale, 25. We consider atoms of all noble gases except He. The polarization of the fullerene shell is expressed in terms of the total photoabsorption cross section of the fullerene. The photoelectron reflection is taken into account in the framework of the so-called bubble potential, which is a spherical δ-type potential. It is assumed in the derivations that the NG is centrally located in the fullerene. It is also assumed, in accordance with the existing experimental data, that the fullerene radius R C is much larger than the atomic radius r A and the thickness ΔC of the fullerene shell. As was demonstrated recently, these assumptions allow us to represent the NG@C n photoionization cross section as a product of the NG cross section and two well-defined calculated factors.

Measurement of angular dependence of M X-ray production cross-sections in Re, Bi and U at 5.96 keV

The M X-ray production differential cross sections in Re, Bi and U elements have been measured at the 5.96 keV incident photon energy in an angular range 135°–155°. The measurements were performed using a 55Fe source and a Si(Li) detector. The present results contradict the predictions of Cooper and Zare [Atomic Collision Processes, Gordon and Breach, New York (1969)] and experimental results of Kumar et al. [J. Phys. B: At. Mol. Opt. 34, 613 (2001)]. that, after photoionization of inner shells, the vacancy state has equal population of magnetic substates and the subsequent X-ray emission is isotropic, but confirm the predictions of the calculations of Flugge et al. [Phys. Rev. Lett. 29, 7 (1972)] and experimental results of Sharma and Allawadhi [J. Phys. B: At. Mol. Opt. 32, 2343 (1999)] and Ertugrul [Nucl. Instrum. Meth. B 119, 345 (1996)]. Total M X-ray production cross sections from the decay at the 5.96 keV photon energies are found to be in good agreement with the calculated theoretical results using the theoretical values of M shell photoionization cross section.

Measurement of total M shell photoionization cross sections for Au, Pb, Th and U in the energy region 6–12 keV

The total M shell relative photoionization cross-sections for Au, Pb, Th and U have been measured in the energy region 6–12 keV. External conversion K X-rays of suitable elements has been employed as incident photons to photo ionize the total M shell of elements under investigation. The method provides relative cross-sections therefore does not make use of theoretically calculated average M shell fluorescence yields which involve uncertainties of the order of 20%. No evidence of deviation from calculated values of cross-sections have been observed within experimental errors for all incident photon energies.

Measurement of K shell fluorescence cross-section of Ca and K compounds

The cross-section for Ca and K compounds were determined by measuring the KX-ray yields from targets excited 5.96 keV photons and using theoretical K shell photoionization cross-section. By comparing the experimental results with relativistic Hartree–Fock calculation, a good agreement has been obtained considering the experimental errors.

Vibrationally resolved photoionization of the 1σg and 1σu shells of N2 molecule

Theoretical and experimental study of vibrationally resolved partial photoionization cross sections and angular asymmetry parameter β for the 1σg and 1σu shells of N2 molecule in the region of the σ* shape resonance is reported. The measurements were made at the synchrotron radiation facility SPring-8 in Japan. The calculations in the random phase approximation have been performed using the relaxed core Hartree–Fock wavefunctions with the fractional charge of the ion core equal to 0.7. With its help, the role of interchannel coupling between the closely spaced 1σg and 1σu shells was studied. The experiment demonstrates the existence of a correlational maximum in the 1σu shell photoionization cross section induced by the σ* shape resonance in the 1σg shell. This maximum reveals itself even more clearly in the angular asymmetry parameter β for the v′ = 0 and v′ = 1 vibrational states of the ion. The calculation in the random phase approximation gives a consistent interpretation of the experimental data.

Total M shell X-ray production cross sections and average fluorescence yields in 11 elements from Tm to U at photon energy of 5.96 keV

Total M shell X-ray production cross section for 11 elements with 69 ⩽ Z ⩽ 92 have been measured using an incident photon energy of 5.96 keV. Measurements have been performed using an 55Fe annular source and a Si(Li) detector. Average M shell fluorescence yield at each incident photon energy has been deduced, using the experimental total M X-ray production cross section and theoretical M shell photoionization cross section. Present experimental results are compared with other experimental and theoretical values. Reasonable agreement (to within 0.3–28%) is typically obtained between present and other experimental and theoretical values.

Measurement of K to L shell vacancy transfer probabilities for the elements 46≤ Z≤55 by photoionization

The K to L shell vacancy transfer probabilities for nine elements in the atomic region 46≤ Z≤55 were determined by measuring the L X-ray yields from targets excited by 5.96 and 59.5 keV photons and using the theoretical K and L shell photoionization cross-sections. The L X-rays from different targets were detected with an Ultra-LEGe detector with very thin polymer window. Present experimental results were compared with the semi empirical values tabulated by Rao et al. [Atomic vacancy distributions product by inner shellionization, Phys. Rev. A 5 (1972) 997–1002] and theoretically calculated values using radiative and radiationless transitions. The radiative transitions of these elements were observed from the relativistic Hartree–Slater model, which was proposed by Scofield [Relativistic Hartree–Slater values for K and L shell X-ray emission rates, At. Data Nucl. Data Tables 14 (1974) 121–137]. The radiationless transitions were observed from the Dirac–Hartree–Slater model, which was proposed by Chen et al. [Relativistic radiationless transition probabilities for atomic K- and L-shells, At. Data Nucl. Data Tables 24 (1979) 13–37]. To the best of our knowledge, these vacancy transfer probabilities are reported for the first time.

Measurement of K, L and higher shell photoionisation cross-sections at 59.5 keV

A simple and direct method has been developed to measure the K, L and higher shell photoionisation cross-sections of elements in the range 57≤ Z≤68 at 59.5 keV. The K and L i ( i=1, α, β, γ) X-ray intensities emitted by these elements, from irradiating their samples by the photons of above energy, are measured using a Si(Li) spectrometer system. The Kα and L i X-ray fluorescence cross-sections of the above elements are determined, and the total, K and L shell photoelectric cross-sections are evaluated. The present experimental results are in agreement with the theoretical values.

Measurement of Coster–Kronig vacancy transfer factor for L 3 subshell X-rays of Au, Hg, Pb, Tl, Bi, Th and U at 59.5 keV

The Coster–Kronig vacancy transfer factors were measured for L 3 subshell X-rays using the experimental L α X-ray production cross section, the fraction of L α X-rays, L 3 subshell fluorescence yield and L 3 shell photoionization cross section. The obtained experimental results were compared with the theoretical values. It showed that the agreement between the present experimental and theoretical results was very good.

M X-ray fluorescence cross sections and yields in the atomic region [formula omitted] excited by 6.47 and 7.57 keV photons

Experimental M X-ray fluorescence cross sections for the elements Pt, Au and Pb have been measured at incident photon energies 6.47 and 7.57 keV. Theoretical M X-ray fluorescence cross sections for the elements Yb, W, Hg, Tl, Bi and Ra at 6.47 and 7.57 keV are also calculated. Experimental results are compared with the theoretical values based on relativistic Dirac-Hartree-Slater calculations of Chen et al. and non-relativistic calculations of McGuire. The average M shell fluorescence yields ω M have been deduced using experimental cross section values and the theoretical M shell photoionization cross sections. Results are compared with the available theoretical values.

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).