Pauli Fock Research Articles

Cross sections of cascade production of photoions after photoionization of the iodine atom in the 0.01–100 keV incident photon energy range

Ion yields upon the cascade decays of single vacancies in K to O shells of an isolated iodine atom are calculated by the method of construction and analysis of the cascade decay trees. Branching ratios needed for the simulations are calculated based on Pauli–Fock partial transition widths. Partial photoionization cross sections are calculated with accounting for the core relaxation effect and used to calculate the cross sections of I q+ photoions production in the 0.01–100 keV incident photon energy range. Accounting for the spin–orbit splitting and the splitting due to electron–electron interaction is shown to be important when calculating mean energies and probabilities of the transitions between energetically closely lying ionic configurations. On the other hand, inclusion of the additional shake-off electron ejections, in spite of complicating severely the decay trees, is found to affect little calculated cascade ions production probabilities.

Final ion yields upon the cascade decay of single K, L, M, and N vacancies in atomic silver

Final ion yields and mean final ion charges upon the cascade decay of single vacancies in the K, L, M, and N shells of atomic silver are calculated using the method of construction and analysis of the decay trees with accounting for the shake-offs caused by the change of atomic core potential due to cascade transitions. The shake-off effect on the final ion yields is found to be comparatively small, the largest increase of the mean final ion charge being 0.20e in the case of initial 2s vacancy. Total semi-relativistic Pauli–Fock energies of cascade-produced ionic configurations were used to calculate cascade transition energies, which made it possible to accurately account for the closing of some non-radiative transitions in multivacancy cascade configurations. For the transitions with overlapping multiplets of initial and final ionic configurations, only energetically allowed transitions between the multiplet components were counted when calculating mean transition energies and transitions branching ratios. Comparison of calculated charge spectra with those reported earlier by other authors demonstrated crucial importance of accurate calculation of transition energies and accounting for multiplet splitting in simulation of cascades in heavy atoms.

Final ion charge spectra upon cascade decay of inner-shell vacancies in atomic Au

Final ion charge spectra produced by the cascade de-excitations of 1s- to 5p 3/2-vacancies of the gold atom are calculated by direct construction and analysis of the cascade decay trees. The energies of multivacancy configurations arising in the course of the cascade development, and the partial widths of radiation and radiationless cascade transitions are calculated using the Pauli–Fock approximation. The energies of the cascade transitions are calculated as the differences of total Pauli–Fock energies of initial and final ionic configurations which allowed excluding energy-forbidden radiationless transitions in numerous multivacancy configurations. Partial widths of transitions are expressed in the form that allowed accounting for the effect of electron subshell populations on the transition widths. The partial widths of the transitions between the states of the overlapping initial and final state multiplets are corrected so as to exclude energy-forbidden transitions between the multiplet states. It is demonstrated that accurate accounting for possible forbiddance of transitions between cascade configurations and the exclusion of energy-forbidden term-to-term transitions between the multiplets’ states are crucial in deep-initial-vacancy cascade simulations.

Влияние дополнительных монопольных выбросов электронов на зарядовые спектры конечных ионов при каскадном распаде электронных вакансий в атоме золота

The probabilities of the formation of final ions produced by the cascade decays of vacancies in the K, L, M, N, and O shells of the gold atom are calculated. Simulation of the cascade decays of vacancies is performed by direct construction and analysis of decay trees using branching ratios and transition energies calculated in the Pauli–Fock approximation for multivacancy electron configurations arising in the course of the cascade decay. Accounting for additional monopole ejections of electrons (shake-off) accompanying the cascade transitions leads to a slight increase in the average charges of the final ions, by 0.15–0.23e. The largest relative increase in the calculated average charges of the final ions (by 3.6–3.9%) is observed upon the cascade decay of vacancies in 4p3/2, 4d3/2, and 4d5/2 subshells, and the smallest (by 0.8%) occurs in the decay of 4f-vacancy. Despite insignificant changes in the average ion charges, the structure of the charge spectra in some cases changes noticeably enough when additional electron ejections are taken into account. It is expected that in simulation of the cascade energy reemission processes when heavy atoms are used as radiosensitizers, the effect of accounting for shake-off processes will be insignificant.

Cascade reemission of energy by inner-shell-ionized iron atom

Cascade decays of vacancies produced by single K, L and M ionization of the Fe atom are simulated by direct construction of the cascade decay trees based on Pauli–Fock branching ratios and ionic configurations energies. Final ion charge spectra and the spectra of cascade-produced electrons and photons are calculated. It is shown that a large portion of energy transferred to the Fe atom in the ionization processes is reemitted by cascade electrons and photons. This circumstance must be taken into account when describing the effect of ionizing radiation on matter or living tissues.

Charge, photon, and electron spectra upon cascade decay of the states of the neon atom that arise as a result of photoionization near the K-threshold

We have calculated emission spectra of photons and electrons and charge spectra of final ions which are produced by the cascade decay of states created by photoionization of the neon atom near the K-threshold. Calculations have been performed by straightforward construction of cascade decay trees. Branching probabilities have been calculated in the Pauli—Fock single-configuration approximation. We have taken into consideration additional monopole excitations and ejections which accompany the 1s-photoionization process as well as the radiative and nonradiative transitions in the course of cascade. As the energy of excitation photons increases, the spectra of cascade photons and electrons acquire a more and more complicated satellite structure, with the probability of formation of final ions with a higher charges increasing.

On the breakdown of the electric dipole approximation for hard x-ray photoionization cross sections

Photoionization of K- and L-shells of H, He, Be, Ne, Ar and Kr atoms by hard x-ray radiation resulting in the emission of photoelectrons with kinetic energy of up to 20 keV is studied beyond the electric dipole approximation. Thereby we investigate the effect of higher-multipole expansion (retardation) of hard x-ray radiation on the angular-averaged ionization cross section. Numerical calculations, performed in the relativistic Pauli–Fock approximation, demonstrate that in this energy range quadrupole transitions introduce dominant contributions beyond the electric dipole approximation. The computed relative contributions of the nondipole interactions to the cross sections grow as a function of the photoelectron kinetic energy almost equally for the 1s and 2s shells of all considered atoms. The same holds for the 2p shells of Ne, Ar and Kr. We, thus, confirm analytical predictions of the Born approximation suggesting that in the considered energy range the relative error introduced to the ionization cross section of low and intermediate Z elements by the electric dipole approximation is almost independent of the spatial extent of the absorbing atomic orbital.

Valence state of the manganese ions in mixed-valence La1−αBiβMn1+δO3±γ ceramics by Mn 2p and Mn 3s X-ray photoelectron spectra

Valence state of Mn in La1−αBiβMn1+δO3±γ (LBMO) ceramic samples and in orthorhombic manganates RMn2O5 (R=Y, Bi, Eu, Gd), is studied using Mn 2p- and Mn 3s-spectra. Both Mn3+ and Mn4+ ions are shown to be present in those compounds. Relative Mn3+/Mn4+ ions contents are determined by fitting experimental Mn 2p-spectra with weighted superpositions of theoretical spectra of Mn3+ and Mn4+ ions calculated in one-configuration Pauli–Fock approximation considering thermal excitations in initial state. Content of the Mn4+ ions correlates with the deviation δ in La1−αBiβMn1+δO3±γ from stoichiometry, La1−xBixMnO3. Separation of low-spin and high-spin components of Mn 3s-spectrum can be sensible to the relative content of Mn3+ and Mn4+ ions. Mn3+/Mn4+ ratios derived from Mn 2p- and from Mn 3s-spectra compare well in the case of the RMn2O5 manganates, while in the case of the LBMO ceramics the results obtained from the Mn 3s spectra are physically meaningless. Due to a complex interplay between 3d-electrons delocalization and strong many-electron effects the 3s spectra of 3d-elements may be misleading.

Monte Carlo simulation of the cascade decay processes in gaseous boron initiated by photons with energies scanned through L- and K-ionization thresholds

The Monte Carlo technique is applied to simulate the processes of the cascade relaxation of gaseous boron at atomic density of 2.5 × 1022 m−3 ionized by photons with the energies of 0.7–25 Ryd passing through a cylindrical interaction zone along its axis. The trajectories of electrons are simulated based on photoionization and electron-impact ionization cross sections calculated in the one-electron configuration-average Pauli–Fock approximation. Numbers of electrons and photons leaving the interaction zone per one initial photoionization, their energy spectra, the energy transferred to the medium and the probabilities of final ion formations are shown to change noticeably as the incident photon energy is scanned through boron atom ionization thresholds. These variations can be explained only if secondary electron-impact-produced processes are considered. The density of secondary events decreases when going from the zone axis to its border, and the profiles of the density along the radial direction are found to be similar for all the initial exciting photon energies.

Autoionization dynamics of even Ar (3p51/2np′, nf′) resonances: comparison of experiment and theory

The 3p51/2np′J = 0, 1, 2 and 3p51/2nf′J = 2 autoionizing Rydberg states of Ar have been studied by two-step two-color photoionization of ground-state argon atoms via the intermediate levels 3p51/24s′[1/2]1, 3p53/25s[3/2]1 and 3p53/23d[1/2]1, followed by time-of-flight ion detection. Accurate energy positions and widths have been determined for the 15p′[1/2]0, 15p′[3/2]2 and 13f′[5/2]2 resonances. The measured spectra and earlier results obtained for the intermediate levels 5s′[1/2]1,7s′[1/2]1, and 8s[3/2]1 are compared with absolute cross sections, calculated with the configuration interaction Pauli–Fock core-polarization method.

X-ray photoelectron Fe3s and Fe3p spectra of polynuclear trimethylacetate iron complexes

X-ray photoelectron Fe3s and Fe3p spectra are employed to study the electron structure and the spin magnetic state of bi-, tri-, and hexa-nuclear trimethylacetate iron complexes. Assignment of the spectra is performed based on an isolated-ion Pauli–Fock calculation of Fe3s and Fe3p spectra of the Fe atoms in bi- and tri-valent states. Nonequivalent Fe III and Fe II atoms are detected in tri- and hexa-nuclear complexes. Paramagnetic-limit molecular magnetic moments are calculated using effective atomic magnetic moments obtained from spin-sensitive spectral characteristics. Comparison of those values with the magnetic measurements data demonstrates antiferromagnetic interaction within the complexes.

Photoionization of excited Ne*(2p5 3p, J = 3) atoms near threshold

Using the configuration interaction Pauli–Fock with core polarization (CIPFCP) method, we have calculated the total and the partial cross sections for photoionization of excited Ne*(2p5 3p, J = 3) atoms over the photoelectron energy range 0–2.5 eV. The total cross section exhibits nearly the same energy dependence as that for photoionization of excited Na*(3p) atoms, but the absolute size for the former is about 10% smaller. In both cases, some experimental cross sections show unexplained deviations from the theoretical predictions. Between the two ionization thresholds Ne+(2p53/2) and Ne+(2p51/2), the cross sections are predicted to be strongly influenced—albeit over only narrow intervals—by the nd′(J = 2, 3) and ng′(J = 3, 4) resonance series. Partial cross sections for the J = 2, 3, 4 channels and a parametrization of the resonances by Fano–Cooper-type profiles are presented. The partial cross section for leaving the Ne+ ion in the 2P1/2 level amounts to only about 0.03% near threshold, in agreement with the findings of a laser photoelectron spectrometry experiment.

Experimental and theoretical investigation of even mp51/2 np′ autoionizing resonances of rare gas atoms

Using experimental set-ups involving single photon excitation of metastable rare gas atoms Rg(mp5(m + 1)s, J = 2, 0) by a pulsed frequency-doubled dye laser in conjunction with time-of-flight ion detection, we have investigated several even Rg(mp51/2 np′) autoionizing resonances of the heavier rare gas atoms Rg = Ne − Xe (m = 2–5) at experimental bandwidths of 0.06 cm−1 (Ne) and about 0.25 cm−1 (Ar, Kr, Xe). New level energies (quantum defects) and widths for these resonances have been derived by a Fano-type lineshape analysis, thus yielding reduced resonance widths. The experimental spectra and the resonance parameters are compared with theoretical calculations which are based on the configuration interaction Pauli–Fock approach, including core polarization. For Rg = Ne, good agreement between the measured and the calculated results is observed. For the heavier rare gases, significant deviations between some of the existing experimental data and the theoretical results are found, indicating the need for further studies.

Theoretical and experimental study of the extreme ultraviolet photoabsorption spectrum of triply ionized yttrium

The photoabsorption spectrum of Kr-like Y3+ ions in the very soft x-ray/extreme ultraviolet spectral range where single (4s–np) and double (4p4p–nℓn′ℓ′) electron excitations dominate has been measured using a dual laser plasma photoabsorption technique. The corresponding photoionization cross section has been computed within the framework of the configuration interaction Pauli–Fock approach. The calculations confirm that the 4s–5p resonance drops below the 4p ionization threshold so that the first member of the 4s–np photoionization resonance series becomes 4s–6p. Also, whereas the first such series member in Rb+ and Sr2+ appears as a window resonance, in Y3+ it switches to a normal, slightly asymmetric absorption peak. In addition, although the 4s–5p1/2 resonances in the 4p51/2 and 4p53/2 continua are mirror images in Rb+ and Sr2+ and hence cancel each other, they exhibit quite different shapes in Y3+ and hence we observe the residual signature of the 4s–6p1/2 resonance as a weak partner to the main 4s–6p3/2 resonance.

Experimental and theoretical investigation of odd 5p51/2 nl′ autoionizing resonances in xenon atoms: energy dependence of the reduced widths

Using two different experimental set-ups involving optogalvanic spectroscopy and atomic beam spectroscopy with mass spectrometric ion detection, respectively, we have measured the 5p5(2P1/2) nd′ [K′ = 3/2]J=2 and [K′ = 5/2]J=2,3 (7 ⩽ n ⩽ 9) autoionizing resonances of xenon by means of two-step resonant laser excitation from the metastable Xe(J = 2, 0) levels. By selecting particular intermediate 6p′ [1/2]1 and 6p′ [3/2]1,2 levels, autoionizing resonances with specified K′ and J values were addressed. Level energies and resonance widths have been derived by a Fano-type lineshape analysis, thus yielding reduced resonance widths which significantly decrease with rising n. With the aim to obtain a theoretical understanding of these and previous findings for the widths of odd Xe resonances, extended calculations for the Xe(ns′ J = 0, 1), Xe(nd′ J = 1, 2, 3) and Xe(ng′ J = 3) autoionizing series have been carried out. They are based on the Pauli–Fock approach and include core polarization and electron correlation effects at a high level; in all cases, they reveal a substantial energy dependence of the reduced widths. Using this energy dependence and parameters of multichannel quantum defect theory (MQDT) determined in the discrete region, the MQDT widths of autoionizing resonances were derived. These values are in good agreement with recommended experimental values.

The autoionizing Rydberg series 3p1/25nℓ′[K′]J (ℓ′ = 0–5)of Ar: the influence of many-electron effects on the resonance widths

Theoretical results for the autoionization dynamics of 3p1/25nℓ′Rydberg states of Ar atoms into the 3p3/25εℓ continua are presentedfor ℓ′ = 0–5.The quantum defects and the reduced widths of these resonances were calculatedwithin the configuration interaction Pauli–Fock approach including corepolarization. The most significant many-electron effects influencing thedecay dynamics are the polarization of the atomic core by the Rydbergelectron and photoelectron, the correlational decrease of the Coulombinteraction and the interaction between the Rydberg states. For ℓ′ = 0, 2 and4 (where reliable measurements exist) the calculated reduced resonance widthsagree with the experimental results to within 20%.

Experimental and theoretical cross sections for photoionization of metastable Xe*. (6s 3 P 2, 3 P 0) atoms near threshold

Using high resolution laser photoelectron spectrometry we have determined absolute cross sections σJ0J1 and the electron angular distribution parameter for one photon ionization of metastable Xe*(6s3PJ0, J0 = 2, 0) atoms to the resolved Xe+ (2PJ1, J1 = 3/2, 1/2) ion states at several wavelengths near threshold. For comparison with the present and future experimental data we have calculated partial cross sections and s-parameters for photoionization of Xe*(6s3PJ0, J0 = 2, 0) and of the analogous alkali atom Cs(6s) over the photoelectron energy range (0–5) eV. We have used both a term-dependent Pauli-Fock (PF) approach and a configuration interaction method involving Pauli-Fock atomic orbitals (CIPF). Through the PF method we include relativistic effects on the atomic orbitals; the CIPF method was designed to take into account the important electron correlation effects which are found to be essential for obtaining good agreement between the theoretical and experimental results.

Durch schnelle elektronen angeregte schwingungsterme des molekularen wasserstoffs

The progress and the chronology in understanding the influence of electron correlations on the electronic structure of atoms and the dynamics of atomic processes is reviewed focusing on benchmark rare-gas atoms. The contributions and the chronological development of Photon-Induced Fluorescence Spectroscopy (PIFS), measuring dispersed-fluorescence emission cross sections upon excitation by single photons provided by monochromatized synchrotron radiation is described. Selected experimental results obtained by complementary techniques are also discussed for comparison. The basic suites of computer programs used for the investigation of the many-electron effects in atoms and the obtained results are analysed. Special attention is paid to the Configuration Interaction Pauli–Fock approximation with Core Polarization (CIPFCP) method used to interpret the PIFS data.