Search

We report on the radiative decay of double $K$-shell vacancy states produced in solid Ca, V, Fe, and Cu targets by impact with about 10 MeV/amu C and Ne ions. The resulting $K$ hypersatellite x-ray emission spectra were measured by means of high-energy-resolution spectroscopy using a von Hamos bent crystal spectrometer. The experiment was carried out at the Philips variable energy cyclotron of the Paul Scherrer Institute. From the fits of the x-ray spectra the energies, line widths, and relative intensities of the hypersatellite x-ray lines could be determined. The fitted intensities were corrected to account for the energy-dependent solid angle of the spectrometer, effective source size, target self-absorption, crystal reflectivity, and detector efficiency. The single-to-double $K$-shell ionization cross-section ratios were deduced from the corrected relative intensities of the hypersatellites and compared to theoretical predictions from the semiclassical approximation model using hydrogenlike and Dirac-Hartree-Fock wave functions and from classical trajectory Monte Carlo calculations.

Fluorescence yields (FYs) for the Ge $L$ shell were determined by a theoretical and two experimental groups within the framework of the International Initiative on X-Ray Fundamental Parameters Collaboration. Calculations were performed using the Dirac-Fock method, including relativistic and QED corrections. The experimental value of the ${L}_{3}\phantom{\rule{0.28em}{0ex}}\mathrm{FY}\phantom{\rule{0.28em}{0ex}}{\ensuremath{\omega}}_{{L}_{3}}$ was determined at the Physikalisch-Technische Bundesanstalt undulator beamline of the synchrotron radiation facility BESSY II in Berlin, Germany, and the $L{\ensuremath{\alpha}}_{1,2}$ and $L{\ensuremath{\beta}}_{1}$ line widths were measured at the Swiss Light Source, Paul Scherrer Institute, Switzerland, using monochromatized synchrotron radiation and a von Hamos x-ray crystal spectrometer. The measured fluorescence yields and line widths are compared to the corresponding calculated values.

photoexcitation spectra. Both two-electron excitation spectra are well described by a model spectrum builtofconsecutivebound-bounddiscretetransitionsandshake-upandshake-offchannelsgivingpreciseenergiesandintensitiesofthecorrespondingcontributions.Theobtainedresultsarecomparedwithotherexistingexperimentalvalues based on x-ray-absorption measurements and theoretical predictions.DOI: 10.1103/PhysRevA.90.022513 PACS number(s): 32

The photoinduced $K\ensuremath{\alpha}$ and $K\ensuremath{\beta}$ x-ray spectra of argon and krypton were measured by means of high-resolution crystal diffractometry. Ar $K{\ensuremath{\alpha}}_{1,2}{L}^{(1)}$ and $K{\ensuremath{\beta}}_{1,3}{M}^{(1,2)}$ and Kr $K{\ensuremath{\alpha}}_{1}{L}^{(1)}$ and $K{\ensuremath{\beta}}_{2}{M}^{(1,2)}$ satellites were observed and resolved from the corresponding diagram lines. From the satellite to parent diagram line yield ratios, the probabilities for producing via shake processes ${K}^{(1)}{L}^{(1)}$ and ${K}^{(1)}{M}^{(1)}$ double-hole states were deduced. The results are compared to the few other existing experimental data and to theoretical sudden approximation predictions. The latter are found to underestimate somewhat the experimental values.

M. Czarnota,1,* D. Banaś,1 M. Berset,2 D. Chmielewska,3 J.-Cl. Dousse,2 J. Hoszowska,2 Y.-P. Maillard,2 O. Mauron,2 M. Pajek,1 M. Polasik,4 P. A. Raboud,2 J. Rzadkiewicz,5 K. Slabkowska,4 and Z. Sujkowski3,† 1Institute of Physics, Jan Kochanowski University, 25-406 Kielce, Poland 2Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland 3Soltan Institute for Nuclear Studies, 05-400 Otwock-Świerk, Poland 4Faculty of Chemistry, Nicholas Copernicus University, 87-100 Torun, Poland 5National Centre for Nuclear Research, 05-400 Otwock-Świerk, Poland (Received 15 June 2013; published 11 November 2013)

High-resolution measurements of the K{beta}{sub 2} diagram line and its M{sup 1} satellite were performed for zirconium, molybdenum, palladium, and praseodymium. The x-ray spectra were induced by impact with 28-, 40-, 65-, and 100-MeV {alpha} particles and measured with a transmission-type bent crystal spectrometer in modified DuMond slit geometry. From the relative yields of the K{beta}{sub 2}M{sup 1} satellites the experimental average M-shell ionization probabilities for nearly central collisions were deduced. They are compared with theoretical predictions from the semiclassical independent particle approximation using either hydrogenlike wave functions (SCA-HWF) or Dirac-Hartree-Fock wave functions (SCA-DHF), pointing out the relevance of the use of DHF wave functions instead of hydrogenlike wave functions in the SCA model. Moreover, the experimental energy shifts of the satellite transitions with respect to the diagram lines are compared to results of extensive multiconfiguration Dirac-Fock calculations. {copyright} {ital 1998} {ital The American Physical Society}

The KMM radiative Auger (RA) x-ray spectra of solid Ca were induced by monochromatic synchrotron radiation and measured with a high-resolution von Hamos bent crystal spectrometer. Two excitation energies were employed, one in the near K threshold region and the second well above the K absorption edge. The KMM RA spectral structure and relative intensity with respect to the diagram K{beta}{sub 1,3} (K-M{sub 3,2}) line are found to be independent of the excitation energy. The overall RA structure resembles the density of unoccupied s, p, and d states. Due to solid-state effects, however, spectral features resulting from the major discrete shake-up transitions could not be resolved. For the total KMM RA to K{beta}{sub 1,3} yield ratio, a value of 0.053(3) is obtained. The latter is compared to theoretical predictions and available experimental data obtained by various types of target excitation.

The electron-induced ${L}_{3}M$ two-step double ionization cross sections of metallic Pd were determined experimentally for incident electron beam energies ranging from the double ionization threshold up to 18 keV. The double ${L}_{3}M$ ionization cross sections were derived from the intensity ratios (${I}_{L\ensuremath{\alpha}M}$:${I}_{L\ensuremath{\alpha}}$) of the resolved $M$ satellites to the parent diagram lines. The sample was bombarded with monoenergetic electrons from an energy-tunable 20-kV electron gun. The diagram and $M$-satellite x-ray lines were measured by means of high-resolution x-ray spectroscopy, using a reflection-type von Hamos bent crystal spectrometer. The two-step partial cross sections were determined by subtracting from the measured total double ionization cross sections the contributions due to the shake process and ${L}_{1}$-${L}_{3}{M}_{4,5}$ Coster-Kronig transitions. Despite the thick target employed in the present study, the dependence of the two-step cross sections on the incoming electron energy could be derived using a target slice decomposition method. It is shown that the obtained energy dependence can be well reproduced by the semiempirical parametrization model of Pattard and Rost.

Single-photon double $K$-shell ionization of low-$Z$ neutral atoms in the range $12\ensuremath{\leqslant}Z\ensuremath{\leqslant}23$ is investigated. The experimental method was based on measurements of the high-resolution $K\ensuremath{\alpha}{}^{h}$ hypersatellite x-ray spectra following the radiative decay of the $K$-shell double-vacancy states excited by monochromatic synchrotron radiation. The photon energy dependence of the double $K$-shell ionization was measured over a wide range of photon energies from threshold up to and beyond the maximum of the double-to-single photoionization cross section ratios. From the high-resolution x-ray emission spectra the energies and linewidths of the hypersatellite transitions, as well as the $K{\ensuremath{\alpha}}_{1}^{h}$:$K{\ensuremath{\alpha}}_{2}^{h}$ intensity ratios, were determined. The relative importance of the initial-state and final-state electron-electron interactions to the $K$-shell double photoionization is addressed. Physical mechanisms and scaling laws of the $K$-shell double photoionization are examined. A semiempirical universal scaling of the double-photoionization cross sections with the effective nuclear charge for neutral atoms in the range $2\ensuremath{\leqslant}Z\ensuremath{\leqslant}47$ is established.

An observation of the internal structure of the L-shell hypersatellite x rays resulting from the one-photon decay of L{sup -2} double-vacancy states in palladium multiply ionized by oxygen ions is reported. The Pd L{sub 3}{yields}M{sub 4,5} x-ray spectrum was measured with a von Hamos high-resolution crystal spectrometer. The complex shape of the observed spectrum could be interpreted in detail using relativistic multiconfiguration Dirac-Fock calculations. The relative intensities of the measured x rays were found to be in good agreement with semiclassical approximation calculations using relativistic Dirac-Hartree-Fock wave functions.

The xenon $L$-subshell Coster-Kronig (CK) transition yields were revisited via high-resolution measurements of the $L{\ensuremath{\alpha}}_{1,2}$ (${L}_{3}\ensuremath{-}{M}_{4,5}$) and $L{\ensuremath{\beta}}_{1}$ (${L}_{2}\ensuremath{-}{M}_{4}$) x-ray emission lines. The $L$ x-ray spectra were measured employing a Johansson-type curved crystal spectrometer and energy-tunable synchrotron radiation. The CK yields were derived from the relative $L$ x-ray intensity jumps at the $L$ edges by fitting the fluorescence intensities as a function of the photon energy to the $L$-subshell photoionization cross sections. The latter were obtained from the measured $L$-edge photoabsorption spectrum. Values of $0.118\ifmmode\pm\else\textpm\fi{}0.029$, $0.383\ifmmode\pm\else\textpm\fi{}0.037$, and $0.096\ifmmode\pm\else\textpm\fi{}0.016$ were found for the ${f}_{23}$, ${f}_{13}$, and ${f}_{12}$ CK yields, respectively. Thanks to high resolution, the ${L}_{1}$ fluorescence yield of $0.059\ifmmode\pm\else\textpm\fi{}0.002$ was also determined from intensity ratios of the well-resolved $L{\ensuremath{\beta}}_{4}$ (${L}_{1}\ensuremath{-}{M}_{2}$) and $L{\ensuremath{\beta}}_{1}$ (${L}_{2}\ensuremath{-}{M}_{4}$) lines.

The K\ensuremath{\alpha} and K\ensuremath{\beta} x-ray spectra of molybdenum bombarded by 5.5-MeV/amu $^{16}\mathrm{O}$ ions were measured with high resolution. In such heavy-ion--atom collisions, multiple ionization of the M and L shells of the target atoms is extremely likely to occur, resulting in a complex structure of the observed spectra. The ${\mathit{L}}^{\mathit{n}}$-satellite structure was resolved, whereas M vacancies produce only a shift and a broadening of the lines so that it is not possible to obtain in a direct way information about the M-hole distribution. We thus propose a method for the analysis of x-ray spectra of multiply ionized atoms. In this method the measured K\ensuremath{\alpha} and K\ensuremath{\beta} spectra are simultaneously analyzed as a sum of K\ensuremath{\alpha}${\mathit{L}}^{\mathit{n}}$${\mathit{M}}^{\mathit{m}}$ and K\ensuremath{\beta}${\mathit{L}}^{\mathit{n}}$${\mathit{M}}^{\mathit{m}}$ components, respectively, with theoretically determined profiles. A binomial distribution of holes in the M shell is assumed and the M-shell ionization probabilities are treated as adjustable parameters. The profiles are constructed as sums of Voigt functions, whose positions and heights are determined by extensive multiconfiguration Dirac-Fock method calculations. If, in a simultaneous fit to the K\ensuremath{\alpha}${\mathit{L}}^{0}$ and K${\mathrm{\ensuremath{\beta}}}_{1,3}$${\mathit{L}}^{0}$ lines, just one parameter ${\mathit{p}}_{\mathit{M}}^{\mathit{X}}$ describing the M-shell ionization at the moment of the K x-ray transition is used, the experimental data are not reproduced in an entirely satisfactory way (${\mathit{p}}_{\mathit{M}}^{\mathit{X}}$=0.19\ifmmode\pm\else\textpm\fi{}0.02). Therefore, two parameters, one common for the 3s and 3p subshells ${\mathit{p}}_{3\mathit{s}\mathit{p}}^{\mathit{X}}$ and the other for the 3d subshells, were introduced and a much better fit to both lines (${\mathit{p}}_{3\mathit{s}\mathit{p}}^{\mathit{X}}$=0.17\ifmmode\pm\else\textpm\fi{}0.02, ${\mathit{p}}_{3\mathit{d}}^{\mathit{X}}$=0.23\ifmmode\pm\else\textpm\fi{}0.02) was obtained.The importance and influence of alternative ionizing processes as electron-capture and rearrangement processes are discussed and the M-shell ionization probability at the moment of the collision (${\mathit{p}}_{\mathit{M}}$=0.18\ifmmode\pm\else\textpm\fi{}0.02) is deduced from the ${\mathit{p}}_{\mathit{M}}^{\mathit{X}}$ value. It is shown that the differences between ${\mathit{p}}_{3\mathit{s}\mathit{p}}^{\mathit{X}}$ and ${\mathit{p}}_{3\mathit{d}}^{\mathit{X}}$ are mainly due to Coster-Kronig transitions, rather than due to different subshell ionization probabilities. The spectra were also analyzed with respect to the L-shell ionization on the basis of the calculated K\ensuremath{\alpha}${\mathit{L}}^{\mathit{n}}$${\mathit{M}}^{0}$, K${\mathrm{\ensuremath{\beta}}}_{1,3}$${\mathit{L}}^{\mathit{n}}$${\mathit{M}}^{0}$, and K${\mathrm{\ensuremath{\beta}}}_{2}$${\mathit{L}}^{\mathit{n}}$${\mathit{M}}^{0}$ components. The M-shell ionization was taken into account by taking a larger Gaussian width and by shifting the positions of the lines. The intensity yields of the L satellites were determined, the primary vacancy distribution was deduced, and the results from K\ensuremath{\alpha} and K\ensuremath{\beta} spectra are compared.

We report on the experimental determination of the palladium L-subshell Coster-Kronig (CK) transition yields via high-resolution measurements of the L{alpha}{sub 1,2} (L{sub 3}-M{sub 4,5}) and L{beta}{sub 1} (L{sub 2}-M{sub 4}) x-ray emission lines. The L x-ray spectra were recorded by means of curved crystal spectrometers employing energy-tunable synchrotron radiation for fluorescence production. The CK yields were derived from the relative L x-ray intensity jumps at the L edges by fitting the fluorescence intensities as a function of the photon energy to the photoionization cross sections. The L x-ray intensities were corrected for solid-state effects which were estimated from the comparison of the measured and theoretical Pd L-edge x-ray-absorption spectra. Thanks to high resolution, the partial CK yield f{sub 13}{sup L{sub 1}}{sup L{sub 3}}{sup M} could be extracted from the intensities of the resolved L{alpha}M satellite transitions. For f{sub 23}, f{sub 12}, and f{sub 13} CK rates, values of 0.164{+-}0.033, 0.047{+-}0.001, and 0.730{+-}0.039 were found, respectively. For the partial CK yields f{sub 13}{sup L{sub 1}}{sup L{sub 3}}{sup M} and f{sub 13}{sup L{sub 1}}{sup L{sub 3}}{sup N}, results of 0.406{+-}0.023 and 0.324{+-}0.032, respectively, were obtained.

This paper reports on the investigation of the double $K$-shell ionization of metallic aluminum induced by photon and electron impact. The experimental method consisted to measure the $K\ensuremath{\alpha}$ hypersatellite spectra resulting from the radiative decay of double $1s$ vacancy states by means of high-resolution x-ray spectroscopy using a Bragg-type von Hamos crystal spectrometer. Measurements of the photon-induced spectra were carried out at the European Synchrotron Radiation Facility, Grenoble, France, while those of the electron-induced spectra were performed at the University of Fribourg. The double $1s$ ionization probabilities and cross sections were derived from the $K{\ensuremath{\alpha}}_{2}$ hypersatellite to diagram line intensity ratios for photon beam energies ranging between 3.1 and 5.5 keV and for different incident electron-beam energies ranging between 4 and 20 keV. The energy and linewidth of the $K{\ensuremath{\alpha}}_{2}$ hypersatellite x-ray line were also determined for which consistent results were obtained from the photon and electron-beam measurements.

X-ray resonant Raman scattering (RRS) spectra of Al, Al{sub 2}O{sub 3}, Si, and SiO{sub 2} were measured at the European Synchrotron Radiation Facility, using a high-resolution Bragg-type curved crystal spectrometer. The x-ray RRS spectra were collected at several beam energies tuned below the 1s absorption thresholds of Al and Si. Differences in the spectral features between the elemental samples and the oxide ones were clearly observed. The data were interpreted using the second-order perturbation theory within the Kramers-Heisenberg (KH) approach. It is shown that, using the KH formalism, oscillator strengths that are similar to the ones deduced from x-ray absorption measurements can be extracted from emission x-ray RRS spectra. The total cross sections for the x-ray RRS process were derived for the different photon beam energies and compared with theoretical predictions. For elemental silicon, the weak 1s-3p excitation was observed and found to be consistent with results of density of states calculations.

The satellite and hypersatellite $K$ x-ray emission of a thin Mg foil and thick polycrystalline Si target bombarded by $34\text{\penalty1000-\hskip0pt}\mathrm{MeV}$ C and $50\text{\penalty1000-\hskip0pt}\mathrm{MeV}$ Ne ions was measured using high-resolution crystal diffractometry. The corresponding projectile reduced velocities $v∕{v}_{K}$ were 1.09 and 0.92 for C ions and 1.02, 0.86 for Ne ions in case of Mg and Si targets, respectively. An energy resolution of approximately $0.5\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ enabled separation of contributions corresponding to states with different numbers of $K$- and $L$-shell vacancies. The relative intensities of satellite and hypersatellite lines were determined by fitting the measured spectra with line shapes calculated using the GRASP92 computer code. To determine the production yields of initial states from the measured x-ray yields, the total decay schemes of initial states were considered. The decay schemes were also used to determine the relative intensities of components contributing to the observed $K\ensuremath{\alpha}$ satellites and hypersatellites and $K\ensuremath{\beta}$ satellite intensities. Including theoretical predictions in the fitted model is crucial to analyze properly the $K\ensuremath{\alpha}$ hypersatellite region which overlaps the $K\ensuremath{\beta}$ satellites. The initial-state production yields were then used to determine the $L$-shell ionization probabilities and the double- to single-$K$-shell ionization ratio corresponding to the four investigated collisions. The experimental values were compared to the theoretical predictions obtained within the independent electron model using single-electron ionization probabilities calculated by the three-body classical trajectory Monte Carlo (CTMC) method. Since the targets used were thick enough, the equilibrium projectile charge-state distributions in the solid media were assumed. While for the double- to single-$K$-shell ionization ratios a satisfactory agreement was observed between the CTMC predictions and our experimental results, the $L$-shell ionization probabilities were found to be overestimated by the CTMC calculations by a factor of about 2.

The K{beta}{sub 2} x-ray spectra of zirconium, niobium, molybdenum, and palladium targets bombarded with 20.8-MeV/amu {sup 12}C ions were measured with a high-resolution transmission-type bent crystal spectrometer. Well resolved M{sup 1} and M{sup 2} satellite lines were observed. Average M-shell and 3s,p- and 3d-subshell ionization probabilities for nearly central collisions were deduced. These values are compared with theoretical predictions from the semiclassical approximation using hydrogenlike and Dirac-Hartree-Fock wave functions. The experimental energy shifts of the K{beta}{sub 2} M{sup m=1,2} satellite lines are compared with values obtained from extensive multiconfiguration Dirac-Fock calculations.

High-resolution measurements of the photoinduced ${L}_{3}\ensuremath{-}{M}_{1}$ and ${L}_{3}\ensuremath{-}{M}_{4,5}$ x-ray emission lines were performed with a reflection-type bent-crystal spectrometer for a variety of elements ranging from xenon $(Z=54)$ to iridium $(Z=77).$ The measurements were performed at the European Synchrotron Radiation Facility in Grenoble, France. From the observed linewidths of the ${L}_{3}\ensuremath{-}{M}_{1}$ x-ray transitions, the widths of the ${M}_{1}$ levels were determined using the ${L}_{3}$ level widths extracted from the measured ${L}_{3}\ensuremath{-}{M}_{5}$ transitions, and assuming for the ${M}_{5}$ levels the widths reported recently by Campbell and Papp [At. Data Nucl. Data Tables 77, 1 (2001)]. In the rare-earth region a Z-dependent broadening of the ${M}_{1}$ level was observed.

The cross sections for the production of double K and L vacancy states in Al, Ca, and Co as a result of electron bombardment were determined for impact energies ranging from the double excitation threshold up to 20 keV. The cross sections were derived from the measured intensity ratios I K α L (1):I K α L (0) of the satellite-to-parent-diagram x-ray lines. The specific contributions of the shake and two-step electron-electron processes could be probed by comparing the relative satellite yields observed in the electron-induced spectra to those obtained by photoionization. In particular the energy-dependent cross sections for double K and L excitation resulting from two-step-two processes could be deduced. The measurements were performed by means of high-resolution x-ray spectroscopy, using a reflection-type bent crystal spectrometer.

The fluorescence $\mathrm{KL}$ x-ray emission of argon induced by impact with monoenergetic photons was observed with a high-resolution reflecting-type bent crystal spectrometer. The measurements were performed at the European Synchrotron Radiation Facility in Grenoble, France. X-ray beam energies in the range $3455 \mathrm{eV}l~\ensuremath{\Elzxh}\ensuremath{\omega}l~6540 \mathrm{eV}$ were used to investigate the $K+L$ double excitation from threshold to saturation. The excitation probabilities were deduced from the satellite-to-diagram line yield ratios $\mathrm{I}(KL\ensuremath{-}{L}_{2,3}L): \mathrm{I}(K\ensuremath{-}{L}_{2,3}).$ Results were compared to predictions based on the model of Thomas and the one of Roy. From the comparison, parameters such as excitation onset energies, high-energy limit shake probabilities, and radius of the $2p$ orbital in ionic Ar were deduced. The satellite line shapes and their evolution with the excitation energy were analyzed with the aid of multiconfiguration Dirac-Fock calculations.

High-resolution measurements of the photoinduced dipole-forbidden ${L}_{1}{\ensuremath{-}M}_{4,5}$ x-ray emission lines were performed with a reflection-type and a transmission-type bent-crystal spectrometer for ${}_{62}\mathrm{Sm},$ ${}_{67}\mathrm{Ho},$ ${}_{70}\mathrm{Yb},$ ${}_{74}\mathrm{W},$ ${}_{78}\mathrm{Pt},$ ${}_{80}\mathrm{Hg},$ and ${}_{83}\mathrm{Bi}.$ From the observed linewidths of the ${L}_{1}{\ensuremath{-}M}_{4,5}$ x-ray transitions, the level widths of the subshell ${L}_{1}$ were determined assuming for the ${M}_{4,5}$ level widths the values reported recently by Campbell and Papp [X-ray Spectrom. 24, 307 (1995); At. Data Nucl. Data Tables 77, 1 (2001)].

The photoinduced $K\ensuremath{\alpha}$ x-ray spectra of elements between sodium and chlorine were measured by means of high-resolution crystal diffractometry. The $K{\ensuremath{\alpha}}_{1,2}{L}^{(1)}$ satellites were observed and resolved from the corresponding diagram lines. The probabilities for producing via shake processes ${K}^{(1)}{L}^{(1)}$ double-hole states were deduced from the satellite to parent diagram line yield ratios. The results are compared to theoretical sudden approximation predictions. A satisfactory agreement is found except for sodium and chlorine for which our experimental results are markedly underestimated by the calculations.