Search

We propose a new advanced approach to determine the parameters for plasma generated in tokamaks. It is based on a detailed interpretation of the high-resolution X-ray spectra structure for tungsten from Zn-like to Co-like and molybdenum Ne-like ions that can, and have, be registered by the KX1 crystal spectrometer on the JET tokamak with an ITER-like wall. An earlier paper found that high-resolution M X-ray spectra structures of tungsten ions can be properly interpreted only by including separately all the individual contributions from the 4s1, 4p1, 4d1 and 4f1 subshell states for the 4d → 3p transitions in the case of Cu-like (W45+) ions, and also separately both 4s → 3p and 4d → 3p transitions for the Co-like (W47+) ions. Here a similarly detailed analysis is done for the M X-ray line structures coming from Cu-like and Co-like tungsten ions and L X-ray line from Ne-like molybdenum ions in different high-temperature plasmas. The predictions are obtained within the Collisional-Radiative approach by the Flexible Atomic Code package, for plasma electron temperatures from 2.0 keV to 6.0 keV and a single electron density, 3 × 1019 m−3, that is relevant to JET. The obtained shapes of spectra for Cu- and Co-like tungsten and Ne-like molybdenum ions (benchmarks) are important part of prepared reference base, which is crucial for applications of proposed approach. These results should be also useful for ITER, and for tokamaks such as WEST and ASDEX Upgrade, where tungsten plasma-facing components are implemented and kept track of with a high-resolution X-ray diagnostic similar to those based on the KX1 spectrometer.

This work was also supported by the National Science Centre , Poland under grant number 2017/25/B/ST2/00901. We combined different experimental techniques with a theoretical approach to determine a consistent set of diagram lines energies and binding energies. We propose an original approach consisting in determining the mass attenuation coefficients in an energy range covering the L-, M- and N- absorption edges, including a detailed evaluation of the associated uncertainties, to derive precisely the binding energies. We investigated the Lα, Lβ and M spectra of Gd with an independantly calibrated high-resolution anti-parallel double-crystal x-ray spectrometer. All the lines were identified and found in excellent agreement with the binding energies previously derived. Morever, we identified for the first time M5−O2, M4−O2,3 and M4−N2,3 diagram lines. authorsversion published

The $K\ensuremath{\beta}$ x-ray spectra of the elements from Ca to Ge have been systematically investigated using a high-resolution antiparallel double-crystal x-ray spectrometer. Each $K{\ensuremath{\beta}}_{1,3}$ natural linewidth has been corrected using the instrumental function of this type of x-ray spectrometer, and the spin doublet energies have been obtained from the peak position values in $K{\ensuremath{\beta}}_{1,3}$ x-ray spectra. For all studied elements the corrected $K{\ensuremath{\beta}}_{1}$ x-ray lines FWHM increase linearly as a function of $Z$. However, for $K{\ensuremath{\beta}}_{3}$ x-ray lines this dependence is generally not linear in the case of $3d$ elements but increases from Sc to Co elements. It has been found that the contributions of satellite lines are considered to be $[KM]$ shake processes. Our theoretically predicted synthetic spectra of Ca, Mn, Cu, and Zn are in very good agreement with our high-resolution measurements, except in the case of Mn, due to the open-shell valence configuration effect (more than 7000 transitions for diagram lines and more than $100\phantom{\rule{0.16em}{0ex}}000$ transitions for satellite lines) and the influence of the complicated structure of the metallic Mn.

Ionization affects the energy and shape of the characteristic X-ray lines that may be excited by energetic electrons in a partially ionized plasma. We present the first theoretical predictions for copper K-line spectra in different ionization states, one of a systematic series of computations on how ionization affects inner-shell X-ray lines. Detailed computations such as these may make it possible to use individual hard X-rays lines as diagnostics for warm, dense plasmas when high-resolution X-ray spectra are available.

The origin of the complex structure of $L{\ensuremath{\gamma}}_{1}$ $({L}_{2}{N}_{4})$, $L{\ensuremath{\gamma}}_{2}$ $({L}_{1}{N}_{2})$, $L{\ensuremath{\gamma}}_{3}$ $({L}_{1}{N}_{3})$, and $L{\ensuremath{\gamma}}_{6}$ $({L}_{2}{O}_{4})$ x-ray lines of thorium in high-resolution spectra induced by oxygen projectiles has so far resisted reliable quantitative interpretation. Therefore, the detailed structure predictions for satellite (additional holes in $M,N,O$, and/or $P$ shells) and hypersatellite (additional hole in $L$ shell) $L\ensuremath{\gamma}$ x-ray lines of thorium being the results of extensive multiconfiguration Dirac-Fock calculations have been performed. Our predictions reproduce with the excellent precision the positions and shapes of characteristic parts of above high-resolution $L\ensuremath{\gamma}$ x-ray spectrum of thorium what indicates that our study has been carried out with very high accuracy. The results of this study are the precursor for proper quantitative interpretation of the complex origin of $L{\ensuremath{\gamma}}_{1},L{\ensuremath{\gamma}}_{2},L{\ensuremath{\gamma}}_{3}$, and $L{\ensuremath{\gamma}}_{6}$ lines in high-resolution x-ray spectra of thorium induced by different light and heavy projectiles.

For molybdenum wire implosions on the Z-machine at Sandia National Laboratories the high-resolution measurements of x-ray spectra have been recently published. The K and L x-ray spectra modeled here within the framework of Collisional-Radiative Model using the Flexible Atomic Code package reproduce well the published data to show that such model is a reasonable one.

Spectra of the W L transitions in the energy range 8e12 keV from warm dense plasmas generated by theNaval Research Laboratory’s Gamble II pulsed power machine were recorded bya newly developed high-resolution transmission-crystal X-ray spectrometer with 2 eV accuracy. The discharges have up to 2 MVvoltage, 0.5 MA current, and produce up to 2.4 MJ/cm 3 energy density. The plasma-filled rod pinch(PFRP) diode produces a plasma with N e z 10 22 cm 3 and T e z 50 eV during the time of maximum X-rayemission. By analyzing the line shapes, it was determined that the L b 2 inner-shell transition from the4d 5/2 level was shifted to higher energy by up to 23 eV relative to nearby L b transitions from n ¼ 3 levels.In addition, the L b 2 transition was significantly broader and asymmetric compared to the n ¼ 3 transi-tions. The energy shift of the L b 2 transition results from the ionization of electrons outside the 4d shellthat perturbs the transition energies in the ions to higher values. The increased line width and asym-metry result from unresolved transitions from a range of ionization states up to þ28. The ionizationdistribution was determined by comparison of the measured energy shifts and widths to calculatedtransition energies in W ions, and the ionization was correlated with Gamble discharge parameters suchas the anode type and the high voltage delay time. This work demonstrates a new hard X-ray spectro-scopic diagnostic technique for the direct measurement of the ionization distribution in warm denseplasmas of the heavy elements W through U that is independent of the other plasma parameters anddoes not require interpretation by hydrodynamic, atomic kinetics, and radiative simulation codes. 2013 Elsevier B.V. All rights reserved.

We have investigated systematically the $K\ensuremath{\alpha}$ x-ray spectra in elements from Ca to Ge within Berger's two-Lorentzian functions model, using a high-resolution antiparallel double-crystal x-ray spectrometer, in order to obtain in detail the physical meaning of the asymmetry in the spectral profiles. The overall tendency of the corrected full width at half maximum of the $K{\ensuremath{\alpha}}_{1}$ and $K{\ensuremath{\alpha}}_{2}$ lines as a function of $Z$, as well as the linewidths, are in good agreement with the data reported in the literature. It is found, from both the experiments and calculation, that satellite lines arising from shake-off appear between the $K{\ensuremath{\alpha}}_{1}$ and $K{\ensuremath{\alpha}}_{2}$ lines. The asymmetry index of $K{\ensuremath{\alpha}}_{1}$ in $3d$ elements from Sc to Zn is ascribed to the existence of a $3d$ spectator hole. Moreover, the observed Sc $K{\ensuremath{\alpha}}_{1}$ line shows a symmetric profile unlike the Ti $K{\ensuremath{\alpha}}_{1}$ line profile, this discrepancy being explained by the existence of satellite lines on both sides of the Sc profile. Our experimental results yielded around 25% probability for the probability of shake processes creating a second hole in the $3p$ or $3d$ subshells in Sc and around 18% probability for creating a second hole the in the $3p$ in Ca. For the latter process our calculated value, using multiconfiguration Dirac-Fock wave functions and the sudden approximation yielded a 10% probability.

In the future International Thermonuclear Experimental Reactor (ITER), the interaction between the plasma and the tungsten chosen as the plasma-facing wall material imposes that the hot central plasma loses energy by X-ray emission from tungsten ions. On the other hand, the registered X-ray spectra provide alternative diagnostics of the plasma itself. Highly ionized tungsten emits extremely complex X-ray spectra that can be understood only after exhaustive theoretical studies. The detailed analyses will be useful for proper interpretation of soft X-ray plasma radiation expected to be registered on ITER-like machines, that is, Tungsten (W) Environment in Steady-state Tokamak (WEST). The simulations of the soft X-ray spectra structures for tungsten ions have been performed using the flexible atomic code (FAC) package within the framework of collisional-radiative (CR) model approach for electron temperatures and densities relevant to WEST tokamak.

The Kα X-ray emission spectra of the low-density SiO2 aerogel target bombarded by 48Ca ions with initial energy of 11.4 MeV/u were measured with a high spectral and spatial resolution along 80% of the ion beam stopping path. The Si KαL0 diagram and KαLn (up to n = 5) X-ray satellite lines corresponding to the radiative decays of atomic states with one hole in the K-shell and n-holes in the L-shell were measured. Energy shifts of the KαLn satellites with respect to their diagram Kα lines were determined and compared with the results of multiconfiguration Dirac–Fock (MCDF) calculations. The experimental energy shifts are smaller than values obtained from free-ion MCDF theory assuming an empty M-shell. The influence of the valence M-shell configuration on the satellite X-ray spectra is discussed.

Detailed multicon.guration Dirac-Fock calculations with the inclusion of the transverse (Breit) interaction and QED corrections have been carried out on zirconium to elucidate the structure of various M-, N-shell satellite and L-shell hypersatellite L?1,2 (L3M4,5) and L?1(L2M4) lines in its X-ray spectra. For each type of lines two theoretical spectra have been synthesized: one being a sum of the Lorentzian natural line shapes and the other one being a convolution of the sum of the Lorentzian natural line shapes with the Gaussian instrumental response. The results are very helpful in reliable interpretation of various high-resolution L-X-ray spectra of zirconium target bombarded by different light and heavy projectiles.

Simulations of the shapes of Pb K x-ray spectra have been performed for an experimental situation in which single and double L- and M-shell ionization (apart from the single K-shell ionization) of target atoms occurs. The simulations are based on the results of the calculations of the energies and probabilities of various Pb K x-ray transitions, done with the multiconfiguration Dirac-Fock (MCDF) method with the inclusion of the transverse (Breit) interaction and quantum electro dynamic (QED) corrections. It has been found that most contributions to the simulated spectra considerably overlap other contributions. Thus, their extraction from the measured spectra, which provides data about the L- and M-shell ionization probability in a collision process, will only be possible using the results of theoretical studies. Our studies can be crucial in both analysis of a number of observed Pb K x-ray spectra and in designing new experiments concerning the K x-ray spectra of multiply ionized heavy atoms induced in collisions with various light or heavy projectiles of different energies.

Very extensive multiconfiguration Dirac–Fock calculations with the inclusion of the transverse (Breit) interaction and QED corrections have been carried out on thorium to elucidate the structure of various satellite (additional vacancies in N and/or O shells) and hypersatellite (additional vacancies in M or M and N shells) M α 1 , 2 ( M 5 N 6 , 7 ) and M β 1 ( M 4 N 6 ) lines in its X-ray spectra. For each type of lines two theoretical spectra have been synthesized: one being a sum of the Lorentzian natural line shapes and the other one being a convolution of the sum of the Lorentzian natural line shapes with the Gaussian instrumental response. The obtained theoretical results will be very helpful in reliable and quantitative interpretation of various experimental M-X-ray spectra of thorium target bombarded by different light and heavy projectiles (such as O and Ne ions).

Extensive multiconfiguration Dirac–Fock calculations with the inclusion of the transverse (Breit) interaction and QED corrections have been carried out on palladium to elucidate the structure of various satellite (additional vacancies in M and/or N shells) and hypersatellite (additional vacancies in L or L and M shells) L α 1 , 2 ( L 3 M 4 , 5 ) and L β 1 ( L 2 M 4 ) lines in its X-ray spectra. For each type of lines two theoretical spectra have been synthesized: one being a sum of the Lorentzian natural line shapes and the other one being a convolution of the sum of the Lorentzian natural line shapes with the Gaussian instrumental response. The obtained results will be absolutely essential to carry out quantitative interpretation of very complicated structure of L α 1 , 2 and L β 1 satellite and hypersatellite lines in various high-resolution L-X-ray spectra of palladium target bombarded by different light and heavy projectiles.

Predictions about the shapes of the K x-ray spectra of medium-Z and heavy atoms have been made on the basis of the results of theoretical multiconfiguration Dirac–Fock calculations (with the inclusion of the transverse Breit interaction and QED corrections) for various KL0M1 x-ray satellite lines of Pd, Tb, Ta and Th. The construction of theoretical stick and synthesized (the sum of the Lorentzian natural line shapes) K x-ray spectra (including also diagram and KL1M0 satellite lines) has enabled foreseeing such details of experimental spectra as the overlapping and visibility of particular groups of lines. The energy regions possibly best for the extraction of the satellite contributions in the measured K x-ray spectra have been indicated for each studied element. The effect of additional single ionization of the different subshells of the M shell on the structure and shapes of the spectra of various K x-ray lines has been investigated in detail for Pd, Tb, Ta and Th. It has been found that in the KL0M1 satellite spectra the shapes of the bands mainly resemble the shapes of the corresponding K x-ray diagram lines (but they are wider than the latter). For each element, the biggest average energy shifts with respect to the diagram lines are observed for a given kind of the KL0M1 lines mostly in the case of removing a 3p electron in the initial state, whereas the smallest shifts are caused by removing a 3d electron. Our study can enable the correct quantitative interpretation of the K x-ray spectra of different multiply ionized medium-Z and heavy atoms (induced in collisions with light or heavy ions) and can be instrumental in planning various new experiments involving the determination of the M- and L-shell ionization probability.

For Tb and Ta we have performed multiconfiguration Dirac–Fock calculations with the inclusion of the transverse (Breit) interaction and QED corrections, obtaining the positions and intensities of various electric dipole, electric quadrupole and magnetic dipole K X-ray diagram lines and of their KL 1 satellites. We have analyzed the effect of additional L-shell ionization on the structure and shapes of Tb and Ta K X-ray spectra on the basis of theoretically constructed stick and synthesized spectra. By comparing the theoretical spectra of Tb and Ta we have found that generally the structure and shapes of particular satellite line groups are similar for the two elements but in the case of Ta the shapes seem to be smoother than for Tb. Our study can be helpful in reliable quantitative interpretation of the K X-ray spectra of heavy elements induced during collisions with various light or heavy projectiles.

Extensive single-configuration Dirac–Fock (DF) calculations (within the multiconfiguration DF method) with the inclusion of the transverse (Breit) interaction and QED corrections have been carried out on Mo and Pd to elucidate the structure of the Kβ2L0Mr satellite lines in their X-ray spectra. For each type of lines two theoretical spectra have been synthesized: one being a sum of the Lorentzian natural line shapes and the other one being a convolution of the sum of the Lorentzian natural line shapes with the Gaussian instrumental response. The obtained results can be used to determine the M-shell ionization probability in collisions via the theoretical analysis of Kβ2 spectra of Mo and Pd induced by different energetic light and heavy ions.

Multiconfiguration Dirac–Fock calculations (with the inclusion of the transverse Breit interaction and QED corrections) have been performed for various Pb K x-ray lines. The calculated positions and intensities of many electric dipole, electric quadrupole and magnetic dipole KL0M1 and KL1M0 x-ray satellite lines have been analysed. On the basis of theoretically constructed stick and synthesized (the sum of the Lorentzian natural line shapes) K x-ray spectra, the effect of the additional single ionization of different subshells of the M shell on the shapes and structure of Pb K x-ray spectra has been investigated and compared with the effect of the single L-shell ionization. It has been found that in the KL0M1 satellite spectra the sticks are less scattered and the shapes of the bands are narrower and smoother than in the KL1M0 spectra. The much weaker influence of an additional M-shell hole on the K x-ray spectra than of an L-shell hole is also reflected in very small values of the energy shifts (with respect to the corresponding diagram lines) of the KL0M1 satellite lines in comparison with those of the KL1M0 lines. This study provides an exhaustive set of data, enabling not only the correct quantitative analysis of many experimental Pb K x-ray spectra (induced in collisions with various projectiles), but also predictions concerning the K x-ray spectra of multiply ionized Pb or other heavy atoms, which can be helpful in designing new experiments.

The high-resolution spectra of thorium Mα 1,2 (M 5 N 6,7 ) and Mβ(M 4 N 6 ) X-ray lines induced by O and Ne ions with energies 376 and 178 MeV, respectively, have been measured using a von Hamos crystal spectrometer. The measured spectra exhibit the pronounced X-ray satellite structure due to the multiple ionization in the N- and M-shells. In particular the N-shell satellites are well resolved and the M-shell hypersatellites are clearly observed, to the best of our knowledge, for the first time. The observed M-X-ray diagram transitions and their satellites are interpreted using the multi-configuration Dirac-Fock (MCDF) calculations performed for the multi-vacancy configurations including up to two spectator vacancies. The comparison shows that calculations for more vacancies are needed to reproduce the measured X-ray structure. On the other hand, the data are well interpreted qualitatively using a simplified model of the “average” MCDF satellites having binomially distributed intensities. Further MCDF calculations are in the progress, which ultimately allow to extract precise (∼0.5 eV) information on the electronic structure of the multiple ionized thorium.

Extensive single-configuration Dirac–Fock (DF) calculations (within the multiconfiguration DF method) have been performed for sulphur to explain the influence of removing electrons from L and M shells on the shapes and parameters (the average Kα and Kβ transition energies and the values of Kβ/Kα intensity ratio) of its K X-ray spectra. For Kα and Kβ diagram lines and each type of L- and M-satellite lines, the theoretical stick spectra (line positions with their relative intensities) have been presented. The theoretical results obtained can be used for interpreting the measured shapes and parameters of the K X-ray spectra of highly ionized swift sulphur projectiles passing through various foils. They can also be very helpful in interpreting various sulphur target K X-ray spectra induced by photons and different projectiles recorded by high-resolution crystal spectrometer or lower-resolution detector.

The satellite and hypersatellite K X-ray lines emitted by sulphur projectiles (with energies 9.6, 16.0, 22.4, 32.0, 65, 79, 99 and 122 MeV) passing through carbon foils (with different thickness varying from 15 to 210 μg/cm2) have been measured using a Si(Li) detector. We use a theoretical model based on the single-configuration Dirac–Fock calculations and equilibrium charge state distribution to interpret the experimental K X-ray spectra parameters. For all projectile energies, we evaluate the probability of K-hole creation, the average population of L-shell, and the average population of the 3p and 4p subshells. In the case of 9.6–32.0 MeV beam energy we evaluate also the population of L and M shells of sulphur projectiles. For the energy range 65–122 MeV, we estimate the probability of appearance of the most important configurations. The lifetimes of the studied states is also deduced.

High-resolution measurements of the Kα 1,2 X-ray spectra were performed with a bent crystal diffraction spectrometer for zirconium, niobium, molybdenum and palladium targets bombarded by 280 and 360 MeV oxygen ions. The energy differences between the Kα 1,2 diagram and the K h α 1,2 hypersatellite transitions as well as the intensity ratios I ( K h α 1 )/ I ( K h α 2 ) were determined. The L-shell satellites of the diagram and of the hypersatellite lines were resolved. The data are interpreted in terms of the properties of He-like hole states in mid- Z atoms. The Breit interaction correction is determined. The corrections due to the unresolved M-shell satellites and to the QED are found to be much smaller than the Breit terms and comparable to the experimental accuracy.

The {ital K}{beta}{sub 2} x-ray spectra of zirconium, niobium, molybdenum, and palladium bombarded by 150 and 300 keV electrons were measured with a high-resolution transmission curved crystal spectrometer. Multiconfiguration Dirac-Fock calculations were used for the decomposition of the experimental spectra into the {ital K}{beta}{sub 2}{ital M}{sup 0} (diagram) and {ital K}{beta}{sub 2}{ital M}{sup 1} (satellite) components. The probabilities of energy dependent (direct Coulomb and two-step) processes were estimated from the differences in the satellite line yields for electrons and photons. The satellite yields are found to be considerably enhanced in comparison with those for the proton-induced ionization recently measured and analyzed in the same way [T. Ludziejewski {ital et} {ital al}., Phys. Rev. A {bold 52}, 2791 (1995)]. This result indicates the importance of multielectron effects in the {ital K} plus {ital M} shell ionization by energetic projectiles. {copyright} {ital 1996 The American Physical Society.}

$K{\ensuremath{\beta}}_{2}$ x-ray spectra of Zr, Mo, and Pd induced by photons and 16-, 25-, and 45-MeV protons were measured with a transmission bent crystal spectrometer. The average $M$-shell ionization probabilities were determined with the assumption that the yields in the $K{\ensuremath{\beta}}_{2}$ satellite region are due only to the $M$-shell ionization accompanying the removal of the $K$-shell electron. In the case of photoionization, these yields were found to exceed significantly those calculated with the sudden-approximation model for the shakeoff plus shakeup. Likewise, the corresponding yields for collisions with protons exceed those expected for the combined effect of the direct Coulomb ionization and the shake mechanism. The solid-state effects, as well as the direct knockout of the $M$-shell electron by the photoelectron (or the $\ensuremath{\delta}$ electron), are discussed in view of their possible effect on the line intensity in the satellite region. The direct Coulomb ionization probabilities in near central collisions with protons are determined from the difference of the relative yields of $\mathrm{K}{\ensuremath{\beta}}_{2}$ satellites in the proton-and photon-induced ionization. The underlying assumption is that the shake and solid-state effects are independent of the ionizing agent and that the secondary-electron ionization is similar in the two processes. The results are compared with the semiclassical approximation calculations exploiting relativistic hydrogenic and Dirac-Hartree-Fock wave functions.

We propose a novel approach for the theoretical analysis of the photoinduced high-resolution ${K}^{h}{\ensuremath{\alpha}}_{1,2}$ x-ray hypersatellite spectra, which allows us to obtain reliable values of lifetimes of the doubly $K$-shell ionized states and fundamental information about the relative role of $K$-shell double photoionization (DPI) mechanisms. It is demonstrated for the first time that the ${K}^{h}{\ensuremath{\alpha}}_{1,2}$ hypersatellite natural line broadening observed for selected metal atoms with $20\ensuremath{\le}Z\ensuremath{\le}30$ can be well reproduced quantitatively by taking into account the influences of the open-shell valence configuration (adopted from predictions of the band-structure method) and the outer-shell ionization and excitation following the DPI process.

In the present work, an alternative approach for the evaluation of the equilibrium K-, L-, and M-shell ionizations and the mean charge state q for projectiles passing through various targets has been proposed. The approach is based on measured K x-ray energy shifts and line intensity ratios and utilizes the theoretical analysis of projectile spectra using multiconfiguration Dirac-Fock calculations. It was applied for the satellite and hypersatellite K lines in the x-ray spectra emitted by sulfur projectiles passing with energies of 9.6-122 MeV through carbon, aluminium, titanium, and iron targets, recorded by a Si(Li) detector. It was found that only in the high projectile energy region there was significant dependence of mean equilibrium K-shell ionization on the target atomic number. The equilibrium L-shell ionization rises with the increase of sulfur energy until 32 MeV, but for higher energies the changes are very weak. The equilibrium M-shell ionization changes very weakly for low projectile energy while for higher energies this ionization is practically constant. For each target, the estimated value of q rises with the increase of the sulfur energy value. The dependence of the sulfur charge state on the target atomic number was discussed by taking into account the crossmore » sections for ionization, decay, and electron capture processes. The data were compared with the experimental data measured by other authors and with the predictions of Shima's and Schiwietz and Grande's semiempirical formulas. The presented good agreement points out that this alternative approach delivers quantitative results.« less

This article presents a detailed analysis of the K{alpha} x-ray spectra of Si induced by 11.4 MeV/u Ca projectiles penetrating a low-density SiO{sub 2} aerogel target measured with high spectral and spatial resolution at the UNILAC accelerator at GSI-Darmstadt. The low-density material used in the experiment was crucial for the space-resolved studies of the Si x-ray radiation (for different energies of stopping Ca ions). The stopping length of the 11 MeV/u Ca ions reaches up to 10 mm in the low-density SiO{sub 2} aerogel, whereas in regular quartz solid targets it is about 100 times shorter. The analysis of the x-ray spectra emitted by the stopping medium has shown a high level of the L-shell ionization, especially in the later considered phase (E{sub p{approx}}5 MeV/u) of the stopping process. It has been further demonstrated that the population of the highly ionized states produced in the ion-atom collisions can be substantially reduced in the time between the collision and the x-ray emission due to the very intense rearrangement processes occurring in Si situated in the chemical environment of oxygen atoms. Moreover, comparison of the experimental values of the K{alpha} L-shell satellite energy shifts with the results of the multiconfiguration Dirac-Fock calculationsmore » allows us to find that Si valence electron configuration is enriched due to electron transfer from valence-electron-rich oxygen atoms into highly ionized silicon atoms. Our results indicate that the Coulomb explosion in a highly ionized track core is prevented by rapid neutralization in the femtosecond time scale.« less

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 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 demonstrate that in order to interpret the x-ray satellite structure of Pd Lα1,2(L₃M4,5) transitions excited by fast O ions, which was measured using a high-resolution von Hamos crystal spectrometer, the vacancy rearrangement processes, taking place prior to the x-ray emission, have to be taken into account. The measured spectra were compared with the predictions of the multi- con.guration Dirac-Fock (MCDF) calculations using the fluorescence and Coster- Kronig yields which were modiffed due to a reduced number of electrons available for relaxation processes and the effect of closing the Coster-Kronig transitions. We demonstrate that the vacancy rearrangement processes can be described in terms of the rearrangement factor, which can be calculated by solving the system of rate equations modelling the flow of vacancies in the multiply ionized atom. By using this factor, the ionization probability at the moment of collision can be extracted from the measured intensity distribution of x-ray satellites. The present results support the independent electron picture of multiple ionization and indicate the importance of use of Dirac-Hartree-Fock wave functions to calculate the ionization probabilities.

Modeled within the Collisional-Radiative approach, for parameters relevant to plasmas in the centre of JET, the M X-ray line structures for tungsten and L X-ray line structures for molybdenum both occur in the wave length range 5.0-5.35 A; and, their strengths are comparable. Therefore, the spectra obtained with the upgraded high-resolution X-ray spectrometer KX1 on JET should include both tungsten and molybdenum in their interpretation. The same will be true for the high-resolution X- ray diagnostic on tokamaks such as WEST and ITER, where tungsten plasma-facing components will be implemented.

K-X-ray spectra of Zr, Nb, Mo and Pd targets bombarded with 250 MeV carbon and 360 MeV oxygen ions are studied with high resolution diffraction spectrometry. Relative yields and natural widths of the Khα1,2 hypersatellite lines are determined and compared with those of the diagram lines. The widths of Khα1,2 lines are compared with the new phenomenological formula which takes into account the retardation of the Khα₁ transition in the LS coupling scheme. The data significantly exceed the expected values. Deduced lifetimes of the double K-hole states are shorter than expected.

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.

We present the results of modeling of the L and M x-ray line structures for tungsten in high-temperature plasmas predicted with temperatures relevant to large tokamaks including the Joint European Tokamak and the future International Thermonuclear Experimental Reactor. The simulations have been performed using the Flexible Atomic Code within the framework of the collisional–radiative (CR) model. For L x-ray lines, our results predicted for various levels of CR model sophistication have been compared with the spectrum measured using the electron beam ion trap (EBIT) calorimeter spectrometer at the Livermore SuperEBIT that constitutes a rigorous atomic benchmark for tokamak plasmas. In the case of M x-ray lines, we have reproduced the experimental SuperEBIT spectra as a superposition of theoretical contributions for different ions. The obtained results enable us to propose an approach allowing the decomposition of registered experimental tungsten spectra produced in tokamaks into the theoretically predicted contributions, corresponding to different degrees of ionization.

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.

Relative $K$ x-ray intensities of $Mn$ in $Mn$, $MnO_{2}$, $LaMnO_{3}$ and $La_{0.7}B_{0.3}MnO_{3}$ ($B$ = $Ca$, $Sr$, and $Ce$) systems have been measured following excitation by 59.54 keV $\gamma$-rays from a 200 mCi $^{241}$Am point-source. The measured results for the compounds deviate significantly from the results of pure $Mn$. Comparison of the experimental data with the multiconfiguration Dirac-Fock (MCDF) effective atomic model calculations indicates reasonable agreement with the predictions of ionic model for the doped {manganites except} that the electron doped $La_{0.7}Ce_{0.3}MnO_{3}$ and hole doped $La_{0.7}Ca_{0.3}MnO_{3}$ compounds show some small deviations. The results of $MnO_{2}$ and $LaMnO_{3}$ deviate considerably from the predictions of the ionic model. Our measured $K\beta/K\alpha$ ratio of $Mn$ in $La_{0.7}Ca_{0.3}MnO_{3}$ cannot be explained as a linear superposition of $K\beta/K\alpha$ ratios of $Mn$ for the end members which is in contrast to the recent proposal by Tyson et al. from their $Mn$ $K\beta$ spectra., Comment: 14 pages, 4 figures. to appear in NIM-B.Please send an e-mail for figures

The structure of satellite (additional vacancies in N and/or O shells) and hypersatellite (additional vacancies in M or M and N shells) M?1,2 and M?1 lines in the x-ray spectra of heavy atoms can be explained precisely by taking into account the extensive multiconfiguration Dirac?Fock calculations. The presented results are a precursor for the reliable quantitative interpretation of a very complex origin structure of M?1,2 and M?1 lines in various high-resolution x-ray spectra of heavy atoms induced by different light and heavy projectiles. Moreover, the intensities of the M-x-ray lines of uranium can be helpful in the application of x-ray measurements from UO2 as a reference material (virtual standard) for non-destructive wavelength-dispersive electron probe microanalysis.

The K\ensuremath{\alpha} and K\ensuremath{\beta} x-ray spectra of palladium and lanthanum bombarded by 5.5-MeV/amu $^{16}\mathrm{O}$ ions were measured with a high-resolution transmission crystal spectrometer. The observed complex structure of the K\ensuremath{\alpha}${\mathit{L}}^{0}$ and K${\mathrm{\ensuremath{\beta}}}_{1,3}$${\mathit{L}}^{0}$ lines consisting of many M satellites was analyzed by means of theoretical line profiles based on multiconfiguration Dirac-Fock calculations. The average M-shell and M-subshell ionization probabilities in near-central collisions are determined. The experimental results are compared to the predictions of the semiclassical-approximation theory. The agreement is much improved by using Dirac-Hartree-Fock (DHF) wave functions instead of screened relativistic hydrogenic wave functions. The importance of DHF wave functions in the calculation of the M-shell ionization probabilities is illustrated with other examples.

In the present work, an alternative approach for the evaluation of the equilibrium degree of K-, L- and M-shell ionizations and the mean charge state for projectiles passing through various targets has been proposed. The approach is based on measured K x-ray energy shifts and line intensity ratios, and utilizes the theoretical analysis of projectile spectra using the multiconfiguration Dirac–Fock calculations.

The interpretation of L-shell satellites and hypersatellites for Lα1,2 (L3→M4,5) and Lβ1 (L2→M4) x-ray transitions in zirconium multiply ionized by oxygen and neon ions is reported. The x-ray spectra were measured with a high-resolution von Hamos spectrometer and interpreted in terms the relativistic multi-configuration Dirac-Fock (MCDF) calculations. The ionization probabilities of L- and M-shell derived from the data are compared with the predictions of the semiclassical approximation (SCA) calculations.

Very extensive multiconfiguration Dirac-Fock calculations with the inclusion of the transverse (Breit) interaction and QED corrections have been carried out on gold, thorium and uranium to elucidate the structure of various satellite and hypersatellite Mα1,2 (M5N6,7) and Mβ1 (M4N6) lines in their X-ray spectra.

Extensive multiconfiguration Dirac-Fock (MCDF) calculations with the inclusion of the transverse (Breit) interaction and QED corrections have been carried out on molybdenum to explain the dependence of the structure of L? 1,2 and L? 1 lines on the changes in configurations of the valence electrons belonging to two different configuration types: three open-shell 4d6-r5sr (r = 2,1,0) configurations and one closed-shell 4d43/2 5s2 configuration. It has been found that the MCDF predictions for open-shell valence configurations (4d4 5s2, 4d5 5s1, 4d6 5s0) much better reproduce observed structure of L? 1,2 lines in X-ray spectra of molybdenum than closed-shell 4d43/2 5s2 valence configuration. The influence of changes in the valence electronic configuration on the structure of L-X-ray spectra of molybdenum is noticeable. Moreover, the observation of the shapes of L-X-ray spectra seems to be very good method to investigate the changes of the valence electronic configuration caused by the chemical environment.

Extensive multiconfiguration Dirac-Fock calculations with the inclusion of the transverse Breit interaction and QED corrections have been performed for silicon to explain the influence of removing electrons from L and M shells on the shapes and parameters (the average Kα and Kβ transition energies and the values of Kβ/Kα intensity ratio) of its K-X-ray spectra. For Kα diagram lines and for certain L- and M-satellite lines the theoretical stick spectra (line positions with their relative intensities) have been presented. Moreover for each type of lines two theoretical spectra have been synthesized: one being a sum of the Lorentzian natural line shapes and the other one being a convolution of the sum of the Lorentzian natural line shapes with the Gaussian instrumental response.

Extensive multiconfiguration Dirac-Fock calculations with the inclusion of the transverse (Breit) interaction and QED corrections have been carried out on gold and thorium to elucidate the structure of various satellite (additional vacancies in N and/or O shells) and hypersatellite (additional vacancies in M or M and N shells) Mα1,2 (M5N6,7) and Mβ1 (M4N6) lines in its X-ray spectra. For every calculated type of Mα1,2 and Mβ 1 lines the theoretical stick spectra (line positions with their relative intensities) have been presented. Moreover for each type of lines two theoretical spectra have been predicted: one being a sum of the Lorentzian natural line shapes and the other one being a convolution of the sum of the Lorentzian natural line shapes with the Gaussian instrumental response. The obtained results will be very helpful in quantitative interpretation of a very complex origin of Mα 1,2 and Mβ 1 line structures in various high-resolution X-ray spectra of heavy atoms induced by different light and heavy projectiles.

Calculs par la methode multiconfigurationnelle de Dirac-Fock, dans la version du niveau moyen, en incluant les corrections d'interaction de Breit, de self-energie et de polarisation du vide

Relativistic multiconfiguration Dirac-Fock (MCDF) calculations in the average-level (MCDF-AL) version with the inclusion of the transverse (Breit) interaction, self-energy, and vacuum polarization corrections have been carried out for molybdenum, palladium, lanthanum, and holmium to elucidate the structure of the K..cap alpha..L/sup n/ lines in their x-ray spectra. The examination of the effect of removing electrons from M shell on the principal K..cap alpha..(K..cap alpha..L/sup 0/) lines indicates that the most significant is the effect of removing 3p and then 3s subshells and that the effect of additional holes strongly increases with the atomic number. Detailed calculations have been performed on palladium to shed light on the structure of the K..cap alpha..L/sup n/ satellite lines of its x-ray spectrum, which is the first systematic theoretical study on the structure of these lines of a heavy atom. It has been found that in all cases the ''average'' positions of the groups of lines corresponding to the transitions of the type 1s/sup -1/2p/sup -n/..-->..2p/sup -(n+1)/ obtained in the present work are very close to the recently measured experimental positions of appropriate K..cap alpha..L/sup n/ satellite lines. On the other hand, the structure of the satellite lines has been shown to be much moremore » complex than can be observed experimentally. The results of this work can be used to construct different theoretical K..cap alpha..L/sup n/ spectra for palladium, satisfactorily reproducing the shape of various experimental spectra generated by different inducing projectiles.« less

Soft X-ray diagnostics on tokamak fusion reactors such as ITER and the Tungsten (W) Environment in Steady-state Tokamak (WEST) intend to provide valuable information on the plasma, in particular on the tungsten impurities that appear in the central plasma following plasma-wall interaction. Various highly charged tungsten ions occur depending on the plasma’s electron temperature, all with complex N, M and L X-ray spectra structures that can be properly understood only after comprehensive theoretical research. For a nominal density and electron temperatures relevant to WEST, this paper presents the results of tungsten N, M and L X-ray lines modeling, in the region from 0.1 keV to 20 keV, performed within the Collisional-Radiative model using the Flexible Atomic Code package.

The upgraded x-ray crystal spectrometer KX1 on the Joint European Torus (JET) can now measure the M x-ray lines from tungsten with sufficiently high resolution to evaluate how much tungsten may sputter from the plasma-facing tungsten wall planned for the International Thermonuclear Experimental Reactor (ITER). However, a test run on JET found that the L x-ray lines of a molybdenum impurity, which happen to occur in the targeted wavelength region of 5.00-5.35 angstrom, must be taken into account together with the radiation from the M x-ray lines of tungsten to match the high-resolution spectra. Such detailed radiation modeling is expected to be needed for ASDEX Upgrade tokamak, and for other tokamaks such as ITER and tungsten (W) Environment in Steady-state Tokamak (WEST), which will implement tungsten plasma-facing components and a high-resolution spectrometer to keep track of with a similar x-ray diagnostics.