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In order to allow the advanced interpretation of the X-ray spectra registered by the high-resolution crystal KX1 spectrometer on the JET with an ITER-like wall, especially to determine how the relative emission contributions of tungsten and molybdenum ions change during a JET discharge, the X-ray spectra have been carefully modeled over a narrow wavelength range. The simulations have been done in the framework of Collisional–Radiative model implemented in Flexible Atomic Code for an electron density (ne = 2.5 × 1019 m−3), and electron temperatures between Te = 3.0 keV and Te = 4.5 keV, typical for JET. Moreover, performed detailed analysis in the framework of the proposed procedure can be useful in determining temperature of a high temperature plasma generated in tokamaks.

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.

Following the first experimental observation of $^{93m}\mathrm{Mo}$ isomer depletion via nuclear excitation by electron capture (NEEC), we consider another experimental scenario related to the $^{242m}\mathrm{Am}$ isomer for which the probability of the NEEC process is expected to be even higher than for the $^{93m}\mathrm{Mo}$ isomer. The optimum experimental conditions for the production and depletion of the $^{242m}\mathrm{Am}$ isomer in a beam-based scenario are discussed. The relevant beam-target reaction cross sections have been calculated striving to ensure effective production of the $^{242m}\mathrm{Am}$ isomer. Kinetic energies required for the NEEC process to occur have been predicted for the $n=5$, 6, and 7 subshells of $^{242m}\mathrm{Am}$ ions and combined with available ion charge states at subsequent stages of the ion stopping process. The NEEC resonance strengths have been estimated for the partial contributions of individual subshells to the whole NEEC process.

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.

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.

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).

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.

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.

Three semi-classical approaches to the simulation of ion–atom scattering: the Kirschbaum–Wilets, the Cohen energy-bounded, and the wave-packet – are used to calculate the ionization and charge-transfer cross sections for the scattering of fully stripped sulfur ions on atomic hydrogen. Their comparison in the high-energy regime is provided. Elements of microscopic analysis of Kirschbaum–Wilets trajectories are given.

The effect of the projectile K X-rays line shifts with respect to the corresponding diagram lines has been used for evaluation of a mean equilibrium charge, q ¯ , for sulphur ions passing with energies of 9.6, 16.0, 22.4 and 32.0 MeV through Al, Ti and Fe foils. The q ¯ values for sulphur ions passing through Al and reference C foils are approximately equal for the all discussed energies. In the case of Ti and Fe foils the q ¯ values are greater for the smallest energy and the difference between q ¯ values in these two groups of targets is decreasing with increasing sulphur ion energy. For sulphur ions with energy of 32.0 MeV there is no difference in q ¯ values in all targets.

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.

The Kβ spectrum of 42Mo bombarded by 20.8 MeV/amu carbon ions was measured with high-resolution using a transmission-type bent crystal spectrometer operated in the modified DuMond slit geometry. The M-shell satellites of the Kβ2 transition could be well resolved, whereas for the Kβ1,3 transitions only a broadening and shift of the line centroid was observed. The composite structure of the satellite lines which consist of many components that vary in energy and strength was analyzed using theoretical energies and relative intensities obtained from multiconfiguration Dirac–Fock calculations. From the data analysis average M-shell satellite-to-diagram line yield ratios were deduced for both the Kβ1,3 and Kβ2 transitions. For the Kβ2 transition for which the relative contributions of the 3s,p and 3d spectator vacancies to the observed Kβ2M1 satellite yield could be determined, separated X(Kβ2M11,2,3):X(Kβ2M0) and X(Kβ2M14,5):X(Kβ2M0) yield ratios could even be extracted.

Average energy shifts of K and K x-ray satellite lines and K/K intensity ratios have been experimentally evaluated for a 80Se target bombarded by various projectiles with atomic numbers in the region 3 Zp16 at a given projectile energy of 3.3 MeV/u. The data have been analysed using an approach, based on the results of extensive single-configuration Dirac-Fock (DF) calculations, performed within the multiconfiguration DF method for various distributions of holes in subshells of a 80Se ion. This provides information about the average number of holes in various subshells of 80Se ions at the time of emission of the K x-ray lines. The primary average number of L- and M-shell holes in a 80Se target produced at the moment of collisions with projectiles and the average ionization probabilities per electron for L and M shells have been deduced by means of a simple statistical scaling procedure which accounts for all processes that modify the number of L- and M-shell holes prior to the K x-ray emission. It has been found that the average ionization probabilities per electron for L and M shells increase considerably with Zp2. For larger Zp the average ionization probability per electron is significantly higher for M shells than for L shells. On the other hand, for small Zp the ionization probability per electron seems to be slightly higher for L shells than for M shells. Moreover, the dominant role of the simultaneous multiple ionization of L and M shells accompanying the ionization of a K shell has been observed for projectiles with Zp>3.

The radiative decay of double K-shell vacancies in zirconium (Z=40), molybdenum (Z=42), and palladium (Z=46) was observed using a high-resolution transmission crystal spectrometer. The samples were ionized by the impact of 100-MeV $^{4}\mathrm{He}^{2+}$ ions. From the well resolved ${\mathit{K}}^{\mathrm{\ensuremath{-}}2}$\ensuremath{\rightarrow}${\mathit{K}}^{\mathrm{\ensuremath{-}}1}$${\mathit{L}}^{\mathrm{\ensuremath{-}}1}$ transitions, the energies, linewidths, intensity ratios, and double K-shell ionization cross sections were deduced. The experimental energies and linewidths of the hypersatellites are compared with results of Dirac-Hartree-Slater calculations and with multiconfiguration-Dirac-Fock calculations, both taking into account the Breit interaction. For the extracted double K-shell ionization cross sections a comparison is made with the semiclassical approximation predictions within the independent-particle model.

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.

The x-ray satellite structure of Pd Lalpha1,2(L3M4,5) transition excited by an impact of O7+ and Ne6+ ions with energies 279 and 178 MeV, respectively, which were measured using a high-resolution von Hamos crystal spectrometer, is discussed in terms of the multi-configuration Dirac-Fock (MCDF) calculations. We demonstrate, by using the arguments of the general central limit theorem (GCLT), that a structure of complex M-shell satellites of Pd Lalpha1,2(M-m) transitions for a higher number of spectator vacancies (m > 4), which consists of hundreds of thousands of individual x-ray transitions as obtained from the MCDF calculations, can be well described by a single Voigtian profile. The Lorentzian width of such Voigtian line can be well modeled by using the results of the MCDF calculations for simpler configurations with a number of vacancies m < 4 . This method allows one to describe realistically a complex structure of M-shell satellites, thus extending the applicability of the MCDF calculations, which are limited by an increasing complexity of numerical calculations.

X-rays have been detected from highly ionized swift projectiles of 75As and 80Se passing through thin carbon foils. The investigations have been made at two projectile energies of 55 and 80 MeV for 75As ions and 66 and 90 MeV for 80Se ions. The Kβ/Kα ratios of the ions have been found to be almost half of the free atom values which can be attributed to the sum of the effects caused by vacancies in L and M Shells. In addition to two normal L x-ray peaks a third peak corresponding to LREC (L-shell radiative electron capture) has been observed. All the x-ray lines show a shift towards higher energy due to perturbation of the energy levels. The relative REC cross-section between lower and higher projectile energies shows excellent agreement with the theoretical results obtained under the dipole approximation.

The K{alpha} and K{beta} satellite and hypersatellite x-ray lines emitted by highly ionized sulfur projectiles passing with energies from 65 MeV up to 122 MeV through carbon foils of thickness of 15-210 {mu}g cm{sup -2} have been recorded using a Si(Li) detector. The additional hypersatellite Ky{sup h} peak proves that for such high energies of the sulfur ions very high subshells (4p and 5p) could be occupied. In order to study the dynamics of formation of K-shell vacancy fractions of sulfur projectiles passing through a carbon foil the dependence of sulfur K x-ray production cross sections on foil thickness has been examined separately for each recorded line using the three component model. For each projectile energy the values of K-shell hole production cross sections and K-shell electron capture cross sections (both common for all recorded x-ray lines in the case of each projectile energy) have been fitted, as well as the specific values (for each recorded x-ray line) of K-shell hole filling cross sections, which are directly connected with average lifetimes of appropriate states of sulfur ions. The obtained ''experimental'' values of K-shell vacancy production cross sections are much higher than the theoretical predictions. This suggests that apart from themore » ionization process the excitation from K shell into higher shells is responsible for a production of K-shell vacancies, which has been confirmed by recent classical trajectory Monte Carlo calculations.« less

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 Kα hypersatellite X-ray spectrum of 42Mo target bombarded with 17 MeV/u 16O ions was measured with a high-resolution transmission bent crystal spectrometer. Well resolved lines of L-satellites and K-hypersatellites of Kα1 and Kα2 transitions were observed. Such data give valuable and rich information for testing the approximation used for the description of the multielectron system. The Khα1 hypersatellite, treated as spin-flip 1S0→3P1 transition, is forbidden in pure L-S coupling. In that case the relative yields of the Kα hypersatellites reflect directly the degree of intermediate coupling in the atom. Moreover, energies of the Khα1.2L0,1 transitions and the I(Khα1L0,1)/I(Khα2L0,1) intensity ratios are much more influenced by the Breit interaction than the diagram lines. The discussion of these problems is illustrated with the measured Kα hypersatellite spectrum of 42Mo.

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.

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.

Second-order correlation energies for some ions of the Ne isoelectronic series are evaluated within the framework of the Rayleigh-Schr\"odinger Hartree-Fock perturbation theory (RS-HEPT). The variational-perturbation method is applied. Pair functions of definite orbital and spin symmetry are expressed in the form of partial-wave expansions. Special attention is paid to the determination of the $Z$ dependence of both the partial-wave increments to the pair energies and the second-order pair energies, which represent very close approximation to the "all-external" pair-correlation energies. It is found that the partial-wave increments depend in a strictly monotone way on the nuclear charge, whereas the $Z$ dependence of the pair energies is more complicated. A comparison with relevant results of the most extensive variational computation for ${\mathrm{F}}^{1\ensuremath{-}}$ confirms our previous conclusion that for Ne-like atoms the RS-HFPT yields very accurate correlation energies. A very accurate value for the electron affinity of F (3.534 eV) has also been obtained.

Pair energies contributing to the correlation energies of the outer-shell electrons (n = 3) as well as for the 1s2 and 2s2 pairs are computed for the Zn2+ closed-shell ion by means of the variational-perturbation method starting with the sum of one-electron Hartree–Fock operators as the zeroth-order Hamiltonian. The results allow an understanding of the electron correlation for pairs of electrons of the p and d type. For 3p3d pairs it has been found that the correlation energy for the singlet pair of 1D symmetry is lower than for the triplet pair 3D. The 3l-3l′ correlation energies are compared with the MBPT results of Kelly and Ron for Fe. The total correlation energy of the outer shell is −1.032 a. u.

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

A relatively simple approximate ab initio method for the evaluation of correlation effects on atomic energy differences is developed. In this method, which is a modification of the semiempirical version of Sinanoglu's non-closed-shell many-electron theory (NCMET), the all-external contributions to the correlation energies are evaluated by a scheme based on the knowledge of second-order pair energies calculated for approximate closed-shell atomic systems. The present method can be applied to a much larger set of atomic systems than the semiempirical NCMET. To test the reliability of the present approach extensive calculations are performed for energy differences involving states of the 1s22sm2pn configurations for various atomic numbers. These calculations could be to a large extent based on previously published values of both the 'charge' contributions to the energies and the relevant pair energies. The results for (i) term splittings within a single configuration for neutral atoms as well as positive and negative ions, (ii) excitation energies, (iii) ionisation potentials and (iv) electron affinities prove that the present approach can be used for reliable predictions of atomic energy differences. Since the method is non-relativistic, some attempts have been made to account for the relativistic corrections. In all cases considered the inclusion of these corrections has further improved the agreement with the experimental results.

Pair energies contributing to the all-external correlation energies of the 3d electrons are computed for the Zn2+ closed-shell ion by means of second-order perturbation theory starting with the sum of one-electron Hartree-Fock operators as the zeroth-order Hamiltonian. The variation-perturbation symmetry-adapted pair functions are taken in the form of partial-wave expansions. The results for the pair energies and total correlation energy are compared with related theoretical and semiempirical results. Our analysis indicates that nondynamical correlation effects are of little importance in the ground states of transition metal systems.

Partial-wave (PW) increments to the second-order pair correlation energies for K-, KL- and L-shell symmetry-adapted pairs are analysed in order to lay down some rules governing their transferability properties. The changes of the PW increments for members of isoelectronic series (Z dependence) and for sequences of systems with fixed nuclear charge and varying numbers of electrons (N dependence) are discussed. It is found that when considering the transferability properties a distinction has to be made between the contributions defined by the PW that have to be orthogonalised to the occupied Hartree-Fock orbitals (OPW), and the remaining ones (FPW). When analysing the N dependence it is found that the FPW increments increase very slowly and monotonically for increasing N. For dynamical pairs the FPW increments can be considered to be transferable in most practical applications. As a result, when evaluating pair energies for larger systems, one can use the FPW increments obtained for the most simple ion containing the pair considered; this leads to a considerable reduction of computational effort.

Second‐order correlation energies for the ground states of Cu−, Ge2+, Kr6+ (3d104s2 configuration) and Cu+ and Kr8+ (3d10 configuration) are calculated within the framework of the variational‐perturbation formulation of the Rayleigh–Schrodinger Hartree–Fock perturbation theory. The method is based on the application of symmetry‐adapted pair functions taken in the form of partial‐wave (PW) expansions. M‐ and N‐intrashell as well as LM‐ and MN‐intershell correlation effects were considered. Special attention is paid to the determination of the Z‐dependence of both the PW increments to the pair energies and the second‐order pair energies, which represent (for the M and LM shells) very close approximations to the ‘‘all external’’ pair correlation energies. It is found that the PW increments change in a highly regular way according to the rules previously found for the K‐ and L‐shell electrons of the Ne‐isoelectronic sequence. All pair energies calculated in this work disclose a monotone Z dependence, which is...

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.

We analyze classically the scattering of sulfur ions by carbon using the classical-trajectory Monte Carlo method. It is assumed that the scatterer and scattered nuclei are coupled to each other as well as to all electrons, but there is no coupling between electrons themselves. To initialize the state of both atoms, quasiexact energies are used that are obtained from the Dirac-Fock method. Effective charges are used to partially take into account the intra-atomic interactions between electrons. We concentrate on the cross sections for production of vacancies in the K and L shells and capture of electrons to K, L, and M shells of the sulfur ions. The dependence of these cross sections on the energy of the projectile sulfur ions and on the initial charge states of these ions is analyzed. Our results will be helpful in the interpretation of x-ray spectra from highly ionized fast sulfur projectiles passing through a carbon foil.