Extreme ultraviolet spectra and analysis of Δn = 0 transitions in highly charged barium

Barium is commonly used as a dopant in the electron gun cathode of electron beam ion traps (EBITs). As a result, atoms of barium are emitted from the cathode and migrate into the trap region. Once there, their spectra are excited along with spectra of injected elements. Indeed, spectra of Ba have been among the first investigated in nearly every EBIT. In our laboratory at the National Institute of Standards and Technology (NIST), we observed a magnetic-dipole transition in the ground configuration of Ba³⁴⁺(Ti-like) as one of the first investigations after completion of the machine in 1993. This line was seen in the visible/near ultraviolet region at 393.2 nm [1]. Spectra of Ba in the visible have also been reported from the Livermore EBIT [2, 3]. The x-ray spectra of Ba have been a subject of investigation on many EBITs. On the other hand, for the extreme ultraviolet (EUV) region of about 3 nm to 30 nm, there have been no other reports of Ba spectra from EBITs outside of our group. The present paper reports measurements and identifications of 64 spectral lines of Ba in the EUV. Almost all of them are newly observed.

These measurements were an outgrowth of observations performed to measure wavelengths of the D-lines of Na-like lanthanide ions [4]. At a beam energy of about 900 eV two extremely strong lines appeared in our spectra that clearly did not belong to an injected atom. We soon realized that these were the 4s^{2 1}S₀–4s4p ¹P₁ and 4s ²S_1/2–4p ²P_3/2 resonance lines of Zn-like Ba²⁶⁺ and Cu-like Ba²⁷⁺, respectively. Although these lines had been previously observed in laser-produced plasmas [5, 6], they had never been seen in an EBIT. We therefore decided to investigate the EUV spectra of Ba in our EBIT.

The present measurements were carried out with the NIST EBIT. A review of its properties has been given by Gillaspy [7]. The experimental procedure for our measurements has been described in detail in several recent papers [8, 9, 13]. For the present observations, we only used the Ba atoms emanating from the EBIT cathode. Electron beam energies were 700, 740, 790, 900, 830, 960, 1015, 1750, 3945, 5000, 5860, 7530, 8490, 8750, 9000, 10 000, 13 000, and 30 000 eV. The beam current varied between 15 mA and 150 mA.

A flat-field grazing-incidence spectrometer [10] was used to record EBIT spectra from 4.5 nm to 23.8 nm. A gold-coated variable-spaced grating used in the experiment had groove density of about 1200 lines per mm at the center of the grating. The spectra were recorded with a liquid nitrogen-cooled charge-coupled device (CCD) array having a matrix of 2048 pixels × 512 pixels. The full-width-at-half-maximum (FWHM) of our spectral lines was about 0.025 nm with a resolving power of approximately 500 at 12 nm. This FWHM represented about three pixel columns in the array.

At a given energy a complete spectrum consisted of five exposure frames of 60 s each, integrated to a whole. The spectra were corrected for spurious signals due to cosmic rays, and a background noise level of approximately 600 CCD analog-to-digital counts per pixel-column was subtracted from all spectra. Reference spectra consisted of lines of Fe¹⁹⁺–Fe²³⁺, O⁴⁺–O⁵⁺, Ne⁴⁺–Ne⁷⁺, and Kr²⁰⁺–Kr³³⁺. A metal vapor vacuum arc ion source (MEVVA) [11] was used to inject Fe ions, while the gases were injected from a separate gas injection port. A pixel-to-wavelength conversion was produced with a fourth-degree polynomial fit of the reference spectral lines with a standard deviation of about 0.0008 nm. This represents the systematic uncertainty of our measurements. A Gaussian function was used to fit the measured line profiles. Statistical errors for strong lines were less than 0.001 nm. Our final wavelength for each line is the weighted average of the wavelengths measured at the various beam energies. The final uncertainties are the sum in quadrature of the statistical and systematic uncertainties.

The measured spectra for beam energies 740, 790, 830, and 1015 eV are given in figure 1. The vertically shifted curves show second-order lines, with wavelengths doubled and intensities reduced by a factor of three. A number of the identified lines are indicated in these spectra. In addition to the Ba lines, the measured spectra contain several impurity lines. The most prominent are the 16.44 nm line in Zn-like Xe²⁴⁺ and the 22.115 nm line in Be-like Ar¹⁴⁺. The presence of Xe is due to previously conducted experiments in which large amounts of Xe were injected into the EBIT and the ions extracted for surface-interaction studies. This left a persistent residue of Xe in the machine.

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In order to calculate the spectral line intensities in the measured range of wavelengths, we carried out collisional-radiative (CR) modeling of the Ba plasma. The modeling was performed with the CR code NOMAD [12] that has been extensively used for non-Maxwellian EBIT simulations [9, 13, 14]. The radiative and collisional data, such as level energies, radiative transition probabilities and electron-impact cross sections for excitation, de-excitation, ionization, and radiative recombination, were calculated with the Flexible Atomic Code (FAC) [15]. FAC uses the relativistic-model-potential method for determination of atomic wavefunctions and the relativistic distorted-wave approximation for calculation of electron-impact cross sections. The sizes of the atomic structure calculations varied with ion stage, depending on the complexity of electronic structure. For each beam energy they included up to seven thousand levels in 8–9 ions for a single calculation.

The calculated cross sections were fitted with simple formulas and collected in a database. Since the narrow Gaussian energy distribution of the EBIT beam did not overlap with the energies of dielectronic resonances, dielectronic capture was disregarded. Also, because the electron density in the trap is very low (on the order of 10¹² cm⁻³; this value was used in simulations), three-body recombination could be neglected.

Charge exchange (CX) with neutrals is an important recombination process affecting the ionization distribution in the trap. As was discussed in our previous papers (see, e.g., [16]), the CX rate is included as $\;{{R}_{{\rm CX}}}={{N}_{0}}{{\sigma }_{{\rm CX}}}{{v}_{r}}$, where ${{N}_{0}}$ is the density of background neutrals in the interaction region, ${{\sigma }_{{\rm CX}}}$ is the CX cross section, and ${{v}_{r}}$ is the relative velocity between the highly-charged ions and the neutrals. We used a Classical Trajectory Monte–Carlo recommendation ${{\sigma }_{{\rm CX}}}\approx z\times {{10}^{-15}}$ cm⁻² [17] for the cross section of charge exchange with an ion of charge z. Since neither N₀ nor v_r are known experimentally, we used the previously developed collisional-radiative model for Xe ions [13] and the observed intensity ratios for the 16.44 nm line in the Zn-like Xe²⁴⁺ and the 17.39 nm line in Cu-like Xe²⁵⁺ to derive the product ${{N}_{0}}{{v}_{r}}\approx 5\times {{10}^{13}}$ cm⁻² s⁻¹. This value, which reasonably agrees with our previous estimates [16], was then used for the collisional-radiative modeling of the Ba spectra.

Figure 2 shows the observed spectrum of Ba at a nominal beam energy of 900 eV together with our simulated spectrum at 880 eV. This reduction of beam energy, the so-called space charge shift, is due to the presence of electrons in the trap region. These electrons repel incoming electrons in the beam and reduce the effective beam energy. As can be seen, agreement between the calculated and measured spectra is good. The inset in figure 2 shows the calculated ionization distribution of the EBIT plasma. As the ionization potential of Zn-like Ba²⁶⁺ is about 937 eV (see below), the beam energy of about 880 eV to 900 eV is still too low to ionize it to the Cu-like ion.

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Our identifications of the measured barium lines are given in table 1. The identifications were made by comparing the observed and calculated spectra. For individual lines, variation of the intensities with beam energy was used to establish charge stages. In several cases, variation of intensity with beam energy allowed us to obtain accurate wavelengths for lines belonging to different ion stages that are very close in wavelength. This analysis was particularly fruitful for identification of an otherwise-puzzling feature in the spectra at about 12.52 nm. This line appears strongly at beam energies of 700, 740, 790, and 830 eV, and is in fact the strongest of all the features in the spectrum at 740 eV. A very good spectral resolution and accurate modeling of the energy-dependent spectra allowed us to conclude that this feature was due to a coincidence of lines appearing at this wavelength from Ba²³⁺(As-like), Ba²⁴⁺(Ge-like) and Ba²⁵⁺(Ga-like). In Ba²⁵⁺ it is actually a blend of two predicted transitions.

The transitions in table 1 are assigned according to the level designations from FAC, which are given in jj-coupling. The level numbers from FAC are also indicated. Here, 1 corresponds to the ground state, 2 corresponds to the first excited level, and so forth. In jj-designations, a minus sign indicates a j-value for an electron of l − 1/2; a plus sign indicates a j-value of l + 1/2.

4.1. Beam energy 700 eV–1750 eV

4.2. Beam energy 3945 eV–7530 eV

4.3. Beam energy 30 000 eV

At the highest energy, 30 keV, we observed spectral lines from B-like Ba⁵¹⁺, Be-like Ba⁵²⁺, and Li-like Ba⁵³⁺ (see figure 3). These are the first observed spectra for these ions in this spectral range. The Xe impurity lines are prominent here. The similarity of the L-shell spectra for Ba and Xe is clear in this spectrum.

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4.4. Comparison with theory and with previous measurements

4.5. Energy levels

Our analysis of the measured Ba spectra is based in part on the knowledge of ionization potentials of the ions under study. Ionization energies for Ba in all stages of ionization are given in the NIST Atomic Spectra Database (ASD) [32]. Most of these energies are taken from the relativistic Dirac–Fock calculations of Rodrigues et al [33]. This is true for all the ions of Ba in the present study. The one exception is Ba²⁷⁺(Cu-like), where a value of 976.62(11) eV was given by Reader et al [6]. The uncertainty that has been assigned to all of the calculated energies in ASD is 4 or 5 eV. It is possible to determine an improved value for the ionization energy of Ba²⁶⁺(Zn-like) by using the Rodrigues values in connection with experimental values for the Zn isoelectronic sequence.

In table 4 we give the total binding energies for selected Zn- and Cu-like ions calculated by Rodrigues et al [33]. The calculated ionization energy is formed as the difference of the values for the two ions. This table also presents the observed ionization energies for these ions taken from ASD. (The values for Se⁴⁺ and Kr⁶⁺ are semi-empirical, but are given with uncertainties, and for the present purpose we treat them as observed. The experimental value for Br⁵⁺ is taken from Riyaz et al [34].) The differences are plotted as filled circles in figure 4. The solid line is a weighted linear fit to these points. As can be seen, the observed values are higher than the theoretical values by a nearly constant 2–3 eV throughout the sequence.

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In order to quantitatively evaluate this difference, and use it to apply a correction and overall uncertainty to the ionization energies calculated by Rodrigues et al [33], we assign a constant but unknown uncertainty to the calculated energies and then determine its value by requiring that the reduced chi square of the fit discussed in the previous paragraph be equal to 1. This constant of 0.52 eV is then added in quadrature to the experimental uncertainty to produce the total uncertainties in the points plotted in figure 4. The interpolated correction for Zn-like Ba is 2.55(60) eV (shown as a blue square in figure 4). The uncertainty of this correction is taken from the 68% confidence interval, plotted as dotted lines. Because this uncertainty is approximately one-half of the last significant digit tabulated by Rodrigues et al [33], we avoid the loss of a half-digit by applying the above correction not to the individual values in the tables, but to the value obtained by a three-parameter quadratic smoothing the calculated ionization energies over the range Z = 53–59 (Z_c  = 24–30). The result of this procedure for determining the ionization energy of Zn-like Ba is (934.62 ± 0.46) eV + (2.55 ± 0.60) eV = (937.2 ± 0.8) eV.

This research was supported in part by the Office of Fusion Energy Sciences of the US Department of Energy. We thank A Kramida for helpful discussions concerning derivation of the ionization energy of Zn-like Ba.