Observations and identifications of extreme ultraviolet spectra of Ca-like to Na-like neodymium ions using an electron beam ion trap

Extreme ultraviolet spectra from M-shell transitions in highly-charged Ca-like Nd40+ through Na-like Nd49+ ions were measured at the electron beam ion trap (EBIT) facility of the National Institute of Standards and Technology. To produce the ionization stages of interest, the electron beam energies were varied between 3.60 keV and 10.01 keV. A flat-field grazing incidence spectrometer was used to observe the spectra in the wavelength range between 2.67 nm and 17.30 nm. Simulated spectra generated with detailed collisional-radiative modeling of the non-Maxwellian EBIT plasma were used for line identifications. Forty-seven new spectral lines corresponding to electric-dipole and magnetic-dipole transitions were identified. Measurements were compared to the available previously calculated and predicted values.


Introduction
The lanthanides, along with scandium and yttrium, are known as rare-earth elements. These elements are valuable in a variety of technologies due to their unique electronic and magnetic properties. They are used in a wide range of applications, including in optical lattice clocks [1,2], scintillators [3], and solid-state lasers [4], which has led to extensive research on their atomic and spectroscopic properties in neutral and lowcharged states. This research aims to better understand these properties and develop new technologies that can benefit from them, particularly in the area of precision measurement. The spectra of highly-charged rare-earth ions in the extreme ultraviolet (EUV) and soft x-ray ranges are important for both fundamental research and industrial applications. These ions are used as a diagnostic tool to measure the temperature, density, and composition of plasmas in laboratory and industrial settings. In addition to this, EUV and soft x-ray spectral lines of these ions are discussed as a potential source for lithography [5] in the microelectronics industry.
In EUV lithography, the majority of the detailed spectroscopic studies focus on emissions near 13.5 nm [6]. This is because projection optics in EUV nanolithography machines are characterized by a 2% reflectivity bandwidth centered at 13.5 nm wavelength [7]. However, most EUV emission occurs outside of the 2% reflectivity bandwidth [5,6]. Identification of EUV radiation is essential to nanolithographic applications [8]. However, experimental spectroscopic data of highlycharged ions of lanthanides (Z = 57-71) are sparse due to the limitation of experimental facilities and the complexity of their atomic structure. This lack of data not only results in difficulties in the correct spectral identification but also limits the verification of complex theoretical models of multi-electron lanthanide ions [9]. Interest in lanthanide spectroscopy has recently increased due to its possible applications as the industrial short-wavelength light source in EUV lithography [5,[10][11][12]. Another relevant recent development is due to the fact that lanthanide opacities are known to be highly important for the kilonova events due to mergers of neutron stars [13][14][15].
Among the most efficient devices for spectroscopy of highly-charged ions are the electron beam ion traps (EBITs), which are highly tuneable and capable of producing, trapping, and probing highly-charged ions [16]. Charge-resolved spectra produced in EBITs are useful for systematic analyses of spectra and line identifications in highly-charged ions of high Z elements. For instance, over the past two decades, the EBIT at the National Institute of Standards and Technology (NIST) was used to produce a wealth of spectroscopic data from various heavy elements including, e.g. Xe, W, Kr, Hf, Ta, and Au [17][18][19][20]. Some lanthanides (Gd, Dy, Yb, Sm, Er) have also been the subject of spectroscopic investigations on several EBIT facilities (see, e.g. [1,[21][22][23][24]).
Neodymium is a lanthanide element with the atomic number 60. Neodymium compounds are used as glass dyes, and neodymium magnets are very powerful permanent magnets which are used in various applications such as microphones, speakers, headphones, electric motors, and computer hard disks where high magnetic fields are required. As for its spectroscopy, Nd spectral lines of the N-shell isoelectronic sequences have not yet been extensively explored, and there have been no EBIT data reported for Nd ions. Recently, Suzuki et al [25] reported the first line identifications for N-shell transitions in Br-like to Ni-like Nd ions using the NIST EBIT. Another systematic observation of EUV spectra of highlycharged Nd ions was carried out in the large helical device [26]. Additional lines of Cu-, Zn-, and Ga-like ions were identified, and the reported wavelengths are in excellent agreement with the EBIT results.
Similar gaps in knowledge exist for M-shell ions as well. Prior to recent studies, there were limited measurements performed for the n = 3 to n = 3 transitions for lanthanides. However, recent developments in ab initio methods, such as multi-configuration Dirac-Hartree-Fock (MCDHF), R-matrix, and relativistic many-body perturbation theory (RMBPT) have enabled accurate atomic structure calculations for one-electron Na-like [27,28] and two-electron Mg-like ions [29]. In this work, we extend the accurate EUV measurements of the M-intrashell transitions in highly-charged Nd ions to Ca-like Nd 40+ through Na-like Nd 49+ .

Experimental approach
The highly-charged ions of Nd for the current spectroscopic measurements were produced with the NIST EBIT. A detailed description of the EBIT facility at NIST is presented in [30]. EBITs use a high-density, tightly-focused, and energy-tunable electron beam to trap, ionize, and excite the injected atoms. The three central drift tube (DT) electrodes float on top of a surrounding shield electrode, which can be tuned up to 30 kV. The DTs accelerate the electron beam and provide an axial electrostatic trap. For the present observations, the nominal electron beam energy was varied between 3.60 keV and 10.01 keV with full width at half maximum of about 40 eV [31]. However, the actual electron beam energy is lower (approximately 3.45 keV-9.80 keV) due to the space charge shift [32]. The electron beam energy determines the ion charge states observed in the trap, and the beam energies used in this work are sufficient to produce ions up to the Ne-like ionization stage with the ionization energy of E = 9742 eV [33]. The electron beam current in our experiment was varied between 112 mA and 134 mA. Observations were made at 90 • with respect to the direction of the electron beam and were taken using a steady-state mode, in which the electron beam energy and current remain constant during measurements.
A superconducting Helmholtz-pair magnet provided a 2.7 T axial magnetic field, compressing the electron beam to a radius of about 30 µm to give a high current density. The lowcharge Nd ions were injected into the EBIT using a metal vapor vacuum arc (MeVVA) ion source [34]. The trapping voltage with respect to the shield electrode voltage was 220 V, 0 V, and 500 V for the upper, middle, and lower DTs, respectively. The trap was emptied every 5 s to remove contaminating ions, such as Ba and Xe. The EUV spectra of Nd ions in the range of λ = (2.67-17.30) nm were analyzed using a flat-field grazing incidence spectrometer [35] with a 1200 lines mm −1 grating and the slit width of 500 µm. The spectral lines were recorded by a liquid-nitrogen-cooled back-illuminated charge-coupled device (CCD) array having a matrix of 2048 pixels by 512 pixels. The resolving power in our experiment was λ/∆λ ≈ 350. Each spectrum consists of ten one-minute exposures. An algorithm has been used to remove outliers, including a majority of the cosmic rays and aberrant electronic noise [36].
The spectra were calibrated using the well-known lines of Ne and Ar [17] as well as impurity ions of Xe, Ba, and O [33]. The center positions of the calibration lines (in CCD pixels), determined by fitting a Gaussian profile, were matched to well-known wavelengths (in nm). The final uncertainty of the wavelength is calculated as the quadrature sum of three sources of uncertainty: Gaussian fit uncertainties, the uncertainty in assigned calibration wavelengths, and a statistical systematic uncertainty [37]. The statistical systematic uncertainty in line positions arises from factors such as device vibrations or uneven pixel response. A third-order polynomial was used to represent the calibration function that establishes the relation between the pixel number and the wavelength [36].
The measured EUV spectra in the nominal beam energy range of 3.60 keV-10.01 keV are shown in figures 1 and 2. In addition to Nd lines, there are also lines from several impurities, such as Xe, Ba (from the cathode of the e-gun), O, Ar (from the EUV ion pump), and Ne. The spectra also contain the second-order and third-order contributions. To this end, it is helpful to generate an artificial second-order spectrum by doubling the wavelengths of the original spectra with a simultaneous reduction of the intensity by a factor of 2.5 and a vertical shift. This spectrum which is shown in red in both figures, allows one to easily identify the higher-order diffraction contributions.
The measured Nd spectra are first plotted as a function of calibrated wavelength and fitted with Gaussian line profiles [25]. The total uncertainty for each identified line is calculated as the quadrature sum of the adopted wavelength uncertainty from the literature, the uncertainties from the fitting procedure, and the systematic uncertainty estimated from the calibration data [36,38]. For lines observed in the second order, the wavelengths and corresponding uncertainties were divided by two [36]. A weighted average was calculated based on these values to obtain a more accurate estimate of the wavelength. If the same line was observed at different beam energies, the reported wavelengths are the weighted average (the weights are based on the total uncertainties) of the positions of the same transition at several beam energies [36].

Comparison with collisional-radiative modeling
The simulations of the Nd emission spectra are based on the collisional-radiative (CR) modeling using the code NOMAD [39]. This code has been extensively used in numerous analyses of EBIT spectra and therefore we refer the reader to our previous publications for the details on the NOMAD structure and methods (see, e.g. [40][41][42]). The most abundant Nd ions are expected between Ca-like Nd 40+ and Ne-like Nd 50+ for the range of E b = 3.60 keV-10.01 keV due to the quasi-monoenergetic nature of the electron beam as the charged states with an ionization energy I greater than the beam energy cannot be ionized. Therefore, our model includes these eleven Nd ionization stages and the most important physical processes affecting the level processes.
All the relevant atomic data, such as energy levels, transition probabilities, and collisional cross sections, were calculated using the Flexible Atomic Code (FAC) [43]. The atomic states in the CR model were represented by the fine-structure levels. For the M-shell ions (Na-like to Ca-like ions), the configurations included were: (i) the ground state configuration, (ii) the excited configurations with single-and double-electron excitations within the n = 3 shell, and (iii) the singly-excited configurations from n = 4 to n = 6 shells. For Ne-like Nd 50+ , the ground state (2s 2 2p 6 ) and the excited configurations with single electron excitation from the n = 2 shell to n = 6 were included. The total number of levels included in the model was about 11 000. Additional calculations were performed to improve the level energies of interest by considering all possible excitations within n = 3 shell, and thus calculated energies were then used in the model.
The physical processes included in the model are electronimpact (de-)excitation, radiative transitions, electron-impact ionization, and radiative recombination. Electron-impact excitation was considered both from the ground state and between the excited states. Radiative transitions for electricdipole, magnetic-dipole, and electric-quadrupole transitions were taken into account. In addition, the charge exchange (CX) between ions and neutral particles in the trap was also included in our model. The CX recombination was directed into the ground state of the lower charge state, and the rates were calculated as R CX = N 0 · v r · σ Z CX where N 0 is the density of neutrals inside the trap, v r is the relative velocity of neutral atoms with respect to the trapped ions, and σ Z CX is the cross section from Z+1 into Z. For the cross section, the Classical Trajectory Monte Carlo method recommendation σ Z CX = Z · 10 −15 cm 2 [44] was used while the CX parameter N 0 · v r was taken to be between 10 12 cm −2 s −1 and 10 13 cm −2 s −1 . All the inverse processes were included in the model using the detailed balance principle.
Using the generated atomic data, NOMAD calculated the rate coefficients for the Gaussian distribution representing the electron beam profile at a given electron density (n e = 10 11 cm −3 ) and solved a set of rate equations to determine the level populations, and consequently, the spectrum was generated. The simulated spectral line intensities were convolved with a 0.12 nm Gaussian function due to the finite spectrometer resolution (this is the only substantial line broadening mechanism) and also corrected by the spectrometer efficiency curve [35,45].
An example of a comparison between the experiment and theory is shown in figure 3. The experimental beam energy is 7.01 keV and the best matched simulated beam energy is 6.85 keV, which is lower than the experimental beam energy due to the space charge correction [32]. The dominant charge states at the nominal beam energy of 7.01 keV were Na-like Nd 49+ and Mg-like Nd 48+ . The theoretical spectrum shown in the bottom panel reproduced the measured Nd lines well and was used for the line identifications. Some of the Nalike Nd 49+ and Mg-like Nd 48+ lines were also observed in the second order and third order of diffraction.

Results and discussion
4The derived identifications of the strong spectral lines in the highly-charged Nd ions are summarized in table 1. Fortyseven lines that originate from ∆n = 0 transitions within the principal quantum number n = 3 states from Ca-like Nd 40+ through Na-like Nd 49+ ions have been identified. Most of the identified lines are electric-dipole (E1) transitions, and a few lines are magnetic-dipole (M1) transitions. Most of the M1 lines correspond to transitions within the ground state configurations 3s 2 3p m (m = 1-5) for different charge states, except for the line at 9.7585(15) nm, which is the transition from Mglike Nd ions within the excited configuration 3s3p. Forbidden M1 transitions within the ground state configuration have relatively long wavelengths compared to the allowed (E1) transitions since the energy levels within the ground configuration are close.
In table 1, the first column shows the isoelectronic sequences of the ion charge states followed by the configurations of the lower and upper levels. The numbers in square brackets represent the lower and upper levels in the FAC calculations. The atomic states were given in relativistic notation where n is the principal quantum number, l is the orbital quantum number, and nl and nl represent the subshells with a total angular momentum j = l + 1/2 and j = l − 1/2, respectively. The measured wavelengths and uncertainties are listed together. The total uncertainty was evaluated as a combination of the calibration uncertainty, the fitting uncertainty, and the systematic uncertainty. Unresolved features due to complicated line blending or weak intensities are excluded.
Further justifications for the identifications of spectral lines from neighboring charge states were provided by the variation of line intensities as a function of electron beam energy.  [46]; b [54]; c [55]; d [56,57]; e [52]; f [53]; g [28]; i [50]; j [59]; k [27]; l [49]. To provide a unified scale for comparisons, the measured spectra were normalized to the corresponding beam current and collection time. Then each peak was fitted with a Gaussian profile to determine its normalized intensity. The careful analysis of the electron beam energy dependence of the specific lines provides information about the evolution of charge states with beam energy, which can be used to confirm the derived assignments and to identify the lines that are close in wavelength. Figure 4 shows the spectral line intensities at 9.5222(10) nm and 5.8481(10) nm corresponding to Nd 45+ Plike (blue), and the spectral line intensities at 6.7079(16) nm and 5.3799(09) nm corresponding to Nd 44+ S-like (black) with their respective ionization energies, versus the nominal beam energies. Clearly, the intensities of the lines emitted from the same ionization state vary with the electron beam energy in a similar way. This observed evolution of the line intensities distinctly confirms their identifications based on the collisional-radiative model simulations. In cases where a specific spectral line is blended with a line from another charge state, identification can sometimes be achieved by carefully examining the electron beam energy dependence. However, specific assignments require more sophisticated techniques due to the high concentration of ion stage lines in the wavelength range below approximately 5 nm. One such method involves using double-Gaussian fitting to distinguish partially blended lines. For example, Si-like and Mg-like lines at 4.6313(07) nm and 4.6261(03) nm were fitted using a double-Gaussian fitting with a constrained fit applied to the Si-like peak position at a nominal beam energy of 5.8 keV. In this case, the experimental data of the Si-like line at 4.6313(07) nm, measured at lower beam energies, was used as the input for the constrained multi-peak fitting.

Ca-like Nd 40+ to Si-like Nd 46+
To the best of our knowledge, no measured spectral lines from Ca-like Nd 40+ to Na-like Nd 49+ charge states have been previously reported for the EUV region. Table 1 presents one E1 3p 6 3d 2 − 3p 5 3d 3 transition in Ca-like Nd and five E1 spectral lines due to 3p 6 3d − 3p 5 3d 2 transitions in K-like Nd. Three E1 lines have been identified for Ar-like Nd ions, all of them are due to the 3p − 3d transition into the ground state configuration 3p 6 from 3p 5 3d. In addition to five E1 lines, one M1 transition within the 3p 5 configuration was observed in the measured spectra from Cl-like Nd ions at 9.7074(06) nm. Similarly, two forbidden transitions were observed for the S-like charge state arising from transitions within the 3s 2 3p 4 ground configuration at 9.2668(11) nm and 9.8285(15) nm while the other six newly identified E1 lines connect the ground configuration with 3s3p 5 and 3s 2 3p 3 3d. Two P-like M1 transitions at 9.5222(10) nm and 10.2556(10) nm within the 3p 3 ground configuration and one Si-like M1 transitions at 9.9521(11) nm within 3p 2 ground configuration were identified.
Huang [46][47][48] and Chou et al [49] used the MCDF approach to calculate the energy levels of Cl-like, S-like, Plike, and Si-like systems, incorporating the Breit interaction and Lamb shift contributions perturbatively as corrections to the Dirac-Fock energy. However, unlike the present FAC calculations, their calculations only included excitations within the n = 3 complex. This is the likely reason why the FAC wavelengths, on the average, better agree with the present measured results.

Al-like Nd 47+
Al-like ions have three valence electrons outside a closed n = 2 core and provide an example to study effects of strong correlation on closely spaced levels in heavy atoms. It is known (see, e.g. [50]) that 3s3p 2 , 3s3p3d, and 3p 3 levels may cross the 3s 2 nl(l = 0 − 4). In the present work, we have identified one M1 and four E1 new ∆n = 0 spectral lines in Al-like Nd ions connecting the ground level with excited levels.
Similar to the previous case of Cl-like thorugh Si-like ions, the calculations of Huang [51] with MCDF method only included ∆n = 0 excitations with a total of 127 relativistic configurations. In turn, our FAC calculation, in addition to the n = 3 complex includes core-valence excitations up to n = 6 with more than twice that number. As a result, the typical deviation from the experimental values for the FAC results is factor of 3 to 10 smaller than that for the MCDF values.

Mg-like Nd 48+
The transitions of Mg-like sequence have been a subject of interest for a long time due to their various applications in fields such as astrophysics, plasma, and thermonuclear fusion research [52]. For Mg-like lines, in pure LS coupling, where the spin-orbit interaction is negligible, the radiative decay into the ground level 3s 2 1 S 0 from the triplet level 3s3p 3 P 1 is forbidden. However, the relativistic spin mixing allows for the 3s 2 1 S 0 -3s3p 3 P 1 intercombination transition to appear, and its radiative rate increases quickly with the increasing atomic number (Z). The intercombination transition is observable in low-density plasmas where the radiative decay rate is greater than the collision rate. This transition has been identified for several highly charged ions up to Ag with Z = 47 [53]. For Nd, our measured value for the 3s 2 1 S 0 − 3s3p 3 P 1 transition energy was found to be 11.0829(04) nm. There are a number of theoretical works reporting the wavelength of this transition (e.g. [53][54][55][56][57]). It seems that the best agreement among various theoretical methods is provided by the relativistic Multi-Reference Møller-Plesset (MRMP) many-body perturbation theory [56,57]-their reported value of 11.08 085 nm is within 0.013 % from the measured wavelength. Table 1 also presents the wavelengths of an M1 transition within the 3s3p configuration at 9.7585(15) nm as well as the resonance 3s 2 1 S 0 − 3s3p 1 P 1 transition at 4.6261(03) nm which again very well agrees with the MRMP wavelength of 4.627 53 nm [56,57].

Na-like Nd 49+
The Na-like ions have only one electron outside closed shells in its ground configuration and therefore their energy structure and wavelengths can be calculated to high precision. Accordingly, this isoelectronic sequence was a subject of extensive experimental and theoretical studies (see, e.g. [27,28]). In this work we recorded the two most prominent D1 3s 1/2 − 3p 1/2 and D2 3s 1/2 − 3p 3/2 lines which fall into the spectral range of our spectrometer. Their wavelengths were measured to be 10.6521(04) nm and 4.8300(05) nm, respectively. Table 1 also presents the most advanced theoretical results calculated with a number of the well-developed methods. Those include the RMBPT [50], RMPBT with account of high orders of QED expansion [28], S-matrix-based QED approach [27], and older semi-empirical analysis based on the Dirac-Hartree-Fock code GRASP [58]. For the latter, the calculations were based on a single-configuration Dirac-Fock method but included QED, Breit and finite nuclear size effects. Then, from a systematic difference between the observed (Z = 39-51, Z = 53-55, Z = 64) and calculated wavelengths the semi-empirical corrections were derived and predicted values determined. The Nd L D1 and D2 transition wavelengths were thus determined to be 10.6501 nm and 4.8317 nm [59], that is, about 0.02% and 0.035% from our results. The most recent theoretical papers [27,28] show quite good agreement with the D1 wavelength, however, their results for the D2 line are outside the experimental uncertainties. This difference calls for new calculations and independent measurements in order to pinpoint the source of discrepancy.

Conclusions
In this work the EUV spectra from highly-charged ions of neodymium were measured using the NIST EBIT. Ion stages of Ca-like to Na-like neodymium ions were produced by varying the beam energy from 3.60 keV to 10.01 keV. CR modeling of the EBIT plasma led to the discovery of 47 new lines with wavelengths ranging from 2.67 nm to 17.30 nm. The newly assigned wavelengths are in excellent agreement with the theoretical predictions. The identification results would be helpful to test the existing theory for highly-charged heavy ions and further extension of the experimental data of EUV spectra. Benchmark tests of the current theoretical framework can benefit from our identification of previously unobserved transitions in highly charged Nd. Similar studies of other lanthanide elements are also planned for the future. These data are expected to be valuable for the future modeling of plasmas and the development of next-generation EUV lithography sources.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).