Charge Exchange Studies with n-, l-, and spin-Quantum State Population in Ar⁷⁺-He Collisions

Abstract

The energy-dependent population of fine quantum states in single electron capture (SEC) reflects the intrinsic collision dynamics. Here we report experimental studies of Ar⁷⁺ ions colliding with He in the energy range of 1.05–17.5 keV/u. Owing to the high resolution of a recoil-ion momentum spectrometer, the n-, l-, and spin-state electron capture populations are well resolved, and a strong energy dependence of the SEC cross sections is observed. Most importantly, a clear inversion of the cross-section ratio between the spin-resolved triplet and singlet 3s3d configurations is found, demonstrating a breakdown of spin statistics. Together with recent spin-resolved studies of C³⁺-He collisions (PRL 133, 173002 (2024)), these results suggest that the breakdown of spin statistics is likely a general feature of charge exchange in open-shell highly charged ion systems.

1. Introduction

Charge exchange (CX), in collisions between multiply charged ions and neutral atoms, is a fundamental process in atomic collision physics with broad applications, ranging from plasma diagnostics to the modeling of X-ray emissions in astrophysical systems [1,2,3], as their dynamics illustrate the effects of static and dynamical electronic correlations [4], strong Coulombic interactions [5], and many-channel close-coupling schemes related to the charge asymmetry between the target and projectile [6]. A critical probe for understanding CX dynamics is the cross section, which quantitatively links the electron transition probability to measurable collision observables.

Extensive experimental and theoretical efforts have been devoted to total [7,8,9], state-selective [10,11,12], and differential capture cross sections [13,14,15], establishing the gross features of single- and many-electron capture. These studies consistently reveal a pronounced velocity dependence in the cross sections, particularly for nl-resolved capture, indicating that simple scaling laws or classical models are insufficient. At intermediate and higher collision energies, four-body scattering frameworks [16,17], such as the continuum distorted-wave approach (CDW-4B), provide a dynamically consistent description and demonstrate that dynamic interelectron correlations remain important for capture into excited states, often in good agreement with experiments. In slow collisions, the different dynamical coupling effects on the state-selective process manifest the quasi-molecular effects [18,19,20]. By comparing the measured projectile scattering angle distributions to the theoretical calculations, Zhang et al. [19] and Siddiki et al. [21] attributed state-selective capture primarily to radial and rotational couplings. Through a two-active-electron semiclassical asymptotic-state close-coupling (SCASCC) approach [12,15,22], quantitative agreement with various CX cross sections has been achieved, underscoring the critical role of electron correlation and revealing that impact-parameter-sensitive transition probabilities can strongly mediate state-selective capture. More recently, nonperturbative close-coupling approaches such as the semiclassical two-center basis generator method (TC-BGM) [23] and the wave-packet convergent close-coupling (WP-CCC) [24] method enable converged calculations of electron capture, excitation, and ionization with explicit treatment of two-center and continuum couplings, and have been successfully applied to collisions involving H, He, and H₂ targets.

Continual advances in experimental techniques—especially in spectral resolution—have pushed state selectivity beyond nl distributions to resolve even finer quantum branching. Importantly, both the nl populations and the branching among spin multiplets can depart markedly from the statistical prescriptions often assumed in CX modeling, and the magnitude—and even the sign—of these departures may change with collision velocity. This sensitivity indicates that state-selective cross sections encode detailed dynamical information rather than simple degeneracy factors, motivating systematic measurements over broader energy ranges and across distinct projectiles. In particular, recent state-resolved studies have reported a pronounced breakdown of spin-statistical weighting for Li-like C³⁺ ions [25], raising the question of whether such a breakdown of spin statistics also exists in more complex multielectron systems beyond Li-like ions, for which theoretical calculations are extremely challenging and corresponding theoretical data are still missing.

By extending these investigations to the next alkali sequence, the Na-like Ar⁷⁺ offers an ideal testbed for examining the generality of this phenomenon and for gaining insight into the underlying dynamical mechanisms. Moreover, Ar⁷⁺ is not only of intrinsic atomic-physics interest but is also routinely detected in diverse astrophysical sources, where it serves as a sensitive probe of plasma conditions [26]. For the Ar⁷⁺-He collision system, Marseille et al. [27] and Bliman et al. [28] provided the first systematic analysis of the energy levels and population distributions in Ar⁶⁺ resulting from Ar⁷⁺ collisions, enabling measurements of excitation cross sections and state-resolved population distributions. Bouchama et al. [29] employed high-resolution spectroscopy to measure emission lines from excited states, yielding detailed information on fine structure and partial cross sections, demonstrating good agreement with the Extended Classical Over-Barrier (ECB) model in predicting angular momentum. While prior experimental studies on Ar⁷⁺-He collisions exist [27,28,29], they are largely restricted to a limited low-energy range and do not provide a systematic picture over a broad collision energy range.

In this work, we determine absolute n- and l-resolved SEC cross sections in Ar⁷⁺-He collisions over 1.05–17.5 keV/u, and compare the l-distributions in n = 4 against commonly used model prescriptions and reference Ar⁸⁺ data. Crucially, we further extract s-resolved SEC cross sections for the 3s3d ³D and ¹D channels to directly probe the spin-dependent dynamics and find the violation of statistical weighting in a Na-like open-shell system.

2. Materials and Methods

Measurements were carried out on the 150 kV highly charged-ion collision platform equipped with cold target recoil ion momentum spectroscopy (COLTRIMS) at Fudan University (Shanghai, China) [30]. Here we give a brief summary of the essential features. Ar⁷⁺ beams were produced by a 14.5-GHz ECR ion source from PANTECHNIK S.A. (Caen, France) and accelerated to the desired energies. Before entering the collision chamber, the Ar⁷⁺ ion beam was adjusted to approximately 100 pA, with a beam diameter of less than 1 mm. High-purity helium gas was fed through a 20 μm nozzle at a pressure of 2 bar, where it underwent adiabatic expansion into the vacuum chamber. The gas was then selected and confined by a three-stage skimmer, forming a localized, high-density supersonic gas jet. The ion beam intersected the supersonic He target in the reaction region, where the target chamber pressure was maintained at about 1 × 10⁻⁷ Pa.

The time-of-flight (TOF) spectrometer consisted of a uniform-field acceleration region and a field-free drift region. In our setup, the lengths of the acceleration and drift regions were approximately 100 mm and 300 mm, respectively [31]. Recoil ions produced in the collisions were extracted along the TOF axis by a focused electric field of approximately 3 V/cm and detected by an 80 mm diameter position-sensitive detector (PSD). Charge-changed projectiles were separated from the primary beam by an electrostatic deflector and recorded by a second PSD, while the unreacted primary beam was collected by a Faraday cup.

The positions of the scattered ions detected by the first PSD and the flight times of the recoil ions detected by the second PSD form a two-dimensional position–time spectrum, from which single- and double-electron capture channels, as well as transfer ionization channels, can be identified in the reaction. SEC events were identified by the coincident detection of Ar⁶⁺ projectiles and He⁺ recoils.

The longitudinal momentum ${\mathrm{P}}_{\mathrm{z}}$ of the recoil ion refers to its momentum transfer along the axial direction of the projectile ion. According to the principle of the conservation of energy and momentum, ${\mathrm{P}}_{\mathrm{z}}$ can be derived from the following relationship [32]:

$$\mathrm{Q}=-{\displaystyle \frac{1}{2}}{\mathrm{v}}_{\mathrm{p}}^2-{\mathrm{v}}_{\mathrm{p}}·{\mathrm{P}}_{\mathrm{z}}$$

(1)

$${\mathrm{P}}_{\mathrm{z}}=-{\displaystyle \frac{\mathrm{Q}}{{\mathrm{v}}_{\mathrm{p}}}}-{\displaystyle \frac{{\mathrm{v}}_{\mathrm{p}}}{2}}$$

(2)

where ${\mathrm{v}}_{\mathrm{p}}$ is the velocity of the projectile ion, and Q represents the difference between the binding energy of the initial and final states. The longitudinal momentum of the recoil ion can be reconstructed according to its position and time-of-flight information on the PSD. The Q-value spectra were fitted using multiple Gaussian functions. The peak positions were fixed to the calculated Q values based on the first ionization energy of He, together with the energies of the relevant Ar⁶⁺ states taken from the NIST Atomic Spectra Database. The energy resolution of the Q-value spectra is approximately 3–5 eV (FWHM), mainly limited by the thermal spread of the target jet and the finite size of the interaction volume. The state-selective contributions were extracted by multi-peak Gaussian fitting, with the peak centers constrained by the theoretical Q values of the corresponding final states. In this way, the relative yields of different capture channels were obtained from the fitted peak areas.

The uncertainty of the absolute state-selective cross sections consists of two parts: the uncertainty of the absolute total cross sections and that of the relative state-selective fractions. The uncertainty of the absolute cross sections has been determined to be 8.2% [9,33], mainly arising from the fluctuations in temperature (1%) and gas pressure (3%), detector efficiency (5.8%), counting statistics (1%), and beam instability (4%). The uncertainty of the relative state-selective fractions is dominated by the Gaussian fitting error (4%) and the statistical uncertainty (1%). By the error transfer formula, the overall uncertainty of the absolute state-selective cross sections is estimated to be 9.1%.

3. Results and Discussion

Figure 1 displays representative Q-value spectra for SEC in Ar⁷⁺-He collisions at four selected energies between 1.05 and 17.5 keV/u. Each peak in the Q spectrum corresponds to capture into a specific final quantum state. As the collision energy increases, additional reaction channels become more prominent and can be clearly resolved in the spectra, including capture into the 3p and 3d manifolds. Channels involving single-electron capture accompanied by excitation of the projectile valence electron are also observed and are assigned to the final Ar⁶⁺ configurations 3p3p, 3p3d, and 3p4d, assuming that the residual target ion remains in the ground state He⁺ (1s). The observation of these channels is consistent with the interpretation of Bouchama et al. [29], in which the population of the 3pnl states was attributed predominantly to capture accompanied by projectile-electron excitation.

The dependence of principal n-state capture on collision energy is shown in Figure 2a, spanning the collision energy range of 1.05 to 17.5 keV/u. In this energy interval, the absolute total SEC cross section decreases from about 2.36 × 10⁻¹⁵ cm² to 1.55 × 10⁻¹⁵ cm², as reported in prior work [9]. The state-selective cross sections presented here are obtained by normalizing the relative branching ratios measured to these total SEC values, with contributions from transfer ionization (TI) and autoionizing double capture (ADC) removed during the normalization to ensure that they correspond to pure SEC processes [33]. For Ar⁷⁺ colliding with He, the coincidence events of Ar⁶⁺ ions and recoiling He²⁺ ions arise from the TI and ADC channels, resulting in a contribution of 2–8% within the experimental energy range. The data clearly show that SEC is strongly selective into the n = 4 level, consistent with the trends predicted by Bouchama et al. [29] and Bliman et al. [28]. As the collision energy increases, the absolute cross section for n = 4 declines significantly, whereas the contributions for n = 3 and 5 increase.

Owing to the high resolution, the l-resolved SEC processes are obtained. The absolute cross sections for 4s, 4p, and 4d + 4f captures are shown in Figure 2b. It should be noted that, at high impact energies, the 4d and 4f peaks become partially unresolved; accordingly, the present work reports their summed cross section (4d + 4f) for comparison with the literature value. Our results agree well with the existing data at 1.75 keV/u, while deviations arise in the comparison with Bouchama et al. [29] at 0.875 keV/u. The discrepancy at 0.875 keV/u may be attributed to differences in the experimental methods: the COLTRIMS approach directly resolves final l states without cascade corrections, while the optical method in Ref. [29] relies on cascade analysis, which may be more challenging at lower collision energies.

Within a given principal capture level, the population distribution among substates varies with collision energy. Specifically, the 4p channel dominates at low collision energies. The 4s contribution exhibits a non-monotonic energy dependence, increasing at first and then decreasing as the collision energy increases. In contrast, 4d and 4f become increasingly important toward higher energies.

To predict the quantum state population during electron capture processes, Janev and Winter [34] describe several methods for estimating the l distribution, including statistical models, the Landau–Zener model, and low-energy models which are widely used in astrophysical CX spectral modeling [35]. The l-state populations calculated from these models are only an approximation, determined solely by the m-distribution and Clebsch–Gordan “geometrical” factors [34], without accounting for electron–electron interactions at different impact energies, particularly at the low energies where the quasi-molecular orbital coupling is strong.

A comparison of the measured l-resolved population fractions with the models’ predictions is shown in Figure 3, for the n = 4 manifold in Ar⁷⁺-He collisions at 1.05 and 6.5 keV/u, together with the reference Ar⁸⁺ data [31]. At low collision energies, the Ar⁷⁺ n = 4 L-distribution resembles the low-energy model, while Ar⁸⁺ exhibits a distribution closer to the Landau–Zener model. The difference in the captured electron’s final l-distribution between Ar⁷⁺ and Ar⁸⁺ may be attributed to the correlation effects of remaining electrons at low energy. Near 6.5 keV/u, both systems exhibit a broader l distribution with a strengthened high-l component (notably 4f), deviating further from the low-energy and Landau–Zener models. Moreover, the statistical l-distribution is in clear disagreement with both Ar⁷⁺ and Ar⁸⁺ at these energies. According to the explanation put forward by Gu et al. [35] and Abramov et al. [36], at low velocities, the captured electron possesses insufficient angular momentum to populate high-l orbitals, leading to a pronounced peak in the population of l = 1 or 2 states. As the velocity increases, rotational coupling between molecular orbitals becomes significant and redistributes the population into higher angular momentum orbitals.

Beyond nl selectivity, the present data also determine spin-resolved cross sections in the 3s3d capture channels. The cross-sections for electron capture populating the triplet (3s3d ³D) and singlet (3s3d ¹D) states were determined through Gaussian fitting of their corresponding peaks in the Q-value spectra. The energy gap between these two states is approximately 5.72 eV. The experimental resolution allowed us to partially resolve the contributions from the singlet and triplet states, and the fitting process reliably extracted their relative intensities. The ratio of these cross sections, denoted as $\mathrm{R} = \left(\mathsf{\sigma }\right(3\mathrm{s}3\mathrm{d} {}^3\mathrm{D}\left)\right)/\left(\mathsf{\sigma }\right(3\mathrm{s}3\mathrm{d} {}^1\mathrm{D}\left)\right)$, serves as a key indicator of the spin-dependent electron capture dynamics.

Figure 4 summarizes the collision energy dependence of the triplet-to-singlet capture ratio R. Within the present measured range, R increases monotonically from 0.29 ± 0.03 at 1.05 keV/u to 2.28 ± 0.24 at 17.5 keV/u, revealing a clear spin-statistical inversion: singlet capture dominates at low energies (R < 1), while triplet capture becomes predominant once the collision energy exceeds 3.75 keV/u. Similar departures from the naive statistical expectation (R = 3) have also been predicted in theoretical studies of other collision systems (e.g., N⁶⁺-H [37] and C⁵⁺-H [38]), and have been discussed as strong influencers of the electron–electron interaction during the collision.

An analogous but more pronounced evolution was reported for Li-like C³⁺-He collisions over 0.25–70 keV/u by Zhu et al. [25] and Lennon et al. [39]. A notable difference lies in the energy scale of the effect: in C³⁺-He, R < 1 below ~1 keV/u and R > 3 around 10 keV/u, whereas in Ar⁷⁺-He, R = 1 appears at 3.75 keV/u and R remains below 3 up to 17.5 keV/u. This indicates that the detailed energy dependence of spin-resolved populations is sensitive to the projectile’s specific electronic configuration. In the present Ar⁷⁺-He measurements, R does not exceed 3 within the accessible energy range, primarily due to technical limitations that constrained our measurements to the present energy window. Extending the measurements to higher collision energies would therefore be important to test whether an R > 3 regime can also emerge in the Na-like system.

As discussed by Zhu et al. [25], the strong energy dependence of R likely reflects a molecular representation of the collision system, relevant in the energy domain. At lower energies, the dominance of the capture to singlet states is related to the different evolution of the molecular curves. With increasing energies, the molecular mechanisms get weaker, and the ratio increases. The present Na-like results support the view of spin-statistics breaking in electron capture involving an open-shell system, suggesting that the violations of spin statistics may be a general feature of CX processes. Further theoretical investigation is needed to explain the observed differences in the energy dependence, which are probably raised from underlying electron correlations in different systems.

4. Conclusions

In summary, we have performed high-resolution COLTRIMS measurements of state-selective SEC in Ar⁷⁺-He collisions from 1.05 to 17.5 keV/u, resolving capture channels in the n-, l-, and spin-quantum states. First, the measured l-resolved populations within the dominant n = 4 manifold evolve strongly with energy and deviate clearly from statistical expectations: capture into low-l states dominates at low energies but decreases markedly as energy increases, accompanied by an enhanced population of high-l states. Second, we observe a clear inversion in the spin population for the 3s3d configuration, with the triplet-to-singlet ratio R increasing from 0.29 ± 0.03 at 1.05 keV/u to 2.28 ± 0.24 at 17.5 keV/u. This experiment provides clear evidence of the breakdown of spin statistics in open-shell highly charged ion systems, thereby offering insights into the underlying collision mechanisms.