State-selective Charge Exchange in 19.5–100 keV amu⁻¹ O⁶⁺ Collision with He and H₂

Highly charged ions (HCIs) widely exist in hot astrophysical plasmas (Nicastro et al. 2008, 2018; Nakashima et al. 2018; Kaaret et al. 2020). When the outflowing HCIs therein meet the ambient neutrals, charge exchange (CX) can occur and is followed by X-ray and extreme ultraviolet (EUV) emissions. CX-induced emission is important not only for X-ray and EUV emissions due to solar wind ions' interaction with comet and planet atmospheres (Cravens 1997, 2000; Krasnopolsky & Mumma 2001; Weaver et al. 2002; Beiersdorfer et al. 2003; Gunell et al. 2004, 2007; Bodewits et al. 2007; Dennerl et al. 2012; Mullen et al. 2017), but also for supernova remnants (Katsuda et al. 2011), star-forming regions in nearby galaxies (Liu et al. 2012), and extragalactic flows (Fabian et al. 2011), among others. Therefore, CX is an important diagnostic tool for these astrophysical plasmas.

For astrophysical EUV and X-ray spectrum modeling, the principal quantum number n and orbital angular momentum number l resolved state-selective CX cross sections are necessary, since they determine the following X-ray and EUV line emissions and intensity ratios. Mostly in modeling, the state-selective data are obtained with theoretical methods like classical trajectory Monte Carlo (CTMC; Olson & Salop 1976, 1977; Olson 1981), multichannel Landau–Zener (Cumbee et al. 2016; Lyons et al. 2017), and two-center atomic orbital close coupling (TC-AOCC; Fritsch & Lin 1984; Zhao et al. 2010). For example, using CX data calculated with CTMC, several studies (Kharchenko et al. 2008; Hui et al. 2010; Schultz et al. 2017; Houston et al. 2018, 2020) have made attempts to reproduce the X-ray emission spectrum and the flux of Jupiter's polar caps (Liu & Schultz 1999). Simpler approaches include velocity-independent approximation like the classical over-the-barrier model (Ryufuku et al. 1980) and using scaling laws (Janev & Winter 1985; Otranto et al. 2006), which have some success in predicting the dominant CX channel in the keV collision energy range (Okuno et al. 1983; Schmeissner et al. 1984; Dijkkamp et al. 1985; Beijers et al. 1992; Xu et al. 2021). However, it remains a challenge to accurately calculate the state-selective CX cross sections, whose uncertainties can significantly impact astrophysical modeling (Kuntz 2018; Houston et al. 2020; Gu et al. 2022).

Over the past two decades, significant progress has been made in laboratory measurements. This not only enables the study of collision mechanisms for photon emissions, but also can provide "reality" in extensive test cases for theoretical data. For example, Beiersdorfer et al. (2000) measured the hardness ratios of the X-ray emissions following CX between 10 bare and hydrogenic ions up to U⁹¹⁺ and neutrals, and found that the assumptions of statistical distribution break down at low collision energies. Seely et al. (2017) found that autoionizing double capture can lead to an enhancement of X-ray emission following single capture. In addition, basic CX mechanisms for doubly excited state formation have been extensively studied in the keV energy range (Stolterfoht et al. 1986; Winter et al. 1987; Roncin et al. 1989; Posthumus et al. 1992; Raphaelian et al. 1993; Chesnel et al. 1996; Fléchard et al. 2001; Zhang et al. 2001, 2016; Roncin 2020; Guo et al. 2023). However, the collision energy dependence of doubly excited states has been sparsely reported for state-resolved double CX. Recently, with the development of the COLTRIMS detection technique, nl-resolved state selectivity in Ar⁸⁺ and C⁴⁺ CX with He has been measured and commonly used n scaling laws and l distributions by astrophysical modelers have been tested (Guo et al. 2022; Xia et al. 2022). This has significantly advanced studies of state-resolved CX, of which a complete understanding has not been achieved.

In this paper, we measure the relative state-selective cross sections of CX between O⁶⁺ and He and H₂ by using a momentum-resolution-improved COLTRIMS apparatus. O⁶⁺ is used because it is the most abundant HCI in the solar wind (Cravens 2002), and because of its importance for Jovian auroras (Liu & Schultz 1999). Since O^q+ (q = 0–8) ions initially are in the keV to MeV range at the upper atmosphere of Jupiter and then slow down as they pass through the atmosphere, CX would be importantly involved during the slowing down of the ions (Schultz et al. 2017). Note that with the increase of collision energy the state-selective channels will be squeezed and cannot be well resolved with the COLTRIMS method (Alessi et al. 2012; Xu et al. 2021; Xia et al. 2022). Based on these considerations, the present collision energy range is chosen to be 19.5 to 100 keV amu⁻¹ (i.e., 0.31 to 1.6 MeV), which can contribute to Jupiter's EUV aurora emission induced by O⁶⁺ CX collisions at the transition energy range from intermediate to high. The present measurements are important for benchmarking theories that provide a CX database for modeling Jupiter's EUV aurora emissions.

Experiments on CX between O⁶⁺ and He and H₂ were performed with the COLTRIMS apparatus mounted on the 320 kV high-voltage platform for multidisciplinary research with HCIs at the Institute of Modern Physics, Chinese Academy of Sciences (IMP-CAS), shown in Figure 1. The working principles of COLTRIMS have been described in detail elsewhere (Dörner et al. 2000; Ullrich et al. 2003; Ma et al. 2011; Zhang et al. 2016, 2017; Guo et al. 2021).

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Briefly, O⁶⁺ ions extracted from a 14.5 GHz electron cyclotron resonance (ECR) ion source (Ma et al. 2011) were first charge-analyzed and then accelerated to the desired energies. With a series of slits and quadruple magnets, the ion beam was collimated to a few millimeters in diameter before entering into an ultrahigh-vacuum (UHV) chamber. Two sets of electrostatic deflectors upstream of the UHV chamber were used to clean the ion beam of impurities and steer the primary ion beam to the target. The base pressure inside the UHV chamber was around 2 × 10⁻⁹ mbar. At the center of the TOF spectrometer, the O⁶⁺ ions crossed a local high-density He or H₂ supersonic gas jet erupted from a two-stage differential pumping system.

In order to improve the experimental momentum resolution, the TOF spectrometer was modified to a small intersection angle of 14° with respect to the beam direction. The recoil ions were extracted by applying an electric field of about 0.85 V cm⁻¹ to the TOF spectrometer (the obtained kinetic energies for recoil ions He⁺, ${{\rm{H}}}_{2}^{+}$, and He²⁺ are 5.3, 32, and 10.6 eV amu⁻¹, respectively). This is the so-called longitudinal extraction mode for recoil ions. A similar design can be seen in previous publications (Moshammer et al. 1994; Fischer et al. 2002). This mode is suitable for studying CX reactions because it allows a high resolution for determination of state selectivity (Fischer et al. 2002). The position and flight time information of recoil ions were registered by a two-dimensional position-sensitive microchannel plate detector (PSD). The O⁵⁺ and O⁴⁺ projectile ions via single and double CX were separated from the primary O⁶⁺ ion beam by an electrostatic deflector immediately downstream of the reaction zone and detected by another PSD. Unreacted projectile ions were collected by a Faraday cup.

Coincidence measurement between the recoil ions and the scattered projectile ions was used to suppress contamination from other processes. An event-by-event mode was employed for digital readout. From the measured two-dimensional spectrum of the positions of the scattered projectile ions versus the flight times of the recoil ions, single and double CX channels can be identified (Ma et al. 2011). With the recorded flight time and position information, the three-dimensional momentum of the recoil ions can be constructed for single and double CX channels. Here, Cartesian coordinates were used, as seen in Figure 1, and the measured momentum component along the ion beam direction was defined as the longitudinal momentum of recoil ions.

According to the principle of energy and momentum conservation, state selectivity can be reflected by the measured longitudinal recoil-ion momentum. Straightforwardly, the state selectivity of CX can be reflected by the following dynamical relationship (Cassimi et al. 1996; Dörner et al. 2000; Ullrich et al. 2003; Xu et al. 2021; Xia et al. 2022):

$$\begin{eqnarray}&&Q=-\displaystyle \frac{n}{2}{{V}_{p}}^{2}-{V}_{p}\cdot {P}_{{zr}}\end{eqnarray} \tag{ 1 }$$

where V_p is the projectile velocity; the number of captured electrons n = 1, 2 represents single or double CX, respectively; P _zr is the longitudinal momentum of recoil ions; and Q is the binding energy difference of the active electron(s) before and after collision and is defined as

$$\begin{eqnarray}&&Q={\epsilon }_{i}-{\epsilon }_{f}\end{eqnarray} \tag{ 2 }$$

where _i and _f are the binding energy of the active electron(s) in the initially ground-state target and finally excited ion, respectively.

The energy levels of He, H₂, He⁺, O⁵⁺, and O⁴⁺ are available from the NIST Atomic Spectra Database (Kramida et al. 2022). Note that the Q spectrum of O⁶⁺ single CX with H₂ at 19.5 keV amu⁻¹ was measured with the COLTRIMS at Fudan University (Zhang et al. 2018). With the present setup, it has been reported that the momentum resolution is three times better than the previous one with the transversal extraction mode (Guo et al. 2022).

3.1. State Selectivity in Single CX

Figure 2 shows the measured Q spectra of O⁶⁺ single CX with He and H₂ for the collision energy of 19.5 to 100 keV amu⁻¹. The Q spectrum range shown is from −50 eV to 150 eV. Through the present measurements, we find that the O⁵⁺(1s² nl) with n = 2, 3, 4, 5 or n ≥ 6 states and O⁵⁺(1s² nl) with n = 3, 4, 5 or n ≥ 6 states are populated in O⁶⁺ CX with He and H₂, respectively. Concerning the metastable O⁶⁺ CX contamination, first, the lifetime of the 1s2s³S metastable state of O⁶⁺ ions is about 956 μs (Crespo López-Urrutia et al. 1998), and the 1s2s¹S lifetime is estimated to be about 0.5 μs (Denis et al. 1999). The former is much longer than the O⁶⁺ ion flight time of a few microseconds from the ion source to the collision chamber, while the latter is shorter than the O⁶⁺ ion flight time. Other metastable levels like 1s2p^1,3P decay very quickly (Denis et al. 1999). Thus, the metastable states of 1s2s¹S and 1s2p^1,3P are negligible when the O⁶⁺ ions reach the collision chamber. Second, the fraction of metastable O⁶⁺(1s2s³S) is only about 2.6% in the ECR ion source (Welton et al. 1991). Third, CX populating nl(n > 2) onto the metastable core is followed by autoionization (Bliman et al. 1992; Kramida et al. 2022). This indicates the final projectile state of an O⁶⁺ ion and that CX with the metastable O⁶⁺(1s2s³S) is not showing up in the present experiments because of the coincidence scheme. Finally, CX involving the metastable O⁶⁺ can be neglected in the present Q spectra.

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It is known that the longitudinal recoil-ion momentum resolution is limited by the width of the supersonic gas jet and thermal spread and the gas jet density is approximately described by a Gaussian profile. Taking Figure 2(b) as an example, an FWHM of 5.06 eV was obtained from the 2p capture peak. The intensity of the state-selective population for n = 3, 4, 5 capture was extracted through Gaussian curve fitting with the FWHM slightly larger than 5.06 due to unresolved l capture and the calculated Q value with Equation (2). The relative cross sections ${\sigma }_{n}^{\mathrm{rel}}$ of n capture were obtained by normalizing to the sum of all measured n capture intensities. Clearly, with the increase of the collision energy, more channels of n capture are opened, and n values can be 6, 7, 8, or ≥9 for He and H₂ targets, as shown in Figures 2(c)–(d) and (g)–(h). These states with n ≥ 6 populations can significantly contribute to the EUV band (Bliman et al. 1992; Kramida et al. 2022), and our measured relative cross sections are presented in Table 3 in the Appendix.

Previous studies show that TC-AOCC calculations are in good agreement with measurements below 10 keV amu⁻¹ (Zhao et al. 2010). In the current study, the l-resolved relative cross sections were only extracted for the n = 3 channel for He at a collision energy of 19.5 keV amu⁻¹ and for the n = 2 channel at a collision energy of 37.5–100 keV amu⁻¹. The fractions are 16.7%, 31.9%, and 51.4% for capture into 3s, 3p, and 3d for He at 19.5 keV amu⁻¹, respectively. These fractions for the 3s, 3p, and 3d populations agree with the results of 18.5%, 30.9%, and 50.5% derived from experimental measurements (Liu et al. 1989); of 16.0%, 29.3%, and 54.7% obtained from TC-AOCC calculations (Zhao et al. 2010); and of 13.0%, 36.6%, and 50.4% obtained from AOCC calculations (Fritsch & Lin 1986).

Table 1 presents the relative n-resolved state-selective capture cross sections. Due to overlap for n ≥ 6, the relative cross sections for n ≥ 6 are summed for convenient comparison with the TC-AOCC theoretical calculations. At the collision energy of 19.5 keV amu⁻¹, the fraction of n = 3 capture is about 72% for He targets, which is predominant over those of other minor captures of n = 2, 4, 5, ≥6. The fraction of n = 4 is dominant over those of other minor captures of n = 3, 5, ≥6 for H₂ targets. This agrees well with the prediction by scaling laws (Janev & Winter 1985; Otranto et al. 2006), by which the main capture is estimated to be n ≈ 3 and 4 for He and H₂, respectively. An explanation is that due to the lower binding energy of electrons in H₂ than in He, an electron is preferentially captured into higher-n states for H₂ than for He. In addition, with the collision energy increasing to 100 keV amu⁻¹, the main capture competitively shifts to channels with larger n and finally to those with n ≥ 6 for both targets. This indicates that more single CX channels are open and the dominant capture goes to a high-n state with the increase of collision energy.

Table 1. The Measured Relative Cross Section ${\sigma }_{n}^{\mathrm{rel}}$ of n-resolved State-selective Single CX in O⁶⁺ Collisions with He and H₂

Collision Energy (keV amu−1)	${\sigma }_{n}^{\mathrm{rel}}$ for He (%)					${\sigma }_{n}^{\mathrm{rel}}$ for H2 (%)
	2	3	4	5	≥6	3	4	5	≥6
19.5	...	70.94 (1.66)	27.34 (0.54)	1.71 (0.22)	...	4.31 (0.84)	64.63 (2.76)	26.41 (1.48)	4.65 (1.38)
37.5	0.41 (0.21)	50.59 (0.83)	36.03 (0.62)	8.67 (0.26)	4.30 (0.64)	4.06 (0.58)	34.06 (2.61)	28.93 (2.26)	32.95 (8.14)
75	0.60 (0.16)	28.70 (0.67)	27.41 (0.64)	15.98 (0.40)	27.31 (2.13)	4.58 (0.32)	17.27 (0.73)	18.96 (0.79)	59.18 (4.86)
100	1.29 (0.24)	24.88 (0.41)	24.21 (0.38)	16.04 (0.29)	33.59 (0.99)	5.48 (0.61)	15.63 (1.05)	17.05 (1.12)	61.84 (7.12)

Note. The errors given in brackets were determined from the Gaussian fitting error of the peak.

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In Figure 3, we compare the measured n-resolved state-selective cross sections to the TC-AOCC calculations. The measured relative cross sections were obtained by normalizing to the total capture cross sections by summing the calculated n = 2–6 state-selective cross sections in Zhao et al. (2010). For He targets, the theoretical calculations are in satisfactory agreement with the measured results for n = 3, 4, 5 capture. For n = 2 capture, the theoretical calculations are significantly larger than the measured results, while for n ≥ 6 capture, the theoretical calculations are smaller than the measured results by a factor of 10. For H₂ targets, the theoretical calculations are in limited agreement with the measurements. For the TC-AOCC, the contribution of n > 6 capture was not taken into consideration, while the measurement shows that the fractions increase significantly with the increase of collision energy. The contribution of n = 2 capture is overestimated in the TC-AOCC calculations. It has been pointed out that the uncertainty of TC-AOCC calculations may be reduced by about 10%–15% through adding a sufficient number of positive-energy pseudostates in the expansion basis (Zhao et al. 2010).

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Due to their efficiency in producing a large CX database, CTMC calculations were used for astrophysical modeling. In Figure 4, we show a comparison between the measured relative cross sections of n-resolved state selectivity and the CTMC calculations at 100 keV amu⁻¹. The CTMC-calculated cross-section data are reported for n = 2–8 capture (Liu & Schultz 1999), and normalized to the measured cross sections for n = 4 capture. We find that there is good agreement between the measurements and the CTMC calculations for the relative contributions of n = 5, 6, 7, 8. There is no contribution of n = 2 capture in the present measurements, while the figure shows a 3.2% contribution of n = 2 capture in the CTMC calculations. The relative cross section of n = 3 capture is overestimated by 3.9% and that of n ≥ 6 capture is underestimated by 2.1% for the CTMC calculations. Additionally, the present measurement shows that capture of n ≥ 9 has considerable fractions. This verifies the nonnegligible contribution of n ≥ 9 that can be extrapolated from the CTMC calculations (Liu & Schultz 1999).

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3.2. State Selectivity in Double CX with He

From the fundamental atomic collision perspective, double CX is also important for astrophysical modeling since the doubly excited states can stabilize either through radiative emission (Bliman et al. 1992; Suraud et al. 1992; Barat et al. 1993; Machacek et al. 2014) or through autoionization to singly excited states that radiatively decay (Mack & Niehaus 1987; Seely et al. 2017). For the present COLTRIMS measurement, state selectivity in O⁶⁺ double CX with H₂ cannot be measured in coincidence with O⁴⁺ projectile ions, because the two protons undergo Coulomb explosion of [H₂]²⁺. The state selectivity of double CX is measured for O⁶⁺ on He collisions. Considering spin conservation before and after two-electron capture (Myers et al. 1978), only doubly excited singlet states can be populated.

In Figure 5, we present the measured Q spectra of O⁶⁺ double CX with He for the collision energy of 19.5 to 100 keV amu⁻¹. The doubly excited states of ${{\rm{O}}}^{4+}(1{s}^{2}{nln}^{\prime} l^{\prime} )$ are identified as 2s2p (¹P), 2p² (¹D), 2p² (¹S), 2s3l, 2p3l−2s4l, and 2s5l–2p5l. It is known that if two electrons are transferred into doubly excited states with the same n, these doubly excited states are described as a symmetric configuration; otherwise they are described as an asymmetric configuration (Stolterfoht et al. 1986; Roncin et al. 1989; Fléchard et al. 2001; Zhang et al. 2001, 2016; Roncin 2020; Guo et al. 2023). Accordingly, the doubly excited states of 2s3l, 2p3l–2s4l, and 2s5l–2p5l marked A, B, and C are categorized as asymmetric configurations. The doubly excited states of 2s2p (¹P), 2p² (¹D), and 2p² (¹S) are categorized as symmetric configurations.

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Since the internal excitation energies of these doubly excited states are below the ionization threshold O⁴⁺, they cannot decay via autoionizing electron emissions, only via radiative emissions. Taking into account the selection rules, the symmetric 2s2p (¹P) and the doubly excited singlet in asymmetric configuration can contribute an EUV photon emission of 19.7 eV (Kramida et al. 2022) and 80–100 eV (Bliman et al. 1992), respectively. A 19.7 eV EUV emission induced by double CX was rarely reported in previous laboratory measurements partially due to the limited spectrum range of the Bragg spectrometer and the grazing spectrometer (Bliman et al. 1992).

Quantitatively, the relative cross sections of state-selective double CX were obtained by multipeak Gaussian fitting and are presented in Table 2. Note that the normalization of state selectivity for double CX was separated from that for single CX due to the difficulty in measuring the detection efficiency for He⁺ and He²⁺ recoil ions with very low kinetic energy. As the collision energy increases, the relative cross sections of the 2s3l and 2p3l–2s4l states decrease slightly, while the contributions of the 2s2p–2p² and 2s5l–2p5l states increase. In order to quantify their dependence on the collision energy, we defined the intensity ratio between symmetric and asymmetric configurations by R = I_Sym/I_Asy, where I_Sym and I_Asy are the symmetric and asymmetric configuration intensities, respectively. The ratios are given in Table 2 as well as presented in Figure 6. The ratios show that the cross sections of the asymmetric configurations are about 10 times larger than those of the symmetric configurations at 19.5 keV amu⁻¹. With the collision energy increasing to 100 keV amu⁻¹, the cross sections of the symmetric configurations increase to about one-third of the cross sections of the asymmetric configurations. Due to the characteristic EUV emission at 19.7 eV and the EUV band from 80 to 100 eV, double CX between O⁶⁺ and He can be used as an EUV spectroscopic diagnostic of astrophysical objects with hot plasmas interacting with cold gases.

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Table 2. The Measured Relative Cross Section ${\sigma }_{nln\mbox{'}l\mbox{'}}^{\mathrm{rel}}$ of nl-resolved State-selective Double CX in O⁶⁺ Collisions with He

Collision Energy (keV amu−1)	Symmetric Configurations (%)				Asymmetric Configurations (%)			R
	2s2 (1S)	2s2p (1P)	2p2 (1D)	2p2 (1S)	2s3l	2p3l−2s4l	2s5l−2p5l
19.5	0.22 (0.16)	3.99 (0.27)	1.65 (0.21)	2.34 (0.23)	19.75 (0.89)	43.60 (2.67)	28.45 (1.40)	0.09 (0.028)
37.5	1.91 (0.49)	5.72 (0.56)	3.34 (0.53)	1.63 (0.47)	19.22 (1.03)	45.50 (1.86)	22.67 (1.27)	0.14 (0.021)
75	1.04 (0.34)	4.45 (0.43)	5.37 (0.46)	4.06 (0.43)	16.13 (0.85)	43.41 (1.60)	25.54 (1.11)	0.18 (0.018)
100	1.37 (0.18)	6.21 (0.29)	11.60 (0.40)	2.07 (0.25)	12.86 (0.38)	34.55 (0.73)	31.33 (0.79)	0.27 (0.013)

Note. The errors given in brackets were determined from the Gaussian fitting error of the peak.

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State-resolved CX between O⁶⁺ ions and He and H₂ is systematically measured in the collision energy range of 19.5 to 100 keV amu⁻¹. The collision energy and target dependence are clearly observed for state selectivity in O⁶⁺ single CX with He and H₂. For He targets, it is found that TC-AOCC calculations are in satisfactory agreement with the present measurement for n = 3, 4, 5 capture; overestimate the cross sections for n = 2; and underestimate the same for n ≥ 6 capture in the single CX process. For O⁶⁺ single CX with H₂, TC-AOCC and CTMC calculations are in limited agreement with the measurement. For O⁶⁺ double CX with He, we find that the contribution of doubly excited states with asymmetric configurations is dominant and the contribution of doubly excited states with symmetric configurations slightly increases with the increase of collision energy in the present collision energy range. The present measurements can be used as experimental benchmarks for full quantum-mechanical calculations, which can provide an accurate database for modeling EUV emissions of Jupiter auroras (Kimura et al. 2015; Dunn 2020).

This work is supported by the National Natural Science Foundation of China (NSFC) under grant Nos. U1832201 and 11934004, and by the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB34020000). Y.G. acknowledges support from the Young Scholars in Western China of the Chinese Academy of Sciences (2021). Many thanks are given to the engineers who operated the 320 kV platform of the HIRFL complex for their assistance in running the ECR ion source. R.T.Z. is grateful for the support of the Institute of Modern Physics, Chinese Academy of Sciences.

In Table 3 we present the measured relative cross sections for these states with n ≥ 6.

Table 3. The Measured Relative Cross Section ${\sigma }_{n}^{\mathrm{rel}}$ of n-resolved (n ≥ 6) State-selective Single CX in O⁶⁺ Collisions with He and H₂

Collision Energy (keV amu−1)	${\sigma }_{n}^{\mathrm{rel}}$ for He (%)				${\sigma }_{n}^{\mathrm{rel}}$ for H2 (%)
	6	7	8	≥9	6	7	8	≥9
19.5	...	...	...	...	3.58 (0.73)	1.07 (0.65)	...	...
37.5	2.67 (0.19)	0.93 (0.22)	0.71 (0.23)	...	16.02 (1.39)	6.99 (0.78)	2.26 (2.73)	7.69 (3.24)
75	10.07 (0.29)	5.45 (0.25)	3.33 (0.74)	8.45 (0.85)	16.78 (0.75)	11.12 (0.84)	6.20 (1.44)	25.08 (1.83)
100	11.08 (0.24)	7.83 (0.24)	5.07 (0.22)	9.61 (0.30)	17.33 (1.16)	12.29 (1.13)	8.67 (2.13)	23.55 (2.70)

Note. The errors given in brackets were determined from the Gaussian fitting error of the peak.

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