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Charge-state distributions and charge-changing cross sections and their impact on the performance of AMS facilities
Nuclear Inst, and Methods in Physics Research B xxx (xxxx) xxx–xxx
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Nuclear Inst. and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Charge-state distributions and charge-changing cross sections and their impact on the performance of AMS facilities ⁎
Martin Suter , Sascha Maxeiner, Hans-Arno Synal, Christof Vockenhuber Laboratory of Ion Beam Physics, ETH Zurich, Otto-Stern-Weg 5, CH-8093 Zurich, Switzerland
A R T I C LE I N FO
A B S T R A C T
Keywords: Accelerator mass spectrometry Charge state distribution Charge changing cross sections Stripping yield Mass fractionation
The charge state distributions of ions passing through gases or foils have a significant influence on the performance of AMS facilities. Most important is the stripping process in the terminal of the accelerator. Published data on charge state distributions have been collected as well as associated charge-changing cross sections for various projectiles and targets relevant to AMS. Based on these data, the stripping yields as function of the stripper thickness and ion energy are calculated. This allows to evaluate the stripping thickness required for reaching charge state equilibrium, as well as mass fractionation effects depending on energy and stripper thickness. The significantly different behavior of helium compared to other gases leads to very high stripping yields for specific charge states at low energies. The cross sections for electron detachment of negative ions give a tool for estimating beam losses in the low energy acceleration tube. Further, electron capture and loss cross sections allow the estimation of backgrounds caused by charge exchange processes in the acceleration tubes. The effects discussed here are illustrated with calculations and simulations for Carbon beams. The data are useful for the design of new AMS facilities or improving existing ones.
1. Introduction When fast ions pass through matter (gases or solids) they interact with the target atoms or molecules. A possible consequence of these interactions is that electrons are removed from the projectile, thereby increasing its charge state. This process is called electron loss (or ionization, but this term is not appropriate for negative ions because the electron detachment leads to neutral atoms). Typically one electron is removed in a single collision, but multi-electron removal is also possible though less probable. Alternatively, the projectile can capture electrons from the target atoms or molecules leading to a decrease of the projectile charge. The rates (strengths) of these processes are characterized by cross sections. In this paper, cross sections are given in units of 10−16 cm2 (equivalent to Å2); they typically fall in the range from 10−2 to 100). According to this convention the target thickness (x) is always given in units of 1016 atoms/cm2. The product of the cross sections with the thickness element (dx) gives the probability of such a charge changing process. The electron-loss cross section for a specific initial and final charge state is always the sum of all possible processes. Not only can the most loosely bound electron be removed, but other more tightly bound electrons can also be removed in a collision, leaving the projectile in an excited state. Similarly, the electron-capture cross section is also a sum ⁎
over various possible transitions, since electron-capture can also result in the projectile or target being in an excited state. The charge state distributions Yq(x) are then a result of these electron loss and capture processes. The relation between charge state distributions and the charge changing cross sections (σq’q) for a specific energy can be described by a system of coupled linear differential equations (see Betz [1]):
dYq (x ) dx
q'max
=
∑ (σ q'q Y q' (x )−σqq' Yq (x ) )
q ≠ q'
(1)
These equations are based on the fact that the changes of the charge state q (dYq) within target thickness dx are determined by the competition between gain and loss of electrons. The sum of all charges states is normalized to ΣYq = 1. For the stripping process in a tandem accelerator, the initial condition at x = 0 is described by Y(0) = (1,0,0…) meaning that all ions are in the charge state −1. Such a system of equations can be solved numerically or analytically. The analytic solution consists of a sum of exponential functions. In various programming languages, such a system of linear differential equations can be solved in a single command when the cross sections are given in a matrix representation (see e.g. Mathematica, MatLab, Maple): The available data for charge-changing cross sections and charge
Corresponding author. E-mail address: [email protected] (M. Suter).
https://doi.org/10.1016/j.nimb.2018.08.014 Received 31 January 2018; Received in revised form 9 August 2018; Accepted 13 August 2018 0168-583X/ © 2018 Elsevier B.V. All rights reserved.
Please cite this article as: Suter, M., Nuclear Inst, and Methods in Physics Research B (2018), https://doi.org/10.1016/j.nimb.2018.08.014
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state distributions have been collected from the literature for fast carbon ions in Ar or He gas. It will be shown what can be learned from these data for the design and behavior of AMS facilities. Charge-state distributions and charge-changing cross sections are typically measured for the most abundant isotope, which in this case is 12 C. Because these processes are functions of the projectile velocity, the cross sections and the distributions as function of energy are not identical for all isotopes. 2. Charge state distributions of carbon in Ar gas 2.1. Data sets and their processing Carbon is the most important element for AMS and high performance is required. It is therefore valuable to understand the physics behind the stripping process in order to optimize the operating conditions for this application. Ar is one of the most common stripper gases for larger tandem accelerators and the charge state distributions were studied early in the history of in the relevant energy range 2–7 MeV [2]. Later, the associated charge changing cross sections were also published [3]. With the development of smaller instruments, the charge state distributions were also measured in the range between 200 and 600 keV [4]. For completeness, older data for charge state distributions and cross sections in the range of 20–80 keV are included in this discussion [5]. Data from many other publications on charge changing cross sections have also been included in this project [6–16]. Because no simple and reliable models are available for calculating the charge-changing cross sections, one has to rely on experimental data. In principle, these data allow the charge state distributions to be derived as a function of projectile energy and target thickness as shown by Eq. (1). But experimentally-determined charge-changing cross sections generally have quite large errors, typically in the range of 10–80%. Sometimes differences of more than a factor of 2 have been seen between data sets of different authors. One of the reasons for these large uncertainties is that the gas target is open and inhomogeneous and therefore it is not so easy to determine the target thickness accurately. Because of the large errors, the calculation of the charge state distribution by solving the differential equations can lead to significant deviations from the measured charge state distributions. Therefore fits to the cross sections must be adjusted in order to reproduce the experimental charge-state distributions. For this paper, the following procedure has been applied. The cross section data on a log-log scale were fitted with a polynomial function. Normally either second or fourth order polynomials were used. The fits were adjusted manually to match distributions by shifting the data series of specific authors by a constant factor (assuming systematic errors), and/or by adding extra (virtual) points for the fitting of the cross sections to match the experimental charge state distributions better. Hereby, also the expected general behavior of the capture and loss cross section was also considered.
Fig. 1. Equilibrium charge state distribution of 12C and 14C (dashed curve) with Ar gas stripping. Calculations are based on measured charge changing cross sections and charge state distribution data.
losses in the range of about 5–10% [20]. For 4+ the maximum is about 72% around 6 MeV. Reported transmissions are around 52–58% implying beam losses of 20–25% compared to equilibrium conditions (see below). 2.3. Charge state distribution as function of target thickness With the cross sections the charge state distribution can also be calculated as a function of the stripper thickness for all energies. As an example this distribution is shown for 2.73 MeV in Fig. 2. The charge state 3+ has the highest yield. When injecting purely negative ions (q = −1), the intensity of 1− decreases as a simple exponential
2.2. Equilibrium charge state distribution as function of energy With the discussed fitting procedure, solutions were found which represent quite well the experimental charge state distribution of 12C as function of the energy, as seen in Fig. 1. The calculated charge state distributions for 14C are also shown, they are clearly displaced from the 12 C distributions as noted above. There are some energy intervals in which no reliable charge state distributions data are available (0.1–0.2 MeV and 0.7–1.6 MeV). The maximum for charge 2+ is in the region of 1 MV that is important for AMS. Several authors have reported transmissions of 54–58% [17–19]. Assuming a few percent transmission losses for these instruments, one would expect stripping yields of around 60% whereas our calculations give values around 55%. The maximum for 3+ is 55% at around 2.5 MeV for 12C and 3.0 MeV for 14C. AMS in this energy range can provide good performance with beam
Fig. 2. Charge state distribution as function of target thickness for 2.73 MeV 12 − C incident ions, equivalent to 3.00 MeV 14C ions. 2
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(e−σ−10 x ) because the capture process can be neglected (σ0−1 « σ−10). As the stripper thickness is increased, the neutrals and the positive charge states are successively populated. The charge states 0, 1, 2 reach a maximum and then decrease toward a final constant value (also often called equilibrium value). These low charge states are reaching maximal yields of 25–40%. It should be emphasized that by summing the maximum yields for each charge state one reaches significantly more than 100% (in this example about 180%). Hence, when measuring the intensity of all charge states in order to get an optical transmission for an AMS system, it is important to keep the stripper pressure very constant. By adjusting the stripper pressure just a little for each charge state, it is easy to obtain a sum for the transmission of 100% or more. When measuring transmission as a function of stripper thickness for a specific charge state, one has to be aware that beam losses occur due to small angle scattering in the stripper gas or by charge-changing processes in the acceleration tubes. These losses typically lead to an exponential decrease in optical transmission (To) as the stripper thickness (x) is increased, which can be characterized by a loss cross section σl; To(x) is then given by e−x σl. This is demonstrated e.g. in a plot from the PhD thesis of Steier [21], which shows the transmission of 12C3+ ions at the VERA facility as a function of the stripper density (in arbitrary units). In Fig. 3 his data are compared with our model distribution. The loss cross section was adjusted to match the experiment and also the target thickness scale was tuned to reproduce the experimental data. Good agreement between data and model is obtained. This figure demonstrates that the maximum transmission is typically obtained at a target thickness that is significantly below that at which the final constant value in the stripping yield is reached. An extrapolation of the higher pressure section of the measured curve back to zero gas pressure, as indicated by the blue line, gives the value which corresponds to this final constant value. A linear approximation is adequate, provided the losses are small.
Fig. 4. Target thickness required for reaching equilibrium conditions as a function of energy of C in Ar. Curves for four different values for the acceptable deviation from equilibrium are shown. The solid and dashed lines are for two different definitions of the acceptable deviation. See text for details.
any more when further increasing the stripper thickness. These conditions are called equilibrium conditions. Data that are published and found in tables (e.g. in Wittkower and Betz [22]) are typically measured under such conditions. The question then arises as to how to get a reasonable estimate for the thickness required for reaching these equilibrium conditions. Because the charge state yields are approaching these conditions exponentially, it is necessary to specify a value for the acceptable deviation (ΔY) from the final value Yequi. Various definitions might be appropriate. In this work, two criteria have been used.
2.4. Equilibrium conditions At a certain thickness, the charge state distribution does not change
1. The deviation ΔY is taken to be the sum of the departure for each individual charge state, i.e. ΔY ≥ |(Yi(x) − Yi(xequi)|. 2. The deviation is taken to be twice that of the charge state with the largest departure, i.e. ΔY ≥ 2 Max |(Yi(x) − Yi(xequi)|. In Fig. 4 the target thickness required for reaching equilibrium condition are shown for deviations of 0.5, 1, 2, and 4%. At low energies of 10–100 kV, the thickness required for reaching equilibrium decreases and reaches a minimum at ∼100 keV. At higher energies, inner shell ionization starts to play a role and because these cross sections are smaller, the required target thickness rises with increasing energy. Similar curves have been also calculated by Dmitriev et al. [23], and Belkova et al. [24]. In addition, Betz gives formulae for the calculation of the equilibrium thickness [25]. For AMS systems that use charge states 1+ or 2+, the thickness required for reaching equilibrium conditions is not relevant, because a higher target thickness is needed to destroy the interfering molecules sufficiently. This is about 3–6 times larger than the equilibrium conditions. For Ar gas, the thickness required for destroying molecules (CH+, CH2+) correspond to around 3 × 1016 atoms/cm2 at around 0.5 MV [4]. This is even more than what is needed for reaching equilibrium with 3 MV instruments, but is similar to the thickness for equilibrium conditions at about 5.5 MV. For 14C instruments using the 2+ charge state at 1 MV, the dominant interfering molecule is CH22+ [4]. This has lower intensity than the CH+ and CH2+ molecules, and hence a smaller target thickness (1.5–2·1016 atoms/cm2) might be enough for sufficiently destroying the molecules.
Fig. 3. Transmission of 12C3+ as a function of stripper thickness at a terminal voltage of 2.73 MV. Due to scattering effects the transmission decreases with increasing pressure after the maximum. The maximum transmission, marked by the red arrow, is reached significantly before the final constant level is reached in the stripping yield shown by the green curve. The experimental data are measured at VERA and kindly provided by Steier [21]. The thickness scale along the upper axis was deduced from the fitting procedure (see text). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 3
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Since the intensity of these ions of the stable isotopes is likely to be orders of magnitude higher than 14C, some may find their way to the 14 C detector and cause background. Knowing the charge changing cross sections, the intensity of such background beams can be estimated. Besides the charge-changing cross sections, the length of the acceleration section which contributes to such ions must be known (this is defined by the energy or the momentum acceptance of the following spectrometer), as well as the pressure profile in this section. For low energy instruments (0.2–1.0 MV), the relevant capture cross sections (σ21, σ32) are certainly larger than the relevant ones (σ43, σ54) for instruments in the range of 3–6 MeV. On the other hand, the relevant length and the corresponding atom thickness is significantly smaller than for larger instruments, therefore these background contributions are not necessarily larger for small instruments, but they depend strongly on the stripper design and the pumping. Such background contributions are typically in the range of 10−7 to 10−5 of the intensity of the corresponding molecular components, which are in the range of 10−4–10−5 of the corresponding atomic beam of 12C, so the final intensity of the background beams at the exit of the accelerator is in the range of 10−9–10−12. For more precise calculations the ion optics and a more detailed pressure profile would be needed. The compact vacuum insulated accelerators have the advantage of providing good pumping in the acceleration sections.
In Fig. 4, the curves for the two different criteria for acceptable deviation are essentially identical. This behavior can be explained in the following way. Typically 2 or 3 charge states contribute to the deviation. Assuming that the largest deviation has a negative sign, then the other two have a positive sign because the sum of the 3 must be zero (because all charge states add up to 1, independent of the thickness), so the absolute sum of all three equals twice the maximum value. In practice, all AMS facilities operated between 2 and 6 MV (3+or + 4 ) are probably tuned to the maximum transmission. Because beam losses due to scattering or ion optics are in the order of 5–20%, it has to be assumed that the target thickness is significantly below that required for equilibrium conditions as seen in Fig. 3. 2.5. Mass fractionation As noted above, the charge changing cross sections are a function of the projectile velocity or (E/m), so at a fixed energy the charge state distributions are mass dependent. It follows that the stripping process is changing the isotopic ratio. This effect is called mass fractionation. Because AMS measurements are normally made relative to standards (for 13C/12C as well as for 14C/12C) this mass fractionation is not relevant as long as it is constant during the measurement. But stripper thickness variations lead to drifts in isotopic ratios if not in equilibrium conditions. An example is shown in Fig. 5: at an energy of 2.73 MeV the maximum transmission is obtained at VERA around 0.8–1.0·1016 atoms/cm2 (shown in Fig. 3), for a ± 10% pressure variation the mass fractionation for 13C/12C as well as for 14C/12C is about ± 4‰. This demonstrates how important it is to keep the stripper density constant during measurements.
2.7. Beam losses due to charge changing processes in the acceleration sections If charge changing cross sections are large enough, a significant fraction of the beam could be lost by charge changing within the acceleration sections. The total losses can be estimated by integrating the losses over the whole tube length Ltot. Here, one has to take the sum of all possible cross sections which can contribute to the losses. The atomic density x(L) can be derived from the pressure profile:
2.6. Background due to charge changing in the acceleration sections Charge changing processes within the acceleration sections are a possible cause of background. Specifically, molecular negative ions such as 13CH− and 12CH2−, which are injected together with 14C−, break up in the stripper. If the 13C or 12C fragments have a charge state that is one higher than the selected one, then an electron capture process within the high energy tube at a specific location can lead to ions having the same energy or the same momentum as the 14C ions.
Ltot
floss = ∫ 0
∑ σij (E ) x (L) dL,
where
E = E0 +
j
L qV Ltot
In the high energy tubes, these losses are small and can be neglected in all cases. In the low energy tubes the electron detachment cross sections are quite large for the negative ions, in the range of 10−15 cm2 and also double electron losses in a single collision can be a significant contribution for C-Ar system. Unfortunately, experimental electrondetachment cross sections are only available in the low energy range up to about 1.5 MeV [9]. Therefore it is difficult to make reliable estimates for these losses for the large accelerators, both because these cross sections are not known at the energies that pertain close to the highvoltage terminal where the gas density is highest due to proximity to the stripper, and because the pressure profiles along the length of the low-energy acceleration tube are poorly known for most facilities. For small instruments these beam losses can be neglected, because the acceleration section are short; for 3 MV instruments however the loss could be in the range of 1–4%, and for 5–6 MV the beam losses might be in the range of 2–10%. 3. Charge state distribution of C in He 3.1. Analysis of the data Already in 1972, extensive studies of charge state distributions with He stripping were made at Aarhus in the range 100–400 keV for projectiles with nuclear charges in the range of 3–17 [26]. The results showed that He behaved significantly differently than other stripper gases. In particular, enhanced stripping yields have been found for certain charge states; e.g. high yields of 60% for C+ at 95 keV and more than 60% for Al2+ in the range of 100–300 keV. This special behavior of He stripping motivated the initial experiments with He as stripper for
Fig. 5. Mass fractionation for 3+ carbon ions at 2.73 MeV as a function of stripper thickness. 4
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the situation is completely different. Between 15 and 180 kV the capture cross section is larger than the loss cross section and therefore the neutrals have the highest yield in this interval. More specifically, the ionization cross sections are not much different in the low energy range for the two gases, whereas the capture cross section for He gas is about an order of magnitude smaller than for Ar. This explains the significantly different behavior of the 2 gases and confirms the hypothesis given by [29], that the reduction of capture cross section due to the high binding energy of the outermost electron in He (24 eV) compared to Ar (16 eV) is responsible for the special behavior of He-stripping. The target thickness needed for reaching equilibrium condition is also compared for the 2 gases He and Ar (see Fig. 8). The thickness required is significantly larger for He stripping, as expected from the cross sections shown in Fig. 7. 4. Additional comments to other elements and targets used in AMS The effects shown here for Carbon exist also for other projectiletarget combinations. A limited number of data on charge state distribution and charge changing cross section is also available for C-N2 and C-O2 system. Also for some other isotopes used in AMS, limited data sets are available for charge changing cross sections as well as for charge state distributions (e.g. Al on N [40,41], I on He [30,42]. But those data sets are not sufficiently complete or accurate enough for evaluating all the effects discussed here for Carbon. For all systems in which molecules are used as an initial beam (e.g. BeO−, CaF3− and UO−), the situation is more complicated, because also the molecular states have to be included in the system of differential equations (see Eq. (1)). For Be a data set of cross sections and charge-state distributions is available from [3]. These data were obtained with an external stripper starting with Be1+ or 2+ ions. Because the BeO molecules exist in charge states of 1−, 0, 1+ and 2+, one has to include also the equations for all these molecular states and consider the corresponding loss and capture processes as well as breakup of these molecules. So the thickness dependency of the yields, the mass fractionation and the thickness required for reaching equilibrium situation cannot be calculated from the atomic data alone. The equilibrium charge state distributions however are independent of the initial molecules. The procedures described in Eq. (1) can also be applied to systems in which positive ions are extracted from an ion source and then converted with gas exchange cells to negative ions. In this case, the yield for producing the negative ions depends strongly on the size of the electron capture cross sections (0 → −1 and 1 → 0). Targets having low binding energies such as alkali vapors have enhanced capture cross sections at low energies and provide yields in the range of 20–30% for carbon with energies of 20–30 keV (Heinemeier [43]) compared to regular stripper gases such as Ar and N2, for which the yields for negative ion formation are low (1.5–6)% [5], see also Fig. 1). This method recently received renewed attention with the developments at the Scottish Universities Environmental Research Centre by Freeman [44], in collaboration with the companies NEC and Pantechnik), using Isobutene as conversion gas. The special behavior of stripping carbon in He stripping which leads to high yields for 1+ can be clearly attributed to the lower electron capture cross sections for He relative to other gases. This effect is also seen with other projectiles in the energy range of compact AMS systems: For Al, Ca and I, charge state 2+ is the dominant charge state and yields are in the range of 50–60% [45–47]. Also for actinides, Hestripping provides high efficiencies for 3+ with yields of 35–45% [28].
Fig. 6. Charge state distribution of 12C with He stripping at low energies. The curves are based on the charge changing cross section (Eq. (1)). The data points are from Hvelplund and Maxeiner. For comparison the corresponding curves for Ar gas are also shown.
low-energy AMS of 14C (Schulze-König et al. [27]) and heavier AMS nuclides (Vockenhuber et al. [28]). The use of He gas as stripper has the additional advantage that scattering cross sections are significantly smaller than for argon which leads to lower beam losses. The special features of He stripping were also recognized for very heavy projectiles where a significantly higher mean charge was achieved with He stripping compared to other gases at energies below 3 MeV (Ta and U [29], as well as I [30]). Already in these early papers, an explanation was provided for this special behavior, attributing it to the small electroncapture cross sections of He gas relative to other gases due to the high binding energies of the electrons in He [29]. For the C-He system, the same procedure as for C on Ar was applied to reproduce the charge state distributions from the electron capture and loss cross sections ([6–10,12,31–39], Unfortunately no charge state distribution data have been found for the MeV range, and therefore the calculation of the charge state distribution based on the cross section is not very reliable above 400 keV. The charge state distribution published by Maxeiner et al. [37] covers a relatively limited range of 50–250 keV. These data confirm the trends seen by [26] in the range of 90–400 keV as seen in Fig. 6. A strong increase of the yield for C+ was found when decreasing the energy to the range of 50–100 keV. The yields for 1+ reach values of 60–80%. 3.2. Comparisons of results with the Ar Also shown in Fig. 6 are the data with Ar. Below 200 keV, the yield of Ar-stripping is significantly smaller. Above about 250 keV Ar gives higher stripping yields. For both stripper gases, 0 and 1+ are the dominant charge states in the range of 20–300 keV. The loss cross section σ01 and the capture cross section σ10 are the relevant processes determining the yield of these charge states. Neglecting multi-electron processes, the number of ions going from the state 0 to 1+ is equal to the reverse process under equilibrium conditions. This means that the relative yields are inversely proportional to the corresponding cross sections: Y0/Y1 = σ10/σ01. The relevant cross sections are shown in Fig. 7 for He and Ar stripping. For He gas the capture cross section is always smaller than the electron loss cross section. This means that 1+ is always the dominant charge state in this energy interval. For Ar gas
5. Conclusions In this paper the impact of charge changing processes on AMS performance in terms of transmission, precision and background have 5
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Fig. 7. Comparison of the relevant chargechanging cross sections between 0 and 1+ for (a) C in He and (b) C in Ar. The red points are the loss cross sections and the blue point represented the electron capture cross section. The capture cross section with He are significantly smaller than those in Ar. The data point are from the following Refs.: [5–7,12,16,34,37,38]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 8. Comparison of the target thickness required for reaching equilibrim conditions for C in Ar and He gas at low energies with 1% deviation from the true equilibrium.
been shown for Carbon with both Ar and He as stripper gas. Mass fractionation in the stripping process has also been discussed. The transmission yields that are measured for AMS facilities are typically smaller than the charge state yields for equilibrium conditions. This is due to beam losses mainly caused by small angle scattering in the stripper, as shown in Fig. 3. But larger yields can be obtained for charge states which are lower than the state with the maximum yield because they go through a maximum before reaching equilibrium (as shown in Fig. 2). The special behavior of He stripping at low energies and the related high yields for certain charge states can be clearly attributed to the lower electron capture cross sections for He relative to other gases. The data and effects discussed here, help to understand the behavior of existing AMS facilities and are useful for designing new and improved AMS instruments. References [1] H.D. Betz, Charge states and charge changing cross-sections of fast heavy ions penetrating through gaseous and solid media, Rev. Mod. Phys. 44 (1972) 465–539.
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[37] S. Maxeiner, M. Seiler, M. Suter, H.-A. Synal, Charge state distributions and charge exchange cross sections of carbon in helium at 30–258 keV, Nucl. Instrum. Methods Phys. Res., Sect. B 361 (2015) 541–547. [38] K. Wohrer, R. Fossé, M. Chabot, D. Gardès, C. Champion, Dissociative and nondissociative electron capture in medium-velocity cluster-atom collisions; evidence of contributions due to multi-electron processes, J. Phys. B: At. Mol. Opt. Phys. 33 (2000) 4469. [39] E.C. Montenegro, G.M. Sigaud, W.E. Meyerhof, Intermediate-velocity atomic collisions. V. Electron capture and loss in C3+ and O5+ collisions with H2 and He, Phys. Rev. A 45 (1992) 1575–1582. [40] G. Ryding, A. Wittkower, G. Nussbaum, A. Saxman, P.H. Rose, Measurement of charge-changing cross sections for 0.4–4.0-MeV aluminum ions in nitrogen, Phys. Rev. A 2 (1970) 1382. [41] G. Ryding, A. Wittkower, G.H. Nussbaum, A.C. Saxman, R. Bastide, Q. Kessel, P.H. Rose, Equilibrium charge fractions of aluminum ions in nitrogen from 0.4 to 4.0 MeV, Phys. Rev. A 1 (1970) 1081. [42] H.D. Betz, G. Ryding, A.B. Wittkower, Cross sections for electron capture and loss by fast bromine and iodine ions traversing light gases, Phys. Rev. A 3 (1971) 197–205. [43] J. Heinemeier, P. Hvelplund, Production of 10–80 keV negative heavy ions by charge exchange in Na vapour, Nucl. Instrum. Methods 148 (1978) 425–429. [44] S.P.H.T. Freeman, R.P. Shanks, X. Donzel, G. Gaubert, Radiocarbon positive-ion mass spectrometry, Nucl. Instrum. Methods Phys. Res., Sect. B 361 (2015) 229–232. [45] C. Vockenhuber, T. Schulze-König, H.A. Synal, I. Aeberli, M.B. Zimmermann, Efficient 41Ca measurements for biomedical applications, Nucl. Instrum. Methods Phys. Res., Sect. B 361 (2015) 273–276. [46] A.M. Müller, M. Christl, J. Lachner, H.-A. Synal, C. Vockenhuber, C. Zanella, 26Al measurements below 500 kV in charge state 2+, Nucl. Instrum. Methods Phys. Res. Section B 361 (2015) 257–262. [47] C. Vockenhuber, N. Casacuberta, M. Christl, H.-A. Synal, Accelerator mass spectrometry of 129I towards its lower limits, Nucl. Instrum. Methods Phys. Res., Sect. B 361 (2015) 445–449.
Physics, Academic Press, 1983, pp. 1–44 vol. 4. [26] P. Hvelplund, E. Lægsgaard, E. Horsdal Pedersen, Equilibrium charge distributions of light ions in helium, measured with a position-sensitive open electron multiplier, Nucl. Instrum. Methods 101 (1972) 497–502. [27] T. Schulze-König, M. Seiler, M. Suter, L. Wacker, H.-A. Synal, The dissociation of 13 CH and 12CH2 molecules in He and N2 at beam energies of 80 to 250keV and possible implications for radiocarbon mass spectrometry, Nucl. Instrum. Methods B 269 (2011) 34–39. [28] C. Vockenhuber, V. Alfimov, M. Christl, J. Lachner, T. Schulze-König, M. Suter, H.A. Synal, The potential of He stripping in heavy ion AMS, Nucl. Instrum. Methods Phys. Res., Sect. B 294 (2013) 382–386. [29] A.B. Wittkower, H.D. Betz, Equilibrium charge-state distributions of 2–15-mev tantalum and uranium ions stripped in gases and solids, Phys. Rev. A 7 (1973) 159–167. [30] G. Ryding, A.B. Wittkower, P.H. Rose, Equilibrium charge-state distributions for iodine in gases (1–12 MeV), Phys. Rev. 185 (1969) 129–134. [31] Y. Huang, S. Wu, E. Yang, M. Gao, X. Zhang, G. Li, F. Lu, Single and double electron detachment cross sections for C− incident on helium, Nucl. Instrum. Methods Phys. Res., Sect. B 229 (2005) 46–50. [32] R.K. Janev, R.A. Phaneuf, H.T. Hunter, Recommmended cross sections for electron capture and ionization in collisions of Cq+ and Oq+ ions with H, He, and H2, At. Data Nucl. Data Tables 40 (1988) 249–281. [33] K. Ishii, T. Tanabe, R. Lomsadze, K. Okuno, Charge-changing cross sections in collisions of Cq+ (q = 2–5) with He and H2 at energies below 750 eV/u, Phys. Scr. 2001 (2001) 332. [34] Y. Nakai, M. Sataka, Electron-capture and loss cross-sections in collisions of C atoms with He, J. Phys. B-Atomic Mol. Opt. Phys. 24 (1991) L89–L91. [35] E. Unterreiter, J. Schweinzer, H. Winter, Single electron capture for impact of (0.5-9 keV) C2+ on He, Ar and H2, J. Phys. B: At. Mol. Opt. Phys. 24 (1991) 1003. [36] A.C.F. Santos, G.M. Sigaud, W.S. Melo, M.M. Sant’Anna, E.C. Montenegro, Absolute cross sections for electron loss, electron capture, and multiple ionization in collisions of C3+ with noble gases, Phys. Rev. A 82 (2010) 012704.
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Nuclear Inst. and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Charge-state distributions and charge-changing cross sections and their impact on the performance of AMS facilities ⁎
Martin Suter , Sascha Maxeiner, Hans-Arno Synal, Christof Vockenhuber Laboratory of Ion Beam Physics, ETH Zurich, Otto-Stern-Weg 5, CH-8093 Zurich, Switzerland
A R T I C LE I N FO
A B S T R A C T
Keywords: Accelerator mass spectrometry Charge state distribution Charge changing cross sections Stripping yield Mass fractionation
The charge state distributions of ions passing through gases or foils have a significant influence on the performance of AMS facilities. Most important is the stripping process in the terminal of the accelerator. Published data on charge state distributions have been collected as well as associated charge-changing cross sections for various projectiles and targets relevant to AMS. Based on these data, the stripping yields as function of the stripper thickness and ion energy are calculated. This allows to evaluate the stripping thickness required for reaching charge state equilibrium, as well as mass fractionation effects depending on energy and stripper thickness. The significantly different behavior of helium compared to other gases leads to very high stripping yields for specific charge states at low energies. The cross sections for electron detachment of negative ions give a tool for estimating beam losses in the low energy acceleration tube. Further, electron capture and loss cross sections allow the estimation of backgrounds caused by charge exchange processes in the acceleration tubes. The effects discussed here are illustrated with calculations and simulations for Carbon beams. The data are useful for the design of new AMS facilities or improving existing ones.
1. Introduction When fast ions pass through matter (gases or solids) they interact with the target atoms or molecules. A possible consequence of these interactions is that electrons are removed from the projectile, thereby increasing its charge state. This process is called electron loss (or ionization, but this term is not appropriate for negative ions because the electron detachment leads to neutral atoms). Typically one electron is removed in a single collision, but multi-electron removal is also possible though less probable. Alternatively, the projectile can capture electrons from the target atoms or molecules leading to a decrease of the projectile charge. The rates (strengths) of these processes are characterized by cross sections. In this paper, cross sections are given in units of 10−16 cm2 (equivalent to Å2); they typically fall in the range from 10−2 to 100). According to this convention the target thickness (x) is always given in units of 1016 atoms/cm2. The product of the cross sections with the thickness element (dx) gives the probability of such a charge changing process. The electron-loss cross section for a specific initial and final charge state is always the sum of all possible processes. Not only can the most loosely bound electron be removed, but other more tightly bound electrons can also be removed in a collision, leaving the projectile in an excited state. Similarly, the electron-capture cross section is also a sum ⁎
over various possible transitions, since electron-capture can also result in the projectile or target being in an excited state. The charge state distributions Yq(x) are then a result of these electron loss and capture processes. The relation between charge state distributions and the charge changing cross sections (σq’q) for a specific energy can be described by a system of coupled linear differential equations (see Betz [1]):
dYq (x ) dx
q'max
=
∑ (σ q'q Y q' (x )−σqq' Yq (x ) )
q ≠ q'
(1)
These equations are based on the fact that the changes of the charge state q (dYq) within target thickness dx are determined by the competition between gain and loss of electrons. The sum of all charges states is normalized to ΣYq = 1. For the stripping process in a tandem accelerator, the initial condition at x = 0 is described by Y(0) = (1,0,0…) meaning that all ions are in the charge state −1. Such a system of equations can be solved numerically or analytically. The analytic solution consists of a sum of exponential functions. In various programming languages, such a system of linear differential equations can be solved in a single command when the cross sections are given in a matrix representation (see e.g. Mathematica, MatLab, Maple): The available data for charge-changing cross sections and charge
Corresponding author. E-mail address: [email protected] (M. Suter).
https://doi.org/10.1016/j.nimb.2018.08.014 Received 31 January 2018; Received in revised form 9 August 2018; Accepted 13 August 2018 0168-583X/ © 2018 Elsevier B.V. All rights reserved.
Please cite this article as: Suter, M., Nuclear Inst, and Methods in Physics Research B (2018), https://doi.org/10.1016/j.nimb.2018.08.014
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state distributions have been collected from the literature for fast carbon ions in Ar or He gas. It will be shown what can be learned from these data for the design and behavior of AMS facilities. Charge-state distributions and charge-changing cross sections are typically measured for the most abundant isotope, which in this case is 12 C. Because these processes are functions of the projectile velocity, the cross sections and the distributions as function of energy are not identical for all isotopes. 2. Charge state distributions of carbon in Ar gas 2.1. Data sets and their processing Carbon is the most important element for AMS and high performance is required. It is therefore valuable to understand the physics behind the stripping process in order to optimize the operating conditions for this application. Ar is one of the most common stripper gases for larger tandem accelerators and the charge state distributions were studied early in the history of in the relevant energy range 2–7 MeV [2]. Later, the associated charge changing cross sections were also published [3]. With the development of smaller instruments, the charge state distributions were also measured in the range between 200 and 600 keV [4]. For completeness, older data for charge state distributions and cross sections in the range of 20–80 keV are included in this discussion [5]. Data from many other publications on charge changing cross sections have also been included in this project [6–16]. Because no simple and reliable models are available for calculating the charge-changing cross sections, one has to rely on experimental data. In principle, these data allow the charge state distributions to be derived as a function of projectile energy and target thickness as shown by Eq. (1). But experimentally-determined charge-changing cross sections generally have quite large errors, typically in the range of 10–80%. Sometimes differences of more than a factor of 2 have been seen between data sets of different authors. One of the reasons for these large uncertainties is that the gas target is open and inhomogeneous and therefore it is not so easy to determine the target thickness accurately. Because of the large errors, the calculation of the charge state distribution by solving the differential equations can lead to significant deviations from the measured charge state distributions. Therefore fits to the cross sections must be adjusted in order to reproduce the experimental charge-state distributions. For this paper, the following procedure has been applied. The cross section data on a log-log scale were fitted with a polynomial function. Normally either second or fourth order polynomials were used. The fits were adjusted manually to match distributions by shifting the data series of specific authors by a constant factor (assuming systematic errors), and/or by adding extra (virtual) points for the fitting of the cross sections to match the experimental charge state distributions better. Hereby, also the expected general behavior of the capture and loss cross section was also considered.
Fig. 1. Equilibrium charge state distribution of 12C and 14C (dashed curve) with Ar gas stripping. Calculations are based on measured charge changing cross sections and charge state distribution data.
losses in the range of about 5–10% [20]. For 4+ the maximum is about 72% around 6 MeV. Reported transmissions are around 52–58% implying beam losses of 20–25% compared to equilibrium conditions (see below). 2.3. Charge state distribution as function of target thickness With the cross sections the charge state distribution can also be calculated as a function of the stripper thickness for all energies. As an example this distribution is shown for 2.73 MeV in Fig. 2. The charge state 3+ has the highest yield. When injecting purely negative ions (q = −1), the intensity of 1− decreases as a simple exponential
2.2. Equilibrium charge state distribution as function of energy With the discussed fitting procedure, solutions were found which represent quite well the experimental charge state distribution of 12C as function of the energy, as seen in Fig. 1. The calculated charge state distributions for 14C are also shown, they are clearly displaced from the 12 C distributions as noted above. There are some energy intervals in which no reliable charge state distributions data are available (0.1–0.2 MeV and 0.7–1.6 MeV). The maximum for charge 2+ is in the region of 1 MV that is important for AMS. Several authors have reported transmissions of 54–58% [17–19]. Assuming a few percent transmission losses for these instruments, one would expect stripping yields of around 60% whereas our calculations give values around 55%. The maximum for 3+ is 55% at around 2.5 MeV for 12C and 3.0 MeV for 14C. AMS in this energy range can provide good performance with beam
Fig. 2. Charge state distribution as function of target thickness for 2.73 MeV 12 − C incident ions, equivalent to 3.00 MeV 14C ions. 2
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(e−σ−10 x ) because the capture process can be neglected (σ0−1 « σ−10). As the stripper thickness is increased, the neutrals and the positive charge states are successively populated. The charge states 0, 1, 2 reach a maximum and then decrease toward a final constant value (also often called equilibrium value). These low charge states are reaching maximal yields of 25–40%. It should be emphasized that by summing the maximum yields for each charge state one reaches significantly more than 100% (in this example about 180%). Hence, when measuring the intensity of all charge states in order to get an optical transmission for an AMS system, it is important to keep the stripper pressure very constant. By adjusting the stripper pressure just a little for each charge state, it is easy to obtain a sum for the transmission of 100% or more. When measuring transmission as a function of stripper thickness for a specific charge state, one has to be aware that beam losses occur due to small angle scattering in the stripper gas or by charge-changing processes in the acceleration tubes. These losses typically lead to an exponential decrease in optical transmission (To) as the stripper thickness (x) is increased, which can be characterized by a loss cross section σl; To(x) is then given by e−x σl. This is demonstrated e.g. in a plot from the PhD thesis of Steier [21], which shows the transmission of 12C3+ ions at the VERA facility as a function of the stripper density (in arbitrary units). In Fig. 3 his data are compared with our model distribution. The loss cross section was adjusted to match the experiment and also the target thickness scale was tuned to reproduce the experimental data. Good agreement between data and model is obtained. This figure demonstrates that the maximum transmission is typically obtained at a target thickness that is significantly below that at which the final constant value in the stripping yield is reached. An extrapolation of the higher pressure section of the measured curve back to zero gas pressure, as indicated by the blue line, gives the value which corresponds to this final constant value. A linear approximation is adequate, provided the losses are small.
Fig. 4. Target thickness required for reaching equilibrium conditions as a function of energy of C in Ar. Curves for four different values for the acceptable deviation from equilibrium are shown. The solid and dashed lines are for two different definitions of the acceptable deviation. See text for details.
any more when further increasing the stripper thickness. These conditions are called equilibrium conditions. Data that are published and found in tables (e.g. in Wittkower and Betz [22]) are typically measured under such conditions. The question then arises as to how to get a reasonable estimate for the thickness required for reaching these equilibrium conditions. Because the charge state yields are approaching these conditions exponentially, it is necessary to specify a value for the acceptable deviation (ΔY) from the final value Yequi. Various definitions might be appropriate. In this work, two criteria have been used.
2.4. Equilibrium conditions At a certain thickness, the charge state distribution does not change
1. The deviation ΔY is taken to be the sum of the departure for each individual charge state, i.e. ΔY ≥ |(Yi(x) − Yi(xequi)|. 2. The deviation is taken to be twice that of the charge state with the largest departure, i.e. ΔY ≥ 2 Max |(Yi(x) − Yi(xequi)|. In Fig. 4 the target thickness required for reaching equilibrium condition are shown for deviations of 0.5, 1, 2, and 4%. At low energies of 10–100 kV, the thickness required for reaching equilibrium decreases and reaches a minimum at ∼100 keV. At higher energies, inner shell ionization starts to play a role and because these cross sections are smaller, the required target thickness rises with increasing energy. Similar curves have been also calculated by Dmitriev et al. [23], and Belkova et al. [24]. In addition, Betz gives formulae for the calculation of the equilibrium thickness [25]. For AMS systems that use charge states 1+ or 2+, the thickness required for reaching equilibrium conditions is not relevant, because a higher target thickness is needed to destroy the interfering molecules sufficiently. This is about 3–6 times larger than the equilibrium conditions. For Ar gas, the thickness required for destroying molecules (CH+, CH2+) correspond to around 3 × 1016 atoms/cm2 at around 0.5 MV [4]. This is even more than what is needed for reaching equilibrium with 3 MV instruments, but is similar to the thickness for equilibrium conditions at about 5.5 MV. For 14C instruments using the 2+ charge state at 1 MV, the dominant interfering molecule is CH22+ [4]. This has lower intensity than the CH+ and CH2+ molecules, and hence a smaller target thickness (1.5–2·1016 atoms/cm2) might be enough for sufficiently destroying the molecules.
Fig. 3. Transmission of 12C3+ as a function of stripper thickness at a terminal voltage of 2.73 MV. Due to scattering effects the transmission decreases with increasing pressure after the maximum. The maximum transmission, marked by the red arrow, is reached significantly before the final constant level is reached in the stripping yield shown by the green curve. The experimental data are measured at VERA and kindly provided by Steier [21]. The thickness scale along the upper axis was deduced from the fitting procedure (see text). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 3
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Since the intensity of these ions of the stable isotopes is likely to be orders of magnitude higher than 14C, some may find their way to the 14 C detector and cause background. Knowing the charge changing cross sections, the intensity of such background beams can be estimated. Besides the charge-changing cross sections, the length of the acceleration section which contributes to such ions must be known (this is defined by the energy or the momentum acceptance of the following spectrometer), as well as the pressure profile in this section. For low energy instruments (0.2–1.0 MV), the relevant capture cross sections (σ21, σ32) are certainly larger than the relevant ones (σ43, σ54) for instruments in the range of 3–6 MeV. On the other hand, the relevant length and the corresponding atom thickness is significantly smaller than for larger instruments, therefore these background contributions are not necessarily larger for small instruments, but they depend strongly on the stripper design and the pumping. Such background contributions are typically in the range of 10−7 to 10−5 of the intensity of the corresponding molecular components, which are in the range of 10−4–10−5 of the corresponding atomic beam of 12C, so the final intensity of the background beams at the exit of the accelerator is in the range of 10−9–10−12. For more precise calculations the ion optics and a more detailed pressure profile would be needed. The compact vacuum insulated accelerators have the advantage of providing good pumping in the acceleration sections.
In Fig. 4, the curves for the two different criteria for acceptable deviation are essentially identical. This behavior can be explained in the following way. Typically 2 or 3 charge states contribute to the deviation. Assuming that the largest deviation has a negative sign, then the other two have a positive sign because the sum of the 3 must be zero (because all charge states add up to 1, independent of the thickness), so the absolute sum of all three equals twice the maximum value. In practice, all AMS facilities operated between 2 and 6 MV (3+or + 4 ) are probably tuned to the maximum transmission. Because beam losses due to scattering or ion optics are in the order of 5–20%, it has to be assumed that the target thickness is significantly below that required for equilibrium conditions as seen in Fig. 3. 2.5. Mass fractionation As noted above, the charge changing cross sections are a function of the projectile velocity or (E/m), so at a fixed energy the charge state distributions are mass dependent. It follows that the stripping process is changing the isotopic ratio. This effect is called mass fractionation. Because AMS measurements are normally made relative to standards (for 13C/12C as well as for 14C/12C) this mass fractionation is not relevant as long as it is constant during the measurement. But stripper thickness variations lead to drifts in isotopic ratios if not in equilibrium conditions. An example is shown in Fig. 5: at an energy of 2.73 MeV the maximum transmission is obtained at VERA around 0.8–1.0·1016 atoms/cm2 (shown in Fig. 3), for a ± 10% pressure variation the mass fractionation for 13C/12C as well as for 14C/12C is about ± 4‰. This demonstrates how important it is to keep the stripper density constant during measurements.
2.7. Beam losses due to charge changing processes in the acceleration sections If charge changing cross sections are large enough, a significant fraction of the beam could be lost by charge changing within the acceleration sections. The total losses can be estimated by integrating the losses over the whole tube length Ltot. Here, one has to take the sum of all possible cross sections which can contribute to the losses. The atomic density x(L) can be derived from the pressure profile:
2.6. Background due to charge changing in the acceleration sections Charge changing processes within the acceleration sections are a possible cause of background. Specifically, molecular negative ions such as 13CH− and 12CH2−, which are injected together with 14C−, break up in the stripper. If the 13C or 12C fragments have a charge state that is one higher than the selected one, then an electron capture process within the high energy tube at a specific location can lead to ions having the same energy or the same momentum as the 14C ions.
Ltot
floss = ∫ 0
∑ σij (E ) x (L) dL,
where
E = E0 +
j
L qV Ltot
In the high energy tubes, these losses are small and can be neglected in all cases. In the low energy tubes the electron detachment cross sections are quite large for the negative ions, in the range of 10−15 cm2 and also double electron losses in a single collision can be a significant contribution for C-Ar system. Unfortunately, experimental electrondetachment cross sections are only available in the low energy range up to about 1.5 MeV [9]. Therefore it is difficult to make reliable estimates for these losses for the large accelerators, both because these cross sections are not known at the energies that pertain close to the highvoltage terminal where the gas density is highest due to proximity to the stripper, and because the pressure profiles along the length of the low-energy acceleration tube are poorly known for most facilities. For small instruments these beam losses can be neglected, because the acceleration section are short; for 3 MV instruments however the loss could be in the range of 1–4%, and for 5–6 MV the beam losses might be in the range of 2–10%. 3. Charge state distribution of C in He 3.1. Analysis of the data Already in 1972, extensive studies of charge state distributions with He stripping were made at Aarhus in the range 100–400 keV for projectiles with nuclear charges in the range of 3–17 [26]. The results showed that He behaved significantly differently than other stripper gases. In particular, enhanced stripping yields have been found for certain charge states; e.g. high yields of 60% for C+ at 95 keV and more than 60% for Al2+ in the range of 100–300 keV. This special behavior of He stripping motivated the initial experiments with He as stripper for
Fig. 5. Mass fractionation for 3+ carbon ions at 2.73 MeV as a function of stripper thickness. 4
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the situation is completely different. Between 15 and 180 kV the capture cross section is larger than the loss cross section and therefore the neutrals have the highest yield in this interval. More specifically, the ionization cross sections are not much different in the low energy range for the two gases, whereas the capture cross section for He gas is about an order of magnitude smaller than for Ar. This explains the significantly different behavior of the 2 gases and confirms the hypothesis given by [29], that the reduction of capture cross section due to the high binding energy of the outermost electron in He (24 eV) compared to Ar (16 eV) is responsible for the special behavior of He-stripping. The target thickness needed for reaching equilibrium condition is also compared for the 2 gases He and Ar (see Fig. 8). The thickness required is significantly larger for He stripping, as expected from the cross sections shown in Fig. 7. 4. Additional comments to other elements and targets used in AMS The effects shown here for Carbon exist also for other projectiletarget combinations. A limited number of data on charge state distribution and charge changing cross section is also available for C-N2 and C-O2 system. Also for some other isotopes used in AMS, limited data sets are available for charge changing cross sections as well as for charge state distributions (e.g. Al on N [40,41], I on He [30,42]. But those data sets are not sufficiently complete or accurate enough for evaluating all the effects discussed here for Carbon. For all systems in which molecules are used as an initial beam (e.g. BeO−, CaF3− and UO−), the situation is more complicated, because also the molecular states have to be included in the system of differential equations (see Eq. (1)). For Be a data set of cross sections and charge-state distributions is available from [3]. These data were obtained with an external stripper starting with Be1+ or 2+ ions. Because the BeO molecules exist in charge states of 1−, 0, 1+ and 2+, one has to include also the equations for all these molecular states and consider the corresponding loss and capture processes as well as breakup of these molecules. So the thickness dependency of the yields, the mass fractionation and the thickness required for reaching equilibrium situation cannot be calculated from the atomic data alone. The equilibrium charge state distributions however are independent of the initial molecules. The procedures described in Eq. (1) can also be applied to systems in which positive ions are extracted from an ion source and then converted with gas exchange cells to negative ions. In this case, the yield for producing the negative ions depends strongly on the size of the electron capture cross sections (0 → −1 and 1 → 0). Targets having low binding energies such as alkali vapors have enhanced capture cross sections at low energies and provide yields in the range of 20–30% for carbon with energies of 20–30 keV (Heinemeier [43]) compared to regular stripper gases such as Ar and N2, for which the yields for negative ion formation are low (1.5–6)% [5], see also Fig. 1). This method recently received renewed attention with the developments at the Scottish Universities Environmental Research Centre by Freeman [44], in collaboration with the companies NEC and Pantechnik), using Isobutene as conversion gas. The special behavior of stripping carbon in He stripping which leads to high yields for 1+ can be clearly attributed to the lower electron capture cross sections for He relative to other gases. This effect is also seen with other projectiles in the energy range of compact AMS systems: For Al, Ca and I, charge state 2+ is the dominant charge state and yields are in the range of 50–60% [45–47]. Also for actinides, Hestripping provides high efficiencies for 3+ with yields of 35–45% [28].
Fig. 6. Charge state distribution of 12C with He stripping at low energies. The curves are based on the charge changing cross section (Eq. (1)). The data points are from Hvelplund and Maxeiner. For comparison the corresponding curves for Ar gas are also shown.
low-energy AMS of 14C (Schulze-König et al. [27]) and heavier AMS nuclides (Vockenhuber et al. [28]). The use of He gas as stripper has the additional advantage that scattering cross sections are significantly smaller than for argon which leads to lower beam losses. The special features of He stripping were also recognized for very heavy projectiles where a significantly higher mean charge was achieved with He stripping compared to other gases at energies below 3 MeV (Ta and U [29], as well as I [30]). Already in these early papers, an explanation was provided for this special behavior, attributing it to the small electroncapture cross sections of He gas relative to other gases due to the high binding energies of the electrons in He [29]. For the C-He system, the same procedure as for C on Ar was applied to reproduce the charge state distributions from the electron capture and loss cross sections ([6–10,12,31–39], Unfortunately no charge state distribution data have been found for the MeV range, and therefore the calculation of the charge state distribution based on the cross section is not very reliable above 400 keV. The charge state distribution published by Maxeiner et al. [37] covers a relatively limited range of 50–250 keV. These data confirm the trends seen by [26] in the range of 90–400 keV as seen in Fig. 6. A strong increase of the yield for C+ was found when decreasing the energy to the range of 50–100 keV. The yields for 1+ reach values of 60–80%. 3.2. Comparisons of results with the Ar Also shown in Fig. 6 are the data with Ar. Below 200 keV, the yield of Ar-stripping is significantly smaller. Above about 250 keV Ar gives higher stripping yields. For both stripper gases, 0 and 1+ are the dominant charge states in the range of 20–300 keV. The loss cross section σ01 and the capture cross section σ10 are the relevant processes determining the yield of these charge states. Neglecting multi-electron processes, the number of ions going from the state 0 to 1+ is equal to the reverse process under equilibrium conditions. This means that the relative yields are inversely proportional to the corresponding cross sections: Y0/Y1 = σ10/σ01. The relevant cross sections are shown in Fig. 7 for He and Ar stripping. For He gas the capture cross section is always smaller than the electron loss cross section. This means that 1+ is always the dominant charge state in this energy interval. For Ar gas
5. Conclusions In this paper the impact of charge changing processes on AMS performance in terms of transmission, precision and background have 5
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Fig. 7. Comparison of the relevant chargechanging cross sections between 0 and 1+ for (a) C in He and (b) C in Ar. The red points are the loss cross sections and the blue point represented the electron capture cross section. The capture cross section with He are significantly smaller than those in Ar. The data point are from the following Refs.: [5–7,12,16,34,37,38]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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