ISOTOPIC COMPOSITION OF LIGHT NUCLEI IN COSMIC RAYS: RESULTS FROM AMS-01

Cosmic rays (CRs) detected with kinetic energies in the range from MeV to TeV per nucleon are believed to be produced by galactic sources. Observations of X-ray and γ-ray emission from galactic sites such as supernova remnants, pulsars, or stellar winds reveal the presence of energetic particle acceleration mechanisms occurring in such objects. The subsequent destruction of these accelerated nuclei (e.g., p, He, C, N, O, Fe) in the interstellar medium gives rise to secondary species that are rare in the CR sources, such as Li, Be, B, sub-Fe elements, deuterons, antiprotons, positrons, and high energy photons. The relation between secondary CRs and their primary progenitors allows the determination of propagation parameters such as the diffusion coefficient and the size of the diffusion region. For a recent review, see Strong et al. (2007).

Along with the ratios B/C and sub-Fe/Fe, it is of great importance to determine the propagation history of the lighter H, He, Li, and Be isotopes. Since ²H and ³He CRs are mainly produced by the breakup of the primary ⁴He in the galaxy, the ratios ²H/⁴He and ³He/⁴He probe the propagation history of helium (Webber 1997). The isotopes of Li, Be, and B, all of secondary origin, are also useful for a quantitative understanding of CR propagation. The relative abundances and isotopic composition of H, He, Li, Be, and B, therefore, might help to distinguish between the propagation models and give constraints on their parameters (Moskalenko et al. 2003).

Low energy data (≲200 MeV nucleon⁻¹) on CR isotopic composition come mainly from space experiments such as the HET telescopes on Voyager 1 and 2 (Webber et al. 2002), the Cosmic Ray Isotope Spectrometer (CRIS) on the Advanced Composition Explorer (ACE) satellite (de Nolfo et al. 2001), the Ulysses high energy telescope (Connell 1998), the Interplanetary Monitoring Platform (IMP; Garcia-Munoz 1977), and the HKH experiment on the International Sun–Earth Explorer (ISEE) spacecraft (Wiedenbeck & Greiner 1980). Light nuclei data at higher energies (up to a few GeV nucleon⁻¹) have been measured by balloon-borne magnetic spectrometers including IMAX (Reimer et al. 1998), ISOMAX (Hams et al. 2004), SMILI (Ahlen et al. 2000), BESS (Wang et al. 2002), and the Goddard Space Flight Center (GSFC) balloon (Hagen et al. 1977).

AMS-01 observed CRs at an altitude of ∼380 km during a period, 1998 June, of relatively quiet solar activity. It collected data free from atmospheric induced background. In this paper, we present measurements of the ³He/⁴He ratio over the kinetic energy range 0.2–1.4 GeV nucleon⁻¹, and the average values of the ratios ⁶Li/⁷Li, ⁷Be/(⁹Be+¹⁰Be), and ¹⁰B/¹¹B over the same energy range. The ratio ²H/⁴He is also presented.

The Alpha Magnetic Spectrometer (AMS) is a particle physics instrument designed for the high-precision and long-duration measurement of CRs in space. The AMS-01 precursor experiment operated successfully during a 10 day flight on the space shuttle Discovery (STS-91).

The spectrometer was composed of a cylindrical permanent magnet, a silicon micro-strip tracker, time-of-flight (TOF) scintillator planes, an aerogel Čerenkov counter, and anti-coincidence counters. The performance of AMS-01 is described elsewhere (Aguilar et al. 2002).

Data collection started on 1998 June 3. The orbital inclination was 517 and the geodetic altitude ranged from 320 to 390 km. The data were collected in four phases: (1) 1 day of check out before docking with the Mir space station, (2) 4 days while docked to Mir, (3) 3.5 days with AMS pointing directions within 0°, 20°, and 45° of the zenith, and (4) 0.5 days before descending, pointing toward the nadir.

The acceptance criterion of the trigger logic in the AMS-01 instrument was a four-fold coincidence between the signals from the four TOF planes. Only particles traversing the silicon tracker were accepted. Events crossing the anti-coincidence counters or producing multiple hits in the TOF layers were rejected. A prescaled subsample of 1 out of 1000 events was recorded with a dedicated minimum-bias configuration. This "unbiased trigger" required only the TOF coincidence.

The AMS-01 mission provided results on CR protons, helium, electrons, positrons, and light nuclei (Aguilar et al. 2002, 2007, 2010). During the flight, a total of 99 million triggers were recorded by the spectrometer, with 2.85 million helium nuclei and nearly 200,000 nuclei with charge Z > 2.

The identification of CR nuclei with AMS-01 was performed through the combination of independent measurements provided by the various detectors. The particle rigidity, R (momentum per unit charge, pc/Ze), was provided by the deflection of the reconstructed particle trajectory in the magnetic field. The velocity, β = v/c, was measured from the particle transit time between the four TOF planes along the track length. The reconstruction algorithm provided, together with the measured quantities R and β, an estimation of their uncertainties δR (from tracking) and δβ (from timing) that reflected the quality of the spectrometer in performing such measurements. The particle charge magnitude |Z| was obtained by the analysis of the multiple measurements of energy deposition in the four TOF scintillators up to Z = 2 (Aguilar et al. 2002) and the six silicon layers up to Z = 8 (Aguilar et al. 2010). The particle mass number, A, was therefore determined from the resulting charge, velocity, and rigidity:

$$\begin{equation} A = \frac{R Z e}{m_{n}\beta c^{2}}\sqrt{ 1 - \beta ^{2} }, \end{equation} \tag{ 1 }$$

where m_n is the nucleon mass.

The response of the detector was simulated using the AMS simulation program, based on GEANT-3.21 (Brun et al. 1987) and interfaced with the hadronic package RQMD (relativistic quantum molecular dynamics; Sorge 1995). The effects of energy loss, multiple scattering, nuclear interactions, and decays were included, as well as detector efficiency and resolution. After the flight, the detector was extensively calibrated at GSI, Darmstadt, with ion beams (He, C) and at the CERN Proton Synchrotron (CERN-PS), Geneva, with proton beams. This ensured that the performance of the detector and the analysis procedure were thoroughly understood.

Further details are found in Aguilar et al. (2002) and references therein.

3.1. Helium Isotopes

Given the large amount of statistics available for Z = 2 data, we considered only the highest quality data collected during the post-docking phase (3) and only while pointing toward the zenith. Data taken while passing near the South Atlantic Anomaly (latitude: 5°–45°S; longitude: 5°–85°W) were excluded. Only events taken when the energy interval 0.2–1.4 GeV nucleon⁻¹ was above the geomagnetic cutoff for both the isotopes ³He and ⁴He were kept; this corresponds to selecting the orbital regions with the highest geomagnetic latitudes, Θ_M, roughly |Θ_M| ≳ 0.9.

Furthermore, the acceptance was restricted to particles traversing the detector top-down within 30° of the positive z-axis. Events with poorly reconstructed trajectories were rejected through quality cuts on the associated χ² or consistency requirements between the two reconstructed half-tracks (Aguilar et al. 2010). To avoid biasing the reconstructed mass distributions, no cuts on the consistency of the TOF velocity versus tracker rigidity measurements were applied. We required that the velocity was measured with hits from at least three out of four TOF planes and that the rigidity was reconstructed with at least five out of six tracker layers. Approximately 18,000 nuclei with charge Z = 2 were selected in the energy range 0.2–1.4 GeV nucleon⁻¹. The charge was determined from the energy depositions in both the TOF and tracker layers. The kinetic energy per nucleon was measured with the TOF system, i.e., through the velocity β. In the energy range considered, the TOF energy resolution is comparable to that of the tracker.

The selected data are shown in Figure 1 distributed in the (β, R) plane. The two curves represent the exact relation between velocity β and rigidity R for a Z = 2 nucleus of mass number A = 3 (dashed line) and A = 4 (solid line), which is

$$\begin{equation} \beta = \left[ 1 + A^{2}\left(\frac{m_{n}c^{2}}{Ze R} \right)^{2} \right]^{-1/2}. \end{equation} \tag{ 2 }$$

The large dispersion of the measured data, apparent from Figure 1, indicates a relatively poor mass resolution in the separation of the two mass numbers. Under these conditions, any event-to-event separation (e.g., through a mass cut) is clearly inapplicable. In addition, the distribution of the reconstructed mass numbers (Equation (1)) exhibits asymmetric tails; so the standard Gaussian fit method (Seo et al. 1997) is not appropriate for describing the observed mass response of the instrument.

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In order to determine the isotopic ratios, it was therefore necessary to develop a comprehensive model for the complete response of the instrument to different masses. The mass resolution is influenced by the intrinsic time resolution of the TOF system and by the bending power of the magnet coupled with the intrinsic spatial resolution of the tracker. Physical processes such as multiple scattering, energy losses, and interactions along the particle path also contribute in shaping the reconstructed mass distributions. Thus, we modeled the AMS-01 mass response by means of our Monte Carlo (MC) simulation program, which includes all the aforementioned physical effects as well as the instrumental readout, providing a realistic description of particle tracking and timing on an event-by-event basis. The program was also tuned with data collected during the test beams. The resulting rigidity resolution δR/R and velocity resolution δβ/β are shown in Figure 2 for test beam data (filled circles) and MC events (histograms). It can be seen that the mass resolution, given approximately by

$$\begin{equation} \left(\frac{\delta A}{A} \right)^{2} = \left(\gamma ^{2} \frac{\delta \beta }{\beta } \right)^{2} + \left(\frac{\delta R}{R} \right)^{2} \;, \end{equation} \tag{ 3 }$$

was correctly simulated as the MC simulation agrees with the data within ∼2%.

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Using a sufficiently large number of simulated events of ³He and ⁴He and with the ratio ³He/⁴He of the detected events as a free parameter, we determined the best composition fit between the simulated mass distributions and the measured one. In these fits the overall normalization, $\mathcal {N}$, was also a free parameter. In principle, $\mathcal {N}$ should be fixed by the data, namely by the number of entries, $\mathcal {N}_{{\rm E}}$, of each mass histogram. Deviations of $\mathcal {N}$ from its expected value $\mathcal {N}_{{\rm E}}$ may indicate the presence of an unaccounted background, e.g., from charge misidentification.

The results of this procedure are shown in Figure 3, where the agreement between the measured mass histograms (filled circles) and the simulated histograms (lines) turned out to be very satisfactory. The fits of the ³He/⁴He mass composition ratios gave unique minima in all the energy bins considered. The uncertainties associated with these ratios were determined directly from the 1σ uncertainties in the χ² statistics of the fitting procedure. The χ² fitting method was cross-checked with the maximum likelihood method. The two methods gave the same results and very similar uncertainties. Double Gaussian fits were also performed in order to provide the corresponding mass resolution, δA/A, for each energy bin, defined as the ratio between the width and the mean.⁴⁴ The fitted ³He/⁴He ratios for all the energy bins considered from 200 MeV nucleon⁻¹ to 1.4 GeV nucleon⁻¹ are listed in Table 1, together with the χ²/df values, the number of events, the mass resolution, and correction factors discussed below.

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Table 1. Fit Results and Correction Factors for the Ratio ³He/⁴He Between 0.2 and 1.4 GeV of Kinetic Energy per Nucleon

Energy	Events	Fit Results	χ2/df	δA/A	ACorr	FCorr
0.20–0.30	2,660	0.125 ± 0.011	32.3/29	13.1%	1.12	0.97
0.30–0.44	3,553	0.158 ± 0.096	51.1/29	12.2%	1.05	0.98
0.44–0.64	3,867	0.182 ± 0.094	65.8/34	11.8%	1.00	0.98
0.64–0.95	4,142	0.211 ± 0.098	62.7/30	12.2%	0.99	0.98
0.95–1.40	3,813	0.223 ± 0.012	55.0/33	13.9%	0.99	0.98

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3.2. Top-Of-Instrument Corrections

The measured mass distribution of Figure 3 was fitted with an MC sample of mixed ³He and ⁴He nuclei that were sent through the same analysis chain (trigger, reconstruction, and data selection) as the data. The free parameter is the ratio ³He/⁴He of the two mass distributions corresponding to the recorded events. Hence, small corrections have to be performed in order to extract the ratio of interest, namely the ratio entering the instrument. These are referred to as Top-Of-Instrument (TOI) corrections.

3.2.1. Acceptance Corrections

The detector acceptance, $\mathcal {A}$, includes trigger efficiency, reconstruction efficiency, and selection efficiency. The acceptance was calculated using our MC simulation program. Nucleus trajectories were simulated in the energy range ∼0.05–40 GeV nucleon⁻¹. They were emitted downward from a square of length 3.9 m placed above the detector. In total, 110 million ³He and 550 million ⁴He nuclei were simulated. The physical processes involved and the detector response are very similar for the two isotopes, i.e., the resulting acceptances are quite similar in magnitude. The contributions from the detector acceptance mostly cancel in the ratio. The associated systematic errors also cancel. The only important factor in determining the isotopic ratios is the knowledge of any isotopic-dependent effects in the detector response. Mass-dependent features are expected from the following effects.

• 1.  
  Rigidity threshold. The instrument acceptance is rigidity dependent, because the tracks of slower particles are more curved, and it is less likely that they pass through both the upper and lower TOF counters and the tracking volume. Since, at the same kinetic energy per nucleon, the lighter isotope ³He has lower rigidity than the heavier ⁴He, the resulting acceptance, particularly at lower energies, is lower for ³He. Above 0.2 GeV nucleon⁻¹, the rigidity threshold affects the ratio by less than ∼1%.
• 2.  
  Multiple scattering. Coulomb scattering is slightly more pronounced for lighter particles. Since multiple scattering affects the event reconstruction and selection efficiency, the acceptance for the lighter isotope is smaller in the lowest energy region. The multiple scattering effect amounts to ∼10% at E ∼ 0.2 GeV nucleon⁻¹ and decreases with energy, down to ∼1% at E  ∼ 1 GeV nucleon⁻¹.
• 3.  
  Nuclear interactions. The attenuation of CRs after traversing the TOI material is isotope dependent and closely related to the inelastic cross sections, σ_int, for the interactions in the various layers of the detector material. For ³He and ⁴He, the attenuation due to interactions differs by ∼2% or less.

Figure 4 shows the ratio of the two acceptances for MC events after the successive application of the trigger, reconstruction, and then selection cuts. Deviations are appreciable below 0.4 GeV nucleon⁻¹ and mainly due to the event selection (filled squares). This indicates the dominance of the "multiple scattering effect" mentioned above, because the selection cuts acted against events with large scattering angles.

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These mass-dependent features, due to the particle dynamics in the detector, did not appreciably influence the AMS-01 trigger system. In Figure 5, we report the reconstructed mass distribution using data collected with the unbiased trigger (Section 2). The comparison of such unbiased data (circles) with all Z = 2 data collected from the flight (solid line, normalized to the unbiased data entries) shows no significant difference in the mass distribution.

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3.2.2. Nuclear Interactions

Table 2 lists the material between the top of the payload and the tracker: a multi-layer insulation (MLI) blanket, a low energy particle (LEP) shield, and two TOF layers of plastic scintillators supported by a honeycomb structure. In total there were ∼5 g cm⁻² of material above the tracking volume.

Table 2. Material Above the Tracker

Detector Element	Composition	Amount
MLI thermal blanket	C5 H4 O2	0.7 g cm−2
LEP shield	C	1.3 g cm−2
TOF scintillator	C/H = 1	2.1 g cm−2
TOF support structure	Al	1.0 g cm−2

Note. The column density is averaged over the angle of incidence.

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The RQMD interface used in the AMS simulation program provided a simulation of all the high energy hadronic collisions involving deuterons, ³He, ⁴He, and heavier ions. These effects give an appreciable contribution to the total acceptance of Section 3.2.1. The survival probability of ³He (⁴He) after traversing the TOI material of Table 2 varies between ∼90% (∼88%) at ∼0.2 GeV nucleon⁻¹ and ∼86% (∼86%) at ∼1.4 GeV nucleon⁻¹.

More critical is the fragmentation of ⁴He into ³He that required a dedicated correction. In this process, if only a neutron is "stripped" above the tracker, the event is recorded as a clean ³He event. The measured ³He/⁴He ratio is then distorted by incoming ⁴He that spill over into the ³He mass distribution. Note that the simulated mass distributions of Figure 3 are referred to the particle identities within the tracking volume, i.e., the ³He mass histograms of the figures (long-dashed lines) also contain the "extra" ³He nuclei generated as fragmentation products of ⁴He. Assuming that the kinetic energy per nucleon is maintained in the mass changing process, the ratio has been corrected for this effect. For each energy interval considered, the ratio η between the "extra" ³He and the total number of detected ⁴He was estimated. The isotopic ratio ³He/⁴He resulting from the composition fit $\mathcal {M}$ is then related to the TOI ratio $\mathcal {R}$ through the relation

$$\begin{equation} \mathcal {M} = \frac{ \mathcal {A}_{3} \,\phi _{3} + \eta \mathcal {A}_{4} \, \phi _{4} }{ \mathcal {A}_{4} \, \phi _{4} - \eta \mathcal {A}_{4} \, \phi _{4} } = \left(\frac{1}{1 - \eta } \right) \left[ \left(\frac{\mathcal {A}_{3}}{\mathcal {A}_{4}} \right) \mathcal {R} + \eta \right], \end{equation} \tag{ 4 }$$

where ϕ₃ and ϕ₄ are the incident (TOI) intensities of the two isotopes ($\mathcal {R}\equiv \phi _{3}/\phi _{4}$) and $\mathcal {A}_{3}$ and $\mathcal {A}_{4}$ the corresponding acceptances. Inverting Equation (4), we obtain the TOI ratio:

$$\begin{equation} \mathcal {R}= \left(\frac{\mathcal {A}_{4}}{\mathcal {A}_{3}} \right) \left[ 1 - \eta - \frac{\eta }{\mathcal {M}} \right] \mathcal {M}. \end{equation} \tag{ 5 }$$

We then define the TOI correction factors as ACorr ≡ $\mathcal {A}_{4} / \mathcal {A}_{3}$ for the acceptance and FCorr ≡ $1-\eta -\frac{\eta }{\mathcal {M}}$ for the fragmentation. Note that ACorr is the quantity shown in Figure 4 (filled squares). These values, to be applied as multiplicative factors to the fitted ratio, are also listed in Table 1. Such corrections are affected by ≲3% uncertainties in total, associated with the various physical and instrumental effects discussed here and in Section 3.2.1. All these errors and their role in the ³He/⁴He ratio are reviewed in Section 3.3.

3.2.3. δ-Ray Emission

The effect of δ-rays was included in our MC simulation. In our previous work (Aguilar et al. 2010), it was noted that energetic knock-on electrons affect the total acceptance at high energies. The production of δ-rays is proportional to the square of the primary particle charge, and the maximum energy of the δ-rays produced, E^δ_max, is proportional to the primary particle energy; for a nucleus of momentum Mγβc, approximately

$$\begin{equation} E^{\delta }_{\max } = 2 m_{e} c^{2} \beta ^{2} \gamma ^{2}. \end{equation} \tag{ 6 }$$

For high energy nuclei (E ≳ GeV nucleon⁻¹), the emitted electrons can reach the anti-coincidence counters and veto the event, leading to an energy- and charge-dependent trigger efficiency. At lower energy, the δ-rays curl up inside the tracking volume, affecting the reconstruction efficiency. The influence of δ-rays below 1.4 GeV nucleon⁻¹ is negligible in this analysis and their effect has no significant difference between isotopes at the same energy, as M ≫ m_e.

3.2.4. Background

The Z = 2 charge separation from Z < 2 and Z > 2 samples was studied with MC simulations and inflight data of e⁻, p, He, and heavier ions. Proton (ion) beam data at CERN-PS (GSI) provided additional validation at 0.75, 2.0, 3.6, and 8 GeV nucleon⁻¹ of kinetic energy (Alcaraz et al. 1999; Aguilar et al. 2002, 2010). The main potential source of background to the helium sample was protons and deuterons wrongly reconstructed as Z = 2 particles. Using the single TOF system or the single silicon tracker only, it can be seen, using flight data, that the probability that a Z = 1 particle is reconstructed as Z = 2 is below 10⁻³, thus affecting the helium sample by ≲1%. Using the combined measurements obtained from both the detectors, the probability of the wrong charge magnitude was estimated to be ∼10⁻⁷ over all energies (Alcaraz et al. 1999). Background from the less abundant Z > 2 particles is completely negligible compared to the statistical uncertainties in the He sample (the He/Li ratio is ∼200 at the energies considered).

3.2.5. Energy Losses and Resolution

Charged CRs that traverse the detector lose energy in the material above the tracking volume. The total energy loss has an appreciable effect on the lowest energy bins. The energy losses by Z = 2 nuclei were estimated and parameterized with the MC simulation program. We made an event-by-event correction to our data according to the average losses.

Once the above corrections are performed, the relation between the reconstructed energy of detected particles, E_REC, and their true energy, E_TOI, is still affected by the finite resolution of the measurement. The probability of a bin-to-bin migration P(E_REC|E_TOI) for He was estimated to affect only adjacent energy bins, to be symmetric, and barely isotope dependent. Through these matrix elements, we estimated that the measured ³He/⁴He ratio has an uncertainty of 1%–3% due to the resolution.

3.3. Uncertainty Estimate

In Figure 6, we summarize the various sources of uncertainty in the measurement of the ³He/⁴He ratio. Errors are organized in four categories.

• 1.  
  Mass fit. The dominant source of uncertainty (∼5%–9%) is that associated with fits to the mass distributions (Section 3.1). The errors were determined directly from the 1σ uncertainties in the χ² statistics of the fitting procedure. These errors are due to statistical fluctuations of the measured data and the inability of the spectrometer to separate the different masses within the mass resolution δA/A.
• 2.  
  Normalization. As discussed in Section 3.1, two parameters $\mathcal {M}$ (ratio) and $\mathcal {N}$ (normalization) were fitted. An ideal fit should lead to $\mathcal {N}$ equal to the number of measured events, $\mathcal {N}_{{\rm E}}$. We took the relative difference $\mathcal {N}$–$\mathcal {N}_{{\rm E}}$ as a source of systematic error (∼1%). Another contribution (∼1%) is due to the acceptance correction factors estimated with our MC simulation program (Section 3.2.1).
• 3.  
  Interactions. Our results rely partially on hadronic interaction models, as discussed in Section 3.2.2. Similarly to Wang et al. (2002), we assumed an uncertainty of 10% in the inelastic cross sections, which corresponds to ∼2% of systematic uncertainty. For the fragmentation channel ⁴He→³He, we assumed an uncertainty in the associated cross section equal to that cross section, obtaining an uncertainty of 2%–3% in the measured ³He/⁴He ratio. Uncertainties in the material thickness were found to be negligible.
• 4.  
  Resolution. As discussed in Section 3.2.5, our measurement is affected by the finite energy resolution of the TOF system. A systematic uncertainty of 1%–3% was estimated to account for this effect.

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The overall error (filled squares in Figure 6) is taken to be the sum in quadrature of the different contributions. All these uncertainties are also reported in Table 3.

Table 3. Uncertainty Summary for the Measured Isotopic Ratios

Error	3He/4He vs. Energy (GeV nucleon−1)					Ratios in 0.2–1.4 GeV nucleon−1
Type (Effect)	0.2–0.3	0.4–0.44	0.44–0.64	0.64–0.95	0.95–1.4	3He/4He	6Li/7Li	7Be/9 + 10Be	10B/11B
Mass fit (δA/A and statistics)	8.9%	6.1%	5.2%	4.7%	5.3%	4.5%	9.0%	15.9%	12.2%
Normalization ($\mathcal {N}$–$\mathcal {N}_{{\rm E}}$)	1.0%	0.9%	1.3%	1.1%	1.9%	1.5%	2.3%	3.0%	2.9%
Normalization (acceptance)	1.3%	1.2%	1.1%	1.1%	1.0%	0.5%	0.5%	0.6%	0.5%
Interactions (inelastic)	1.6%	1.6%	1.8%	1.9%	2.0%	2.0%	2.1%	2.7%	2.4%
Interactions (fragmentation)	2.8%	2.2%	1.8%	2.5%	2.3%	2.7%	2.4%	2.6%	2.4%
Resolution (δβ/β)	2.6%	1.7%	1.4%	0.8%	1.1%	0.6%	0.6%	0.6%	0.6%
Total uncertainty	10.0%	7.0%	6.2%	5.9%	6.6%	5.8%	9.8%	16.7%	13.0%

Note. The various contributions are described in Section 3.3.

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3.4. Lithium, Beryllium, and Boron

In our previous work (Aguilar et al. 2010), the lithium isotopic composition was determined between 2.5 and 6.3 GV of magnetic rigidity. Here we present a unified analysis of the lithium, beryllium, and boron isotopes between 0.2 and 1.4 GeV of kinetic energy per nucleon. In this measurement, we followed the same procedure as for the helium analysis. All the steps described in Section 3.1 were repeated for the study of the ratios ⁶Li/⁷Li, ⁷Be/(⁹Be+¹⁰Be), and ¹⁰B/¹¹B. In this section, we outline the essential parts of the Z > 2 analysis.

The capability of the spectrometer to separate isotopes close in mass was more critical for Z > 2 and the charge identification capabilities were limited by the use of tracker information only. However, the most limiting factor for the Li–Be–B study was the statistics. Hence, we performed the measurement with just one energy bin from 0.2 to 1.4 GeV nucleon⁻¹ and also included data from the Mir-docking (2) and post-docking, non-nadir pointing (3) phases (Section 2). As in our previous work, for data collected during phase (2), a geometric cut on the Mir shadow was applied to the acceptance (Aguilar et al. 2010). The geomagnetic regions considered and the event selection criteria were the same as for the helium analysis. Only four hits were required in the tracker, compared to five in the helium analysis. The particle charge was assigned using the identification algorithm described in Aguilar et al. (2010) and Tomassetti (2009) that was specifically optimized for the Z > 2 species.

Results from the mass composition fit are shown in Figure 7. For comparison, the measurement was also performed on the average ratio of ³He/⁴He over this energy range. The large statistical fluctuations of the Z > 2 data are apparent from the figure, in particular for the less abundant beryllium isotopes (400 events in total). However, the agreement between the measured masses (filled circles) and the simulated histograms (solid lines) was satisfactory. The TOI corrections to the measured composition followed the procedure described in Section 3.2. In contrast to He, the Z > 2 acceptances were found to be a bit smaller for the heavier isotopes (⁷Li, ^{9, 10}Be, and ¹¹B) than the lighter ones (⁶Li, ⁷Be, and ¹⁰B), indicating the dominance of nuclear interactions over other effects (see Section 3.2.1). The Z > 2 mass resolutions, δA/A, were found to be ∼8% larger than for the Z = 2 case, reflecting the slight charge dependence of the spectrometer performance in particle tracking and timing. Corrections for fragmentation were also performed, considering the channels ⁷Li→⁶Li, ^{10, 9}Be→⁷Be, and ¹¹B→¹⁰B.

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A summary of fit results, TOI corrections, and resolutions is given in Table 4.

Table 4. Fit Results and Correction Factors for the Ratios ³He/⁴He, ⁶Li/⁷Li, ⁷Be/(⁹Be+¹⁰Be), and ¹⁰B/¹¹B in the Range 0.2–1.4 GeV of Kinetic Energy per Nucleon

Ratio	Events	Fit Results	χ2/df	δA/A	ACorr	FCorr
3He/4He	18,035	0.174 ± 0.009	67.7/34	12.7%	1.02	0.98
6Li/7Li	1,046	0.951 ± 0.086	16.1/23	13.6%	0.97	0.99
7Be/9 + 10Be	400	1.512 ± 0.238	19.9/23	13.8%	0.96	0.99
10B/11B	1,598	0.494 ± 0.060	28.0/29	13.9%	0.96	0.99

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The errors were estimated as discussed in Section 3.3. The dominant error is that arising from the χ² fit procedure: the small Z > 2 statistics and the broader mass distributions led to less constrained composition fits. Background from helium was estimated not to affect the lithium measurement, as for He–Li charge separation the TOF information was still usable (Aguilar et al. 2010). More critical was the contamination in the Z = 4 sample from adjacent charges that led to larger systematic errors in the beryllium measurement. This channel was also limited by the inability to separate ⁹Be from ¹⁰Be. While for the other ratios it can be safely assumed that each charged species is composed of only two long-lived isotopes, a few percent of ¹⁰Be has been measured in the CR flux in addition to the more abundant isotopes ⁷Be and ⁹Be (Hams et al. 2004; Webber et al. 2002). We therefore determined the ratio ⁷Be/(⁹Be+¹⁰Be) simultaneously with the additional parameter ¹⁰Be/⁹Be in our composition fit. The latter was accounted for in the proper determination of the ratio ⁷Be/(⁹Be+¹⁰Be) and its corresponding error. As shown in Figure 8, the ratio ¹⁰Be/⁹Be is poorly constrained by the data (between ∼0 and ∼0.6 within 1σ of uncertainty). Figure 8 also shows that the uncertainty in the ¹⁰Be/⁹Be ratio has no dramatic consequences on the ⁷Be/(⁹Be+¹⁰Be) ratio, given the weak correlation of the two parameters. The contribution from inelastic collisions and fragmentation was estimated as described in Section 3.2.2. Similar values as for helium (∼2%–3%) were found for both the effects. Finally, the errors from the TOF energy resolution and from the MC acceptance estimation were smaller than 1%. The total error assigned to the measurements was obtained as the sum in quadrature of all the contributions noted. A detailed summary is provided in Table 3.

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In the previous sections, we have described the analysis procedure adopted for the determination of the ratios ³He/⁴He, ⁶Li/⁷Li, ⁷Be/(⁹Be+¹⁰Be), and ¹⁰B/¹¹B. The TOI corrections turned out to be of the same order of magnitude as the estimated uncertainties; hence, the gross features of the measured ratios were apparent directly from the fits to the mass distributions. The error from the fitting procedure was considerably larger than the other contributions. The most important limitations were the mass resolution (for He) and the limited statistics (for Li–Be–B). In particular, the mass resolution was limited by multiple scattering (affecting δR/R at ∼0.2 GeV nucleon⁻¹) and the TOF resolution (affecting δβ/β at ∼1.4 GeV nucleon⁻¹).

The results with all corrections applied are presented in Table 5. Results for the isotopic ratio ³He/⁴He as a function of the kinetic energy per nucleon are shown in Figure 9 between 0.2 and 1.4 GeV nucleon⁻¹ (filled circles). The error bars represent the total errors as discussed in Section 3.3. The figure also shows the existing data between 0.1 and 10 GeV nucleon⁻¹ measured by the balloon-borne experiments BESS (Wang et al. 2002), IMAX (Reimer et al. 1998), the first flight of SMILI (Beatty et al. 1993), Hatano et al. (1995), and Webber & Yushak (1983). Among these, our data are the only data collected directly in space. Our results agree well with data collected by BESS in its first flight in 1993.

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Figure 10 shows our results for Li–Be–B. The AMS-01 data are compared with measurements made by the space experiments CRIS on ACE (de Nolfo et al. 2001), Voyager (Webber et al. 2002), Ulysses (Connell 1998), IMP 7/8 (Garcia-Munoz 1977), ISEE 3 (Wiedenbeck & Greiner 1980), and with balloon data from ISOMAX (Hams et al. 2004) and GSFC (Hagen et al. 1977). Our results are consistent with these data within uncertainties, in particular with ISOMAX.

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In Figure 11(a), we report the ³He and ⁴He differential spectra. These spectra are obtained by the combination of the ³He/He and ⁴He/He fractions, given directly by the ³He/⁴He ratio, with the AMS-01 helium spectrum previously published in Alcaraz et al. (2000). The ³He and ⁴He data points and their errors were extracted through a logarithmic interpolation of helium data along our energy points. An additional 1% of error was added due to the interpolation procedure. Similarly, the resulting ⁴He spectrum has been further combined with the galactic deuteron spectrum published in Aguilar et al. (2002) to extract the ratio between deuterons, ²H, and their main progenitors ⁴He. The AMS-01 data analysis of ²H is described in Section 4.6 of Aguilar et al. (2002), where the extraction of the deuteron signal from the vast proton background is discussed quantitatively and the absolute deuteron spectrum is presented in different geomagnetic latitude ranges. The resulting ²H/⁴He ratio is shown in Figure 11(b) together with the previous experiments BESS (Wang et al. 2002), IMAX (de Nolfo et al. 2000), and Webber & Yushak (1983). While all the measurements give larger ²H/⁴He ratios than the model predictions (see below) by up to a factor of two, our results again show good agreement with the data from BESS. These data are also reported in Table 5.

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To describe our data, we show in all plots the model calculations of the conventional reacceleration model used in standard methodologies and described extensively elsewhere (Strong & Moskalenko 1998). Calculations have been made with the package GALPROP-v50.1.⁴⁵

GALPROP solves the diffusion-transport equation for a given source distribution and boundary conditions for the galactic CRs, providing steady-state solutions for the local interstellar spectra (LIS) for all the charged CRs up to Z = 28. The diffusion of CRs through the magnetic halo is described by means of a rigidity-dependent diffusion coefficient D = βD₀(R/R₀)^δ, where D₀ and R₀ fix the normalization, and the spectral index δ drives its rigidity dependence. The reacceleration of charged particles due to scattering on hydromagnetic waves is described as a diffusion in momentum space. This process is controlled by the Alfvén speed of plasma waves moving in the interstellar medium, v_A. The code also describes energy losses due to ionization or Coulomb scattering, and catastrophic losses over the galactic disk, making use of a large compilation of cross section data and decay rates. To decouple all the transport equations, the fragmentation network starts with the heaviest nucleus and works downward in mass, processing primary and all secondary nuclei produced by the cascade. This loop is repeated twice.

In the parameter setting considered here, no tuning was done to our isotopic data. The nucleon injection spectrum is taken as a "broken" power law in rigidity to better match our total helium and proton spectra from Aguilar et al. (2002). Two indices ν₁ and ν₂ were used below and above R_B. The cross section database was extended using the updated cross section list from the version v54 (Vladimirov et al. 2011), which includes the production of ²H and ³He from fragmentation of heavier isotopes. The transport parameters D₀, δ, and v_A are consistent with our B/C ratio from Aguilar et al. (2010). In our description, we used a cylindrically symmetric model of the galactic halo with radius $\mathcal {R}$ = 30 kpc and height z_h = 4 kpc. The relevant parameters are reported in Table 6; the remaining specifications are as in the file galdef_50p_599278 provided with the package.

Table 6. Propagation Parameter Set

Parameter	Name	Value
Injection, break value	RB (GV)	9
Injection, index below RB	ν1	1.80
Injection, index above RB	ν2	2.35
Diffusion, magnitude	D0 (cm2 s−1)	5 × 1028
Diffusion, index	δ	0.41
Diffusion, ref. rigidity	R0 (GV)	4
Reacceleration, Alfvén speed	vA (km s−1)	32
Galactic halo, radius	$\mathcal {R}$ (kpc)	30
Galactic halo, height	zh (kpc)	4
Solar modulation parameter	ϕ (MV)	450

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In the ratios of Figures 9–11, local interstellar (dashed lines) and heliospheric propagated (solid lines) calculations are shown. The heliospheric modulation is treated using the force field approximation (Gleeson & Axford 1968), with ϕ = 450 MV as the modulation parameter to characterize the modulation strength for 1998 June. This is also in accordance with the study performed in Wiedenbeck et al. (2009) over the full solar cycle 23. It should be noted, however, that the force field approximation has no predictive power, i.e., the value employed for the parameter ϕ is contextual to the propagation framework adopted to predict the interstellar spectra of the CR elements. For instance, the deuteron flux in Aguilar et al. (2002) was described using ϕ = 650 MV after assuming a pure power-law energy spectrum in the ²H LIS.

Though large uncertainties are still present in the heliospheric propagation, the general trend is that higher modulation levels correspond to lower values of the ³He/⁴He ratio. AMS-01 and BESS data come from periods of relatively quiet solar activity as do data from Webber & Yushak (ϕ ≈ 400–650 MV). In particular, the periods of 1998 June (AMS-01 flight) and 1993 July (BESS flight) were characterized by very similar solar conditions according to the sunspot data (Temmer et al. 2002) and can be directly compared. Stronger modulations were present when IMAX (ϕ ≈ 700–850 MV) and SMILI (ϕ ≈ 1200–1300 MV) were active.

In summary, the secondary to primary ratio ³He/⁴He, which is much more sensitive to the propagation parameters, seems to be well described by the model under these astrophysical assumptions. The model is also consistent with the Z > 2 ratios of Figure 10, though large errors are present in the current data. As the Li–Be–B elements are of secondary origin, these ratios are less sensitive to the galactic transport and may be useful to investigate the nuclear aspects of the CR propagation (fragmentation, decay, and breakup). Conversely, our ²H/⁴He data of Figure 11(b) give a larger ratio than the model predictions, and this tendency is also apparent from the other experiments. Understanding this possible discrepancy may require a thorough investigation of the ²H production cross sections, in particular for the reactions induced by CR protons and helium nuclei.

The AMS-01 detector measured charged CRs during 10 days aboard the Space Shuttle Discovery in 1998 June. Owing to the large number of helium events collected and the absence of atmospheric effects, we have determined precisely the ratio ³He/⁴He in the kinetic energy range from 0.2 to 1.4 GeV nucleon⁻¹. The average isotopic ratios ⁶Li/⁷Li, ⁷Be/(⁹Be+¹⁰Be), and ¹⁰B/¹²B have been measured in the same energy range. The ratio ²H/⁴He and the spectra of ³He and ⁴He are also reported. Our results agree well with the previous data from BESS and ISOMAX and can provide further constraints to the astrophysical parameters of CR propagation. In the analysis procedure adopted in this work, MC simulations were essential for understanding the instrument performance, its acceptance, the role of interactions and for modeling the mass distributions. We expect, with AMS-02, to achieve much more precise results over wider energy ranges.

The support of INFN, Italy, ETH Zurich, the University of Geneva, the Chinese Academy of Sciences, Academia Sinica and National Central University, Taiwan, the RWTH Aachen, Germany, the University of Turku, the University of Technology of Helsinki, Finland, the US DOE and MIT, CIEMAT, Spain, LIP, Portugal and IN2P3, France is gratefully acknowledged. The success of the first AMS mission is due to many individuals and organizations outside of the collaboration. The support of NASA was vital in the inception, development, and operation of the experiment. Support from the Max-Planck Institute for Extraterrestrial Physics, from the space agencies of Germany (DLR), Italy (ASI), France (CNES), and China and from CSIST, Taiwan also played important roles in the success of AMS.