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A precision measurement of the nitrogen flux with rigidity (momentum per unit charge) from 2.2 GV to 3.3 TV based on $2.2\times {10}^6$ events is presented. The detailed rigidity dependence of the nitrogen flux spectral index is presented for the first time. The spectral index rapidly hardens at high rigidities and becomes identical to the spectral indices of primary He, C, and O cosmic rays above $\sim 700\mathrm{GV}$. We observed that the nitrogen flux ${\mathrm{\Phi }}_{\mathrm{N}}$ can be presented as the sum of its primary component ${\mathrm{\Phi }}_{\mathrm{N}}^P$ and secondary component ${\mathrm{\Phi }}_{\mathrm{N}}^S$, ${\mathrm{\Phi }}_{\mathrm{N}}={\mathrm{\Phi }}_{\mathrm{N}}^P+{\mathrm{\Phi }}_{\mathrm{N}}^S$, and we found ${\mathrm{\Phi }}_{\mathrm{N}}$ is well described by the weighted sum of the oxygen flux ${\mathrm{\Phi }}_{\mathrm{O}}$ (primary cosmic rays) and the boron flux ${\mathrm{\Phi }}_{\mathrm{B}}$ (secondary cosmic rays), with ${\mathrm{\Phi }}_{\mathrm{N}}^P=(0.090\pm 0.002)\times {\mathrm{\Phi }}_{\mathrm{O}}$ and ${\mathrm{\Phi }}_{\mathrm{N}}^S=(0.62\pm 0.02)\times {\mathrm{\Phi }}_{\mathrm{B}}$ over the entire rigidity range. This corresponds to a change of the contribution of the secondary cosmic ray component in the nitrogen flux from 70% at a few GV to $<30\%$ above 1 TV.

This paper presents the measurements of the angular differential cross sections for the forward production of He, Li, Be, B, C, and N nuclei in the fragmentation process of a $400\text{MeV/nucleon}{}^{16}\mathrm{O}$ beam interacting with a graphite target. Due to the limited data available in this energy regime, these measurements of nuclear fragmentation cross sections are relevant to improve nuclear interaction models for particle therapy and space radioprotection applications. The data analyzed in this paper were collected during a measurement campaign carried out at the GSI Helmholtz Center for Heavy Ion Research facility in Darmstadt (Germany) by the FOOT Collaboration. The results are compared with similar results found in the literature and with a previous FOOT measurement of the same process, using the same setup, from a previous pilot run performed at GSI. The pilot run data, however, had limited statistics and only allowed for the measurement of elemental fragmentation cross sections integrated in the setup acceptance. This data set, with statistics more than 100 times larger compared to the data collected in the previous run, enabled the measurement of angular differential cross sections, fully exploiting the granularity of the FOOT $\mathrm{\Delta }E$-TOF (time-of-flight) system. Furthermore, a better comprehension of the FOOT apparatus allowed to improve the analysis techniques, leading to a reduction in the final systematic uncertainties. The cross section results have been compared with some of the prominent Monte Carlo models of FLUKA and Geant4 dedicated to the energy range of interest for light ion fragmentation physics.

A precision measurement by the Alpha Magnetic Spectrometer on the International Space Station of the positron fraction in primary cosmic rays in the energy range from 0.5 to 350 GeV based on $6.8\times {10}^6$ positron and electron events is presented. The very accurate data show that the positron fraction is steadily increasing from 10 to $\sim 250\mathrm{GeV}$, but, from 20 to 250 GeV, the slope decreases by an order of magnitude. The positron fraction spectrum shows no fine structure, and the positron to electron ratio shows no observable anisotropy. Together, these features show the existence of new physical phenomena.

A precision measurement by AMS of the positron fraction in primary cosmic rays in the energy range from 0.5 to 500 GeV based on 10.9 million positron and electron events is presented. This measurement extends the energy range of our previous observation and increases its precision. The new results show, for the first time, that above $\sim 200\mathrm{GeV}$ the positron fraction no longer exhibits an increase with energy.

We report the observation of new properties of primary cosmic rays He, C, and O measured in the rigidity (momentum/charge) range 2 GV to 3 TV with $90\times {10}^6$ helium, $8.4\times {10}^6$ carbon, and $7.0\times {10}^6$ oxygen nuclei collected by the Alpha Magnetic Spectrometer (AMS) during the first five years of operation. Above 60 GV, these three spectra have identical rigidity dependence. They all deviate from a single power law above 200 GV and harden in an identical way.

We report the properties of primary cosmic-ray sulfur (S) in the rigidity range 2.15 GV to 3.0 TV based on $0.38\times {10}^6$ sulfur nuclei collected by the Alpha Magnetic Spectrometer experiment (AMS). We observed that above 90 GV the rigidity dependence of the S flux is identical to the rigidity dependence of Ne-Mg-Si fluxes, which is different from the rigidity dependence of the He-C-O-Fe fluxes. We found that, similar to N, Na, and Al cosmic rays, over the entire rigidity range, the traditional primary cosmic rays S, Ne, Mg, and C all have sizeable secondary components, and the S, Ne, and Mg fluxes are well described by the weighted sum of the primary silicon flux and the secondary fluorine flux, and the C flux is well described by the weighted sum of the primary oxygen flux and the secondary boron flux. The primary and secondary contributions of the traditional primary cosmic-ray fluxes of C, Ne, Mg, and S (even $Z$ elements) are distinctly different from the primary and secondary contributions of the N, Na, and Al (odd $Z$ elements) fluxes. The abundance ratio at the source for $\mathrm{S}/\mathrm{Si}$ is $0.167\pm 0.006$, for $\mathrm{Ne}/\mathrm{Si}$ is $0.833\pm 0.025$, for $\mathrm{Mg}/\mathrm{Si}$ is $0.994\pm 0.029$, and for $\mathrm{C}/\mathrm{O}$ is $0.836\pm 0.025$. These values are determined independent of cosmic-ray propagation.

We present the analysis of the muon events with all muon multiplicities collected during 21804 h of operation of the first LVD tower. The measured depth-angular distribution of muon intensities has been used to obtain the normalization factor A the power index $\gamma$ of the primary all-nucleon spectrum, and the ratio $R_c$ of the prompt muon flux to that of π mesons—the main parameters which determine the spectrum of cosmic ray muons at the sea level. The values of $\gamma =2.77\mathrm{}\pm 0.05$ (68% C.L.) and $R_c<2.0\mathrm{}\times {10}^{-3}$ (95% C.L.) have been obtained. The upper limit to the prompt muon flux favors the models of charm production based on QGSM and the dual parton model.

A precise measurement of the proton flux in primary cosmic rays with rigidity (momentum/charge) from 1 GV to 1.8 TV is presented based on 300 million events. Knowledge of the rigidity dependence of the proton flux is important in understanding the origin, acceleration, and propagation of cosmic rays. We present the detailed variation with rigidity of the flux spectral index for the first time. The spectral index progressively hardens at high rigidities.

Precision measurements by the Alpha Magnetic Spectrometer (AMS) on the International Space Station of the deuteron ($D$) flux are presented. The measurements are based on $21\times {10}^6$ $D$ nuclei in the rigidity range from 1.9 to 21 GV collected from May 2011 to April 2021. We observe that over the entire rigidity range the $D$ flux exhibits nearly identical time variations with the $p$, ${}^3\mathrm{He}$, and ${}^4\mathrm{He}$ fluxes. Above 4.5 GV, the $D/{}^4\mathrm{He}$ flux ratio is time independent and its rigidity dependence is well described by a single power law $\propto R^{\mathrm{\Delta }}$ with ${\mathrm{\Delta }}_{D/{}^4\mathrm{He}}=-0.108\pm 0.005$. This is in contrast with the ${}^3\mathrm{He}/{}^4\mathrm{He}$ flux ratio for which we find ${\mathrm{\Delta }}_{{}^3\mathrm{He}/{}^4\mathrm{He}}=-0.289\pm 0.003$. Above $\sim 13\mathrm{GV}$ we find a nearly identical rigidity dependence of the $D$ and $p$ fluxes with a $D/p$ flux ratio of $0.027\pm 0.001$. These unexpected observations indicate that cosmic deuterons have a sizable primarylike component. With a method independent of cosmic ray propagation, we obtain the primary component of the $D$ flux equal to $9.4\pm 0.5\%$ of the ${}^4\mathrm{He}$ flux and the secondary component of the $D$ flux equal to $58\pm 5\%$ of the ${}^3\mathrm{He}$ flux.

We report the observation of new properties of primary iron (Fe) cosmic rays in the rigidity range 2.65 GV to 3.0 TV with $0.62\times {10}^6$ iron nuclei collected by the Alpha Magnetic Spectrometer experiment on the International Space Station. Above 80.5 GV the rigidity dependence of the cosmic ray Fe flux is identical to the rigidity dependence of the primary cosmic ray He, C, and O fluxes, with the $\mathrm{Fe}/\mathrm{O}$ flux ratio being constant at $0.155\pm 0.006$. This shows that unexpectedly Fe and He, C, and O belong to the same class of primary cosmic rays which is different from the primary cosmic rays Ne, Mg, and Si class.

A precision measurement by AMS of the antiproton flux and the antiproton-to-proton flux ratio in primary cosmic rays in the absolute rigidity range from 1 to 450 GV is presented based on $3.49\times 10^5$ antiproton events and $2.42\times 10^9$ proton events. The fluxes and flux ratios of charged elementary particles in cosmic rays are also presented. In the absolute rigidity range $\sim 60$ to $\sim 500\mathrm{GV}$, the antiproton $\overline{p}$, proton $p$, and positron $e^{+}$ fluxes are found to have nearly identical rigidity dependence and the electron $e^{-}$ flux exhibits a different rigidity dependence. Below 60 GV, the ($\overline{p}/p$), ($\overline{p}/e^{+}$), and ($p/e^{+}$) flux ratios each reaches a maximum. From $\sim 60$ to $\sim 500\mathrm{GV}$, the ($\overline{p}/p$), ($\overline{p}/e^{+}$), and ($p/e^{+}$) flux ratios show no rigidity dependence. These are new observations of the properties of elementary particles in the cosmos.

We present an analysis of muon events with all muon multiplicities collected during 21804 h of operation of the first Large Volume Detector tower. The measured angular distribution of muon intensity has been converted to the “depth–vertical-intensity” relation in the depth range from 3 to 12 km w.e. The analysis of this relation allowed us to derive the power index $\gamma$ of the primary all-nucleon spectrum: $\gamma =2.78\mathrm{}\pm \mathrm{0.05.}$ The “depth–vertical-intensity” relation has been converted to standard rock and the comparison with the data of other experiments has been done. We also present the derived vertical muon spectrum at sea level.

The measurement of fragmentation cross sections for nuclei up to ${}^{56}\mathrm{Fe}$ on light elements found in the human body (e.g., H, C, and O) is of fundamental importance for particle therapy (PT) and radioprotection in space (RPS), as well as for advancing cosmic-ray physics. These measurements can significantly improve the accuracy of dose calculations for patients during PT treatments and for astronauts exposed to cosmic radiation during deep-space missions. Among the many ions of interest, ${}^{16}\mathrm{O}$ is used in PT and is the most abundant species within the HZE component of cosmic rays. This paper presents the results of angular nuclear fragmentation cross sections for the production of He, Li, Be, B, C, and N nuclei in the interaction of a $400\mathrm{MeV}/\mathrm{nucleon}$ ${}^{16}\mathrm{O}$ beam with a hydrogen and polyethylene target. The fragmentation on the hydrogen was measured by combining the results on polyethylene with recent measurements on a graphite target. While the fragmentation on hydrogen is fundamental for improving nuclear interaction models, allowing more accurate predictions of dose distributions in PT and RPS, polyethylene has proven to be a promising shielding material in radiation protection models. The data analyzed were collected in 2021 at the GSI Helmholtz Center for Heavy Ion Research facility in Darmstadt (Germany) by the FOOT Collaboration. All results were compared with different Monte Carlo models for light ion fragmentation physics in the energy range of interest implemented in FLUKA and Geant4.

Knowledge of the precise rigidity dependence of the helium flux is important in understanding the origin, acceleration, and propagation of cosmic rays. A precise measurement of the helium flux in primary cosmic rays with rigidity (momentum/charge) from 1.9 GV to 3 TV based on 50 million events is presented and compared to the proton flux. The detailed variation with rigidity of the helium flux spectral index is presented for the first time. The spectral index progressively hardens at rigidities larger than 100 GV. The rigidity dependence of the helium flux spectral index is similar to that of the proton spectral index though the magnitudes are different. Remarkably, the spectral index of the proton to helium flux ratio increases with rigidity up to 45 GV and then becomes constant; the flux ratio above 45 GV is well described by a single power law.

Precision results on cosmic-ray electrons are presented in the energy range from 0.5 GeV to 1.4 TeV based on $28.1\times {10}^6$ electrons collected by the Alpha Magnetic Spectrometer on the International Space Station. In the entire energy range the electron and positron spectra have distinctly different magnitudes and energy dependences. The electron flux exhibits a significant excess starting from $42.1_{-5.2}^{+5.4}\mathrm{GeV}$ compared to the lower energy trends, but the nature of this excess is different from the positron flux excess above $25.2\pm 1.8\mathrm{GeV}$. Contrary to the positron flux, which has an exponential energy cutoff of $810_{-180}^{+310}\mathrm{GeV}$, at the $5\sigma$ level the electron flux does not have an energy cutoff below 1.9 TeV. In the entire energy range the electron flux is well described by the sum of two power law components. The different behavior of the cosmic-ray electrons and positrons measured by the Alpha Magnetic Spectrometer is clear evidence that most high energy electrons originate from different sources than high energy positrons.

We present the precision measurement from May 2011 to May 2017 (79 Bartels rotations) of the proton fluxes at rigidities from 1 to 60 GV and the helium fluxes from 1.9 to 60 GV based on a total of $1\times {10}^9$ events collected with the Alpha Magnetic Spectrometer aboard the International Space Station. This measurement is in solar cycle 24, which has the solar maximum in April 2014. We observed that, below 40 GV, the proton flux and the helium flux show nearly identical fine structures in both time and relative amplitude. The amplitudes of the flux structures decrease with increasing rigidity and vanish above 40 GV. The amplitudes of the structures are reduced during the time period, which started one year after solar maximum, when the proton and helium fluxes steadily increase. Above $\sim 3\mathrm{GV}$ the $p/\mathrm{He}$ flux ratio is time independent. We observed that below $\sim 3\mathrm{GV}$ the ratio has a long-term decrease coinciding with the period during which the fluxes start to rise.

We report the properties of sodium (Na) and aluminum (Al) cosmic rays in the rigidity range 2.15 GV to 3.0 TV based on 0.46 million sodium and 0.51 million aluminum nuclei collected by the Alpha Magnetic Spectrometer experiment on the International Space Station. We found that Na and Al, together with nitrogen (N), belong to a distinct cosmic ray group. In this group, we observe that, similar to the N flux, both the Na flux and Al flux are well described by the sums of a primary cosmic ray component (proportional to the silicon flux) and a secondary cosmic ray component (proportional to the fluorine flux). The fraction of the primary component increases with rigidity for the N, Na, and Al fluxes and becomes dominant at the highest rigidities. The $\mathrm{Na}/\mathrm{Si}$ and $\mathrm{Al}/\mathrm{Si}$ abundance ratios at the source, $0.036\pm 0.003$ for $\mathrm{Na}/\mathrm{Si}$ and $0.103\pm 0.004$ for $\mathrm{Al}/\mathrm{Si}$, are determined independent of cosmic ray propagation.

Precise knowledge of the charge and rigidity dependence of the secondary cosmic ray fluxes and the secondary-to-primary flux ratios is essential in the understanding of cosmic ray propagation. We report the properties of heavy secondary cosmic ray fluorine F in the rigidity $R$ range 2.15 GV to 2.9 TV based on 0.29 million events collected by the Alpha Magnetic Spectrometer experiment on the International Space Station. The fluorine spectrum deviates from a single power law above 200 GV. The heavier secondary-to-primary F/Si flux ratio rigidity dependence is distinctly different from the lighter B/O (or B/C) rigidity dependence. In particular, above 10 GV, the $\frac{\mathrm{F}/\mathrm{Si}}{\mathrm{B}/\mathrm{O}}$ ratio can be described by a power law $R^{\delta }$ with $\delta =0.052\pm 0.007$. This shows that the propagation properties of heavy cosmic rays, from F to Si, are different from those of light cosmic rays, from He to O, and that the secondary cosmic rays have two classes.

We report the properties of precision time structures of cosmic nuclei He, Li, Be, B, C, N, and O fluxes over an 11-year solar cycle from May 2011 to November 2022 in the rigidity range from 1.92 to 60.3 GV. The nuclei fluxes show similar but not identical time variations with amplitudes decreasing with increasing rigidity. In particular, below 3.64 GV the Li, Be, and B fluxes, and below 2.15 GV the C, N, and O fluxes, are significantly less affected by solar modulation than the He flux. We observe that these differences in solar modulation are linearly correlated with the differences in the spectral indices of the cosmic nuclei fluxes. This shows, in a model-independent way, that solar modulation of galactic cosmic nuclei depends on their spectral shape. In addition, solar modulation differences due to nuclei velocity dependence on the mass-to-charge ratio ($A/Z$) are not observed.