Cosmic-ray deuterium and helium-3 nuclei

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Abstract
Assuming that cosmic-ray deuterons and helium-3 nuclei are of secondary origin, we show that a unique determination of both the cosmic-ray path-length and the residual interplanetary field modulation at solar minimum may be made from a comparison of the calculated and measured intensities of these two nuclei. This determination does not depend on any assumptions regarding either the source spectra or the unmodulated proton to alpha particle ratio of the primary cosmic rays. The production of deuterium and helium-3 by cosmic-ray interactions in the galaxy is calculated considering energy-dependent cross sections, interaction kinematics, and demodulated cosmic-ray spectra. The resulting flux at the earth is obtained by taking into account leakage from the galaxy, ionization losses, nuclear breakup, and modulation. From a comparison of these calculations with the measured deuterium and helium-3 intensities at the earth, we conclude that within the experimental uncertainties all the data can be understood in terms of an energy-independent cosmic-ray path-length of 4 ± 1 g/cm2 and a residual interplanetary field modulation at solar minimum of the form exp(–η/Pβ) with η = 0.4 ± 0.1 BV, where P and β are the rigidity and velocity.
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