The nuclei fraction in cosmic rays (CR) far exceeds the fraction of other CR species, such as antiprotons, electrons, and positrons. Thus the majority of information obtained from CR studies is based on interpretation of isotopic abundances using CR propagation models where the nuclear data and isotopic production cross sections in p- and -induced reactions are the key elements. This paper presents an introduction to the astrophysics of CR and diffuse α-rays and discusses some of the puzzles that have emerged recently due to more precise data and improved propagation models. Merging with cosmology and particle physics, astrophysics of CR has become a very dynamic field with a large potential of breakthrough and discoveries in the near future. Exploiting the data collected by the CR experiments to the fullest requires accurate nuclear cross sections.
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