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We take a phenomenological approach in a minimal model to understand thespectral intensity of secondary cosmic-ray particles like positrons,antiprotons, Lithium, Beryllium and Boron. Our analysis shows that cosmic raysat $\sim$ GeV energies pass through a significant amount of matter in regionssurrounding the sources. This grammage decreases with increasing cosmic-rayenergy and becomes negligible beyond $\sim 100$ GeV. During the subsequentpropagation in the interstellar medium cosmic rays of all energies up to $\sim10^5$ GeV/$n$ pass through about 1-2 g cm$^{-2}$ of matter before leaking intothe intergalactic medium. It is in the interstellar medium that the bulk of thepositrons and antiprotons are generated. Also cosmic-ray nuclei like C, N, andO at all energies generate additional amounts of Li, Be and B nuclei with aspectrum similar to those of C, O etc. The implications of these findings ofthe minimal model to the observations of gamma rays and also the importance ofspatial and temporal discreteness of cosmic-ray sources for modeling cosmic-raypropagation are briefly pointed out.

A Minimal Model for Understanding Secondary Cosmic Rays