Formula for calculating partial cross sections for nuclear reactions of nuclei withE≳200 MeV/nucleon in hydrogen targets

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Abstract
In this paper we describe a new formula for calculating the partial cross sections for the production of secondary fragments with energy ≳200 MeV/nucleon in hydrogen targets. This formula and the systematics of these cross sections are based on fragmentation studies using 42 beams of 12 separate nuclei between Z=6 and 28. This has resulted in the measurement of more than 100 secondary elemental cross sections and over 300 secondary isotopic cross sections. The systematics of these cross sections allow us to write the cross section formula as a product of three essentially independent terms, one which describes the elemental cross sections, another the isotopic cross sections, and a third term describing the energy dependence. Overall, this formula, which is considerably simpler than earlier semiempirical formulations, is able to predict the cross sections in hydrogen for Z=4–28, A=7–60 nuclei above ∼200 MeV/nucleon to an accuracy ∼10% or better—a substantial improvement over earlier formulations.