Updated Formula for Calculating Partial Cross Sections for Nuclear Reactions of Nuclei with Z ≤ 28 and E > 150 MeV Nucleon–1 in Hydrogen Targets

We have developed an updated and expanded version of our parametric formulation to calculate the charge-changing and isotopic cross sections for reactions of energetic Z ≤ 28 nuclei in hydrogen targets. The goal of this formulation is the calculation of the now-available measured cross sections, which include greater than 98% of all incoming Z ≤ 3 in the Galactic cosmic rays, to an improved level of accuracy. Two important systematics greatly facilitate this parametric formulation. The first is related to the fact that the elemental cross sections into a particular Zf from a beam charge Zi can be well represented by an exponential function of the difference Zi - Zf. The second is related to the fact that the width of the individual mass distributions for a given fragment charge follow closely a Gaussian distribution centered on a value of the neutron excess that can be described in a systematic way. These two systematics alone provide the basis for predicting 75% of all of the measured cross sections. The energy dependence of the cross sections has also been completely revised using newer data at both higher and lower energies. These new cross sections are then used in a set of Galactic cosmic-ray propagation calculations. These calculations made using the leaky box model correctly predict the measured Li, Be, and B ratios and the measured isotopic ratios of those charges at ~100 MeV nucleon-1 to the accuracy of the experimental data itself. They also correctly predict the recently measured energy dependence of the K-capture ratios 49Ti/49V and 51V/51Cr, assuming a solar modulation parameter = 300-400 MV at the time of measurement. The new cross sections also reduce significantly the differences between the path lengths required to simultaneously predict the measured cosmic-ray B/C and Z = 21-23/Fe ratios at ~1 GeV nucleon-1. The new cross sections for B and Z = 21-23 nuclei production are ~15% less at 10 GeV nucleon-1 than earlier formulations. This leads to a significantly smaller cosmic-ray escape length dependence on rigidity for Galactic propagation models than earlier calculations.