Energy Degradation in Cosmic-Ray Nuclear Spallation Reactions: Relaxing the Straight-ahead Approximation

Abstract

We present the first critical look at the so-called straight-ahead approximation, the assumption that the nuclear spallation products of cosmic rays retain the same energy per nucleon as their progenitors, a value typically used in the calculations of the propagation of cosmic rays. To that end we devise a simple microscopic prescription to take into account such nuclear collisional energy losses; i.e., we relax the straight-ahead approximation. We study the effect in a leaky-box-type calculation using isotopic and elemental abundance ratios of carbon as an example. We find that the effect is, in general, small. It amounts to a slight depression in the calculated ratios (∼5%-6%) in some cases around the peak of ∼1 GeV nucleon<SUP>-1</SUP>, even after we have accounted for solar modulation effects. The effect is strongest for ratios of secondary isotopes (with appreciable ΔA) to primary elements and is practically unobservable for ratios of secondary isotopes to secondary isotopes with similar values of A. The effect may not be negligible, however, since the precision of many measured elemental cosmic-ray abundance ratios has reached the 5% level.