Individual charge changing fragmentation cross sections of relativistic nuclei in hydrogen, helium, and carbon targets

In this paper we describe individual elemental cross sections. Over 100 of these cross sections have been measured by studying the fragmentation of beams of 12 charges ranging from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ to ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$ in hydrogen, helium, and carbon targets. The energies of the beams ranged from ∼300 to 1700 MeV/nucleon. The relative cross sections in hydrogen, helium, and carbon targets are examined as a function of both beam charge and energy. Limits are placed on the energy region in which the concept of factorization or scaling of cross sections for different beam charges and targets applies. The approach of these elemental cross sections to the asymptotic high-energy values is examined as a function of the beam charge and the charge change. The systematics of the energy dependence of these cross sections is also described in terms of the beam charge and the charge change. Another important systematic in our data is a regular decrease in the elemental cross sections into a particular charge, $Z_f$, with increasing charge change at a constant energy. It is found that this regular behavior of the cross sections follows a simple exponential law in the charge change, $Z_B$-$Z_f$. This has important implications for constructing an empirical formula to describe these cross sections, as well as having theoretical implications.