Nucleus-nucleus total cross sections for light nuclei at 1.55 and 2.89 GeV/cper nucleon

We have measured total cross sections for protons, dueterons, $\alpha$ particles, and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ on hydrogen, deuterium, helium, and carbon targets at 1.55 and 2.89 GeV/c nucleon using the "good geometry" transmission method. In addition, we measured the inelastic cross sections and elastic slope parameters for reactions initiated by deuterons, $\alpha$ particles, and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. Our results are in good agreement with Glauber theory predictions, but the factorization relation ${\sigma }_T\mathrm{}\left(\mathrm{AA}\right)=\frac{{\left[{\sigma }_T\mathrm{}\right(\mathrm{AB}\left)\right]}^2}{{\sigma }_T\mathrm{}\left(\mathrm{BB}\right)\mathrm{}}$ is not a good guide. We find ${\sigma }_T\simeq 144{({A_T}^{\frac{1}{3}}-{A_p}^{\frac{1}{3}}-1.48)}^2$ mb and ${\sigma }_{\mathrm{IN}}\simeq 78{({A_T}^{\frac{1}{3}}+{A_p}^{\frac{1}{3}}-1.25)}^2$ mb, where $A_T\left(A_p\right)$ is the atomic mass number of the target (projectile).