Energy dependence of proton-nucleus reaction cross sections

Reaction-cross-section data for proton-nucleus scattering up to 1 GeV have been analyzed in a black-disk model. Simple phenomenological relations are derived, which make it possible to predict the energy dependence of proton-nucleus reaction cross sections. The relations require only the total cross sections in nucleon-nucleon scattering and the matter densities of the proton and the target nucleus.

Figure 1

Matter densities for the protons (dashed cuves) and the six targets (solid curves), with their centers of mass separated with $R_1$. The value of $R_1$ was in this case obtained from Eq. (1) and the experimental values for proton nucleus reaction cross sections obtained at 65 MeV [3].

Figure 2

The upper part of the figure shows the crossing densities ${\rho }_x$ obtained in the proton scattering from ${}^{12}\mathrm{C}$. The lower part shows the product of ${\rho }_x$ and the nucleon-nucleon total cross section ${\sigma }_{\mathit{NN}}^{\mathrm{tot}}(E){}^{2/3}$. The line shows the average value for the product.

Figure 3

The solid curves show the reaction cross sections calculated with the values of the exponent α calculated from Eq. (3). The dashed curves show the prediction when the exponent is 3/2. The dot-dashed curves show the prediction with α calculated from Eq. (3) and $C_1$ calculated from Eq. (4).