The power law for mass-dependent nuclear reactions

Many authors have parameterized the nuclear mass dependence of their intermediate and high energy hadron-nucleus data as a power law proportional to A\textasciicircum $\alpha $. A derivation of this law will be presented in this talk, with a simple expression for the exponent $\alpha $ in terms of the hadron-nucleon total cross section SGT and a nuclear radius r0A\textasciicircum 1/3 fm. These exponents have been compiled for many examples of intermediate and high energy hadron-nucleus total, total reaction, and inclusive quasifree cross sections for masses from A$=$12 through 238. These fitted exponents, plotted against SGT, form smooth trends. The exponents for total and total reaction cross sections are similar to the derived expression for r0$=$1.6 fm, while those for quasifree cross sections are similar to the expression for r0$=$1.2 fm. Computations in the Glauber model follow these same trends.