On the Yield of Nuclear Reactions with Heavy Elements

The cross sections for different kinds of nuclear reactions are calculated as functions of the energy of the bombarding particles by means of statistical methods. Their application is restricted to heavy elements ($A>\mathrm{}50\mathrm{}$) and to bombarding energies greater than 1 Mev. The excitation curves of several ($p,n$)-reactions have been measured for elements with $A$ between 60 and 115; it is found that the measured cross sections and their dependence on the energy suggests a nuclear radius of $R=1.3\mathrm{}\times {10}^{-13\mathrm{}}\times A^{\frac{1}{3}}$ cm for these elements. Section I gives a complete discussion of the calculated cross sections. Section II and III contain the derivations of these expressions. Section IV describes the new experimental material and its implications for the theory.