High-Energy Cross Sections. I. The Size of the Nucleus

An analysis is made of the recently available measurements of the absorption (reaction) cross sections of nuclei for 1.4-Bev neutrons. The nature of the approximations involved in interpreting such data is discussed, and it is pointed out that these measurements are more directly related to the nuclear density distribution than are the lower-energy measurements. If it is assumed that the density drops off smoothly to zero at the edge of the nucleus, in accord with electron scattering results, it is found that the size of the nucleus determined from these nuclear experiments is in good agreement with the size determined from electromagnetic experiments. This fact indicates that the spatial distribution of the protons is probably equal to that of the neutrons, and cannot be smaller by as much as 1×{}10^-13 cm, even for heavy nuclei.A simple formula is given for the nuclear density distribution; the radius of the uniform (square-well) density distribution which yields the same 〈r²〉Av is r₀=1.19A1/3×10^-13 cm; the corresponding square-well radius for nuclear interactions is larger, and depends on the type and energy of observation. Some results are presented of a method for treating the effect of the finite range of interaction of the neutrons.