Incoherent-Scattering Function, Total Pair-Production Cross Section, and Pair-Production Length for Helium

A formula for the incoherent-scattering function using either the correlated or the uncorrelated wave-function model of atomic helium is presented. With this the total triplet-production cross section is calculated, and thus the total pair-production cross section is evaluated (triplet+coherent pair). The pair-production length of helium is calculated to be 963.64±1.5 cm for saturated liquid helium at 4.2°K. The pair-production length is defined as $l_{\mathrm{He}}=\frac{A}{N_0{\sigma }_{\mathrm{He}}{\rho }_{\mathrm{He}}}$. The systematic uncertainty of about ±0.15% comes from the choice of screening functions. This is a factor of 10 more accurate than the known pair-production lengths of any other element. It is suggested that this increased accuracy for the pair-production length of helium may find application as a standard in experimental measurements of absolute cross sections for high-photon-energy induced reactions.