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\ifmmode\pm\else\textpm\fi{}1.5 cm for saturated liquid helium at 4.2\ifmmode^\circ\else\textdegree\fi{}K. The pair-production length is defined as ${l}_{\mathrm{He}}=\frac{A}{{N}_{0}{\ensuremath{\sigma}}_{\mathrm{He}}{\ensuremath{\rho}}_{\mathrm{He}}}$. The systematic uncertainty of about \ifmmode\pm\else\textpm\fi{}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.