Distribution of absorbed energy from a point beta-source in a tissue-equivalent medium

Abstract

This work is to determine the point source functions ψ( r) for beta-radiation with energies in the range 18 keV-3· MeV. The conditions that must be satisfied by the functions ψ( r) are formulated and possible methods of finding these functions are discussed (the Loevinger method and the application of Spencer's theory). In order to determine ψ( r) we have found first the values of the function ψ( r, E i ) for an isotropic point source of monoenergetic electrons of energy E i . For ψ( r, E i ) we have used experimental data and the “single dose distribution approximation” (scaling law for dose distributions). The ψ( r) functions for 14 beta sources were obtained by summing the functions ψ( r, E i ) for the narrow energy bands into which the original spectra were divided. We have compared the integrals from the calculated functions with the corresponding experimental values, the latter being determined by ionization measurements, good agreement was found. An empirical formula has been found which describes the dose distributions of the isotopes which were studied and its parameters have been evaluated.