Empirical Expressions for Beta Ray Point Source Dose Distributions

Abstract

Loevinger's well-known analytic expression, plus a constant 'end-of-'range' term, has been fitted to dose distributions, calculated by Monte Carlo methods, from point sources of beta rays in an infinite water medium. Optimum parameters are given for fits to 60 individual nuclides. Addition of the end-of-range term extends the range of good fits from about 0.4Rmax to 0.65Rmax, where Rmax is the maximum beta range. For low energy emitters or those having conversion electrons, the fit is often poor at distances, rmin, less than a few mg.cm-2. The RMA error of the fit at 25 points between rmin and 0.65Rmax ranges from 1.6 to 3.3% for 41 single-component spectra, and from 1.9 to 6% for 19 multi-component spectra. This is considerably smaller than is usually assumed for Loevinger's expression or given by nearly all other expressions for point source distributions. Values of the parameters are given as functions of maximum beta energy.