Accurate Approximations to Average Beta-Particle Energies and Spectra

A simple yet accurate approximation for calculating spectrum-averaged beta-particle energies and spectra is presented. It gives the average beta-particle energy as a ratio of two polynomials and can be easily implemented on pocket calculators. The values calculated by this method differ from those calculated by “exact” methods by <1% for nuclides with atomic numbers in the 20 to 100 range emitting beta particles having energies up to ∼8 MeV (∼1.3 pJ).