On the analytic estimation of radioactive contamination from degraded alphas

Abstract

The high energy spectrum of alpha particles emitted from a single isotope uniformly contaminating a bulk solid has a flat energy spectrum with a high end cutoff energy equal to the maximal alpha kinetic energy (Tα) of the decay. In this flat region of the spectrum, we show the surface rate rb (Bq keV−1cm−2) arising from a bulk alpha contamination ρb (Bq cm−3) from a single isotope is given by rb =ρb Δ R/ 4 Δ E , where Δ E = E1−E2>0 is the energy interval considered (keV) in the flat region of the spectrum and Δ R = R2−R1, where R2 (R1) is the amount of the bulk material (cm) necessary to degrade the energy of the alpha from Tα to E2 (E1). We compare our calculation to a rate measurement of alphas from 147Sm, (15.32 ± 0.03% of Sm(nat) and half life of (1.06 ± 0.01)× 1011 yr [1]), and find good agreement, with the ratio between prediction to measurement of 100.2%± 1.6% (stat)± 2.1% (sys). We derive the condition for the flat spectrum, and also calculate the relationship between the decay rate measured at the surface for a [near] surface contamination with an exponential dependence on depth and a second case of an alpha source with a thin overcoat. While there is excellent agreement between our implementation of the sophisticated Monte Carlo program SRIM [2] and our intuitive model in all cases, both fail to describe the measured energy distribution of a 148Gd alpha source with a thin (∼200μg cm−2) Au overcoat. We discuss possible origins of the disagreement and suggest avenues for future study.