Specific energy spectra at alpha-contaminated bone surfaces

Spectra of specific energy f(z) in spherical and disc-shaped targets are determined for plane sources of alpha-particles. The radioactive plane is assumed to be coincident with bone surfaces or 'buried' within bone. Parameters determining energy straggling and the spectrum of delta-rays generated outside the target were determined from published parallel beam experiments with wall-less counters. An analytical procedure for calculating single and multiple event spectra for the sphere is demonstrated. For discs spectra are derived from Monte-Carlo calculations. In discs of 6.5 micrometers radius and 1 micrometer thickness adjacent to bone surfaces the mean specific energy per event is 2967 erg/g, while tht in a sphere of equal volume is 5247 erg/g. The relative variation of specific energy in the disc is about twice as large as in the sphere.