A general solution was presented for a model which described positrons that diffused within a grain and could then be trapped and de-trapped at a grain boundary of arbitrary shape. Closed-form relationships for the mean positron lifetime and the positron lifetime spectrum were obtained for a grain of spherical shape. The obtained results differed slightly from another report, where a similar problem was considered, and extended other results.

The Diffusion Model for the Trapping and Detrapping of Positrons in Grain Boundaries. J.Dryzek: Journal of Physics - Condensed Matter, 2000, 12[2], 137-41