  The exact solution of a diffusion$-$reaction model for the trapping and
annihilation of positrons at interfaces of precipitate$-$matrix composites is
presented considering both cylindrical or spherical precipitates.
Diffusion-limitation is taken into account for interfacial trapping from the
surrounding matrix as well as from the interior of the precipitate. Closed-form
expressions are obtained for the mean positron lifetime and for the intensity
of the positron lifetime component associated with the interface-trapped state.
The model contains as special case also positron trapping at extended
open-volume defects like spherical voids or hollow cylinders. This makes the
model applicable to all types of cylindrical- and spherical-shaped extended
defects irrespective of their size and their number density.
