The trapping model for positrons diffusing inside the grain of arbitrary shape

We present a general solution of the trapping model for positrons which diffuse inside a grain of arbitrary shape towards its surface. The consideration takes into account both the diffusion and transition regime. The explicit form relations for the mean positron lifetime and the positron lifetime spectrum were obtained. The theoretical relation for the mean positron lifetime was analysed thoroughly for a grain of ellipsoidal shape. We established that the shape of the grain influenced the positron annihilation characteristics.