Positron annihilation in Ge(Li) detector from line shape of single-escape peak

The line shape of the single-escape peak of high-energy $\gamma$ rays has been investigated. A 30-cc Ge(Li) detector was irradiated with 2614.5 and 2753.9-keV $\gamma$ rays from ${}_{}{}^{208}{}_{}{}^{}\mathrm{Tl}$ and ${}_{}{}^{24}{}_{}{}^{}\mathrm{Na}$, respectively. The observed broadening of the single-escape peaks was attributed to the Doppler shift of annihilation radiation, and, by unfolding the instrumental resolution the momentum distribution of the electrons in a germanium crystal was deduced. In addition, an upper limit of 5.4 × ${10}^{-3\mathrm{}}$ for the ratio of the probabilities for positron annihilation with a $K$-shell electron to that with an electron from other atomic shells was determined.