Statistical analysis of the Doppler broadening coincidence spectrum of electron–positron annihilation radiation in silicon

We report a statistical analysis of Doppler broadening coincidence data of electron–positron annihilation radiation in silicon using a 22Na source. The Doppler broadening coincidence spectrum was fit using a model function that included positron annihilation at rest with 1s, 2s, 2p, and valence band electrons. In-flight positron annihilation was also fit. The response functions of the detectors accounted for backscattering, combinations of Compton effects, pileup, ballistic deficit, and pulse-shaping problems. The procedure allows the quantitative determination of positron annihilation with core and valence electron intensities as well as their standard deviations directly from the experimental spectrum. The results obtained for the core and valence band electron annihilation intensities were 2.56(9)% and 97.44(9)%, respectively. These intensities are consistent with published experimental data treated by conventional analysis methods. This new procedure has the advantage of allowing one to distinguish additional effects from those associated with the detection system response function.