3 Complications of germanium Compton telescopes

Finite detector thresholds, energy resolutions, and spatial resolutions produce systematic biases in the imaging capabilities of Compton telescopes. These limitations have been discussed in detail elsewhere in context of two-layer, low-Z converter and high-Z absorber, scintillation detector designs (von Ballmoos et al. 1989), and the conclusions can be directly applied to GCTs. However, GCT designs will introduce additional complications which significantly alter the event reconstruction techniques. Historical Compton telescope configurations make two assumptions about the events which do not generally hold in GCTs: (i) the events are a single Compton scatter in the converter, followed by photoelectric absorption in the absorber, and (ii) the time-of-flight (TOF) between the photon interactions is measured to determine their order.

The distributions of number and type of interaction sites in a GCT for normally incident, fully-absorbed photons ranging from 0.2-10 MeV are shown in Fig. 3, for the instrument configuration discussed in Appendix A. Here we distinguish three event types: a single photoelectric absorption, one or more Compton scatters followed by a single photoabsorption, and one or more pair productions. Compton scatters followed by pair production could potentially be reconstructed; however, here we include these events with other pair productions. These distributions account for the finite spatial resolution of the detectors, so that interactions occurring too closely together are not resolved. From these distributions it is clear that events with $\sim$8 or more interaction sites can be immediately rejected as probable pair production events, with little effect on the Compton photopeak efficiency. For incident photon energies above 0.5 MeV, 3-7 interaction site Compton scatter events dominate the photopeak.

To accurately reconstruct a Compton scatter event, the first and second interaction sites must be spatially resolved, and their order correctly determined. The need to determine the proper ordering of three or more (3+) interaction sites is complicated by the timing capabilities of GeDs. In the scintillation detectors of COMPTEL/CGRO the interaction timing can be performed to $\sim$0.25 ns (Schönfelder et al. 1993), which is adequate to determine the TOF between two interactions in the separate detector planes. With the slower rise time of GeDs one can reasonably expect event timing to $\sim$10 ns, which is inadequate for TOF measurement in reasonably-sized instruments. While Pulse Shape Discrimination methods have been proposed to push the interaction timing in GeDs to $\sim$1 ns (Boggs 1998), even this timing would be unreliable for determining TOF among three or more interaction sites. A method of reliably determining the photon interaction order without timing information must be developed.

Figure 3: Statistical distributions of the number of interaction sites for fully-absorbed photons for the instrument configuration presented in Appendix A. These distributions take into account the finite spatial distribution of the detectors, combining interactions that cannot be spatially resolved. Events are divided into photoelectric absorptions (solid white), pair productions (solid black), and the desired Compton scatter(s) followed by a single photoabsorption (striped). Events with 12 or more sites were combined in a single bin