Analytic Expressions for the Angular Resolution of Compton Gamma-ray Detectors
This paper describes the derivation of analytic expressions for the angular resolution of reconstructing gamma rays detected via Compton interactions. We consider two types of gamma-ray detectors: Compton-ring and electron-tracking devices. In Compton-ring devices, the direction of the scattered electron is not resolved, only the total energy (electron and scattered photon) and the scattered photon direction are measured. The measured quantities define a cone about the axis of the scattered photon direction. The initial photon direction lies along this cone. Thus for single events there is a ring-like ambiguity in the photon direction. By combining multiple events, the intersection of the reconstructed rings will resolve the initial direction of the photon source. In this paper, we derive the resolution of the cone angle for individual rings. Electron-tracking type devices resolve the electron path. Although the scattered electron subsequently undergoes multiple-Coulomb scattering, it is possible to measure the initial electron direction with sufficiently high tracking resolution. By measuring the direction and energy of the electron and the direction of the scattered photon, the initial photon direction can be uniquely determined. The challenge for this type of detector is achieving the high tracking resolution. In Section 2 we derive the well-known Compton formula for Compton-ring devices, an analytic expression for the angular resolution of the cone angle, and discuss the limits for applying the error formula. In Section 3 we repeat the derivation of the error function for the algebraically more complicated electron-tracking device. In the final section (Section 4) we derive the effect of position measurement error on the angular resolution, which applies to both detector types. All of the analytic results are cross-checked against empirical fits to a simple Monte Carlo simulation. Doppler broadening, the effect due to the initial (and intrinsically unknown) momentum of the atomic electron, can be ignored for gamma rays with initial energy greater than a few hundred keV. For all kinematic calculations in this paper, the electron is taken to be initially at rest.
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- US Department of Energy (US)
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 15009768
- Report Number(s):
- UCRL-TR-202187; TRN: US0406615
- Resource Relation:
- Other Information: PBD: 15 Jan 2004
- Country of Publication:
- United States
- Language:
- English
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