Modeling of U-shaped composite detectors

We have investigated the basic operation of a composite detector comprising of elements arranged in the shape of an U-shaped rectangular well. Considering an isotropic scattering of gamma-rays and partial energy absorptions in up to four detector modules, expressions for the addback factor and the peak-to-total ratio have been obtained in terms of only one probability amplitude. We have compared the performance of two U-shaped detectors having different geometries and observed negligible gain in addback due to the longer arms. For completeness, comparisons have been made with composite detectors like the two element stacked detector and the two level pyramidal detector, both being embedded inside the U-shaped detector. Our pen-on-paper approach could be used to understand the operation of modern arrays having detector elements arranged in various sophisticated ways.