There are several applications for which it is desirable to calculate the locations and energies of individual gamma-ray interactions within a high purity germanium (HPGe) detector. These include gamma-ray imaging and Compton suppression. With a segmented detector this can be accomplished by analyzing the pulse shapes of the signals from the various segments. We examine the fundamental limits to the spatial resolution attainable with this approach. The primary source of error is the series noise of the field effect transistors (FETs) at the inputs of the charge amplifiers. We show how to calculate the noise spectral density at the output of the charge amplifiers due to an optimally selected FET. This calculation is based only on the detector capacitance and a noise constant for the FET technology. We show how to use this spectral density to calculate the uncertainties in parameters, such as interaction locations and energies, that are derived from pulse shape analysis using maximum likelihood estimation (MLE) applied to filtered and digitized recordings of the charge signals. Example calculations are given to illustrate our approach. Experimental results are given that demonstrate that one can construct complete systems, from detector through data analysis, that come near the theoretical limits.
