Optimization of a gamma spectrometer setup by a numerical method

Full text: Measuring sources of soils and liquids by gamma spectrometry requires a previous study of the available containers (Marinelli beakers, bottles, Petri boxes, etc.) to optimize the counting efficiency. This is usually done either by measuring a set of standards in various geometries or by analytical or Monte Carlo calculations. Studies about the optimization of specific models have been published, including graphs and tables, but their utility is restricted to users having similar detectors, containers and matrices. We propose here an alternative optimization approach based on numerical methods. First, we define a function of the magnitude that must be optimized, typically a function of the efficiency. The function itself can be an analytical expression or the result of a Monte Carlo calculation. It depends on a series of parameters and the optimization of the measurement system can be reduced to finding the optimal set of parameters that minimize or maximize the function that takes into account the detector response. These parameters are often the dimensions of the containers. Thus, a Marinelli container can be characterized by 4 parameters and a plastic bottle by two. We discuss here the application of several optimization algorithms to approach the problem. Initial values are provided for the parameters to be optimized and an iterative process is followed until convergence is attained. For each step of the algorithm, a set of updated parameters is obtained. Usually only a few iterations are needed. The function to be optimized can be defined by the user, thus emphasizing those features relevant to the measurement needs. Maximum efficiency at low energies, at high energies, or a weighted function of all efficiencies are some of the functions that can be defined. Conclusions about the efficiency of the algorithms tested are presented. The method is applied to a gamma spectrometer system based on an extended range detector with a good response to low energy photons. Optimal dimensions for Marinelli beakers and plastic bottles are obtained. Efficiencies are calculated with the computer code PENELOPE