Consistent empirical physical formula construction for recoil energy distribution in HPGe detectors by using artificial neural networks

The gamma-ray tracking technique is a highly efficient detection method in experimental nuclear structure physics. On the basis of this method, two gamma-ray tracking arrays, AGATA in Europe and GRETA in the USA, are currently being tested. The interactions of neutrons in these detectors lead to an unwanted background in the gamma-ray spectra. Thus, the interaction points of neutrons in these detectors have to be determined in the gamma-ray tracking process in order to improve photo-peak efficiencies and peak-to-total ratios of the gamma-ray peaks. In this paper, the recoil energy distributions of germanium nuclei due to inelastic scatterings of 1–5 MeV neutrons were first obtained by simulation experiments. Secondly, as a novel approach, for these highly nonlinear detector responses of recoiling germanium nuclei, consistent empirical physical formulas (EPFs) were constructed by appropriate feedforward neural networks (LFNNs). The LFNN-EPFs are of explicit mathematical functional form. Therefore, the LFNN-EPFs can be used to derive further physical functions which could be potentially relevant for the determination of neutron interactions in gamma-ray tracking process.