Geant4-Based Differentiable Optimization for Energy-Response Flattening of a Multi-Detector Neutron Long Counter

To address the significant energy dependence of long neutron counter responses in wide-energy-range fluence measurements, this paper proposes a differentiable-optimization-based method for flattening the energy response of a multi-detector long neutron counter. A Geant4 model of the multi-detector long counter was developed, and the energy–position response matrix of this detector was constructed for the energy range of 1 eV to 20 MeV. The relative standard deviation (RSD) of the synthesized response was used as the flatness metric, and two optimization approaches—discrete combinatorial search and differentiable continuous optimization—were compared. The results show that multi-position response synthesis effectively improves the response flatness of the long counter across a broad energy range. For a detector array with K = 8, the sampled combinatorial-search benchmark identified a configuration with an RSD of 3.79%, whereas differentiable optimization yielded 2.98%, indicating a lower RSD under the present calculation settings. Additionally, embedding tungsten rods in the moderator of a long neutron counter was found to improve the overall flatness of its response. Independent verification simulations were performed by placing 6 Li micro-detectors at the eight optimized axial positions, yielding a verified RSD of 2.84%. This study demonstrates that the proposed method effectively enhances the wide-energy-range response consistency of the multi-detector long counter and provides a reproducible computational framework for position optimization in such detector systems.