Techniques for Neutron Spectrum Unfolding from Pulse Height Distributions Measured with Liquid Scintillators

Radiation detectors for neutron measurements typically include neutron thermalization and capture as primary mechanisms for detection. On the contrary, liquid scintillators detect fast neutrons via scattering interactions with hydrogen and carbon, which are the main constituents of the scintillator. The pulse height distribution measured with this kind of detector includes information on the energy spectrum of the incident neutrons. Indeed, the relationship between the pulse height distribution and the energy spectrum is uniquely characterized by the detector’s “response matrix”, which relates pulse height to incident neutron energy. However, uncovering this relationship is extremely difficult because the unfolding problem is ill-posed, in the sense that small variations in the measurement of the pulse height distribution or the detector response matrix lead to large variations in the unfolded energy spectrum. This requires the development of robust unfolding procedures and accurate analyses of the effect of noise on these procedures. In this paper, we present the results from three unfolding techniques, which are based on: (i) matrix inversion, (ii) iteration, and (iii) artificial neural networks (ANN). The first two methodologies rely on the explicit knowledge of the detector response matrix, whereas the third does not require this knowledge. To compensate for this lack of information, a certain training of the ANN is required. The three techniques are compared and evaluated in terms of: (i) accuracy in the prediction of the energy spectrum, (ii) energy resolution, (iii) computational efficiency, and (iv) robustness to noise. The unfolding is performed on pulse height distributions generated with the Monte Carlo code MCNP-PoliMi. In this code, neutron energy depositions on the constituents of the scintillator are individually tracked, and the light output generated at each interaction is suitably modeled. This procedure allows for a very accurate simulation of the liquid scintillator detector response. The precise knowledge of the neutron energy spectrum gives information not only about the presence or absence of fissile material, but also about the characteristics of the material. Thus, the unfolding procedures presented in this paper have direct and important application in the fields of nuclear nonproliferation and homeland security.