Center-of-Mass Corrections in Associated Particle Imaging

Associated Particle Imaging utilizes the inelastic scattering of neutrons produced in deuterium-tritium fusion reactions to obtain 3D isotopic distributions within an object. The locations of the inelastic scattering centers are calculated by measuring the arrival time and the position of the associated particle, the alpha particle in the fusion reaction, and the arrival time of the prompt gamma created in the scattering event. While the neutron and its associated particle move in opposite directions in the center-of-mass (COM) system, in the laboratory system the angle is slightly less than 180 degrees, and the COM movement must be taken into account in the reconstruction of the scattering location. Furthermore, due to energy loss of ions in the target, the fusion reactions are produced by ions of different energies, and thus the COM velocity varies, resulting in an uncertainty in the reconstructed positions. In this paper, we analyze the COM corrections to this reconstruction by simulating the energy loss of beam ions in the target material and identifying sources of uncertainty in these corrections. We show that an average COM velocity can be used in the reconstruction and discuss errors as a function of ion beam energy, composition, and alpha detection location. When accounting for the COM effect, the mean of the reconstructed locations can be considered a systematic error leading to shift/tilt in the reconstruction. However, the distribution of reconstructed locations also have a spread that will introduce an error in the reconstruction that cannot be corrected. In this paper, we will use the known stopping powers of ions in materials and reaction cross-sections to examine this effect.