Deblurring decay-energy distribution from an invariant-mass measurement

Measured decay-energy spectra from invariant mass spectroscopy can give insights into the shell structure of particle-unbound systems. However, it is challenging to extract the underlying physics from a measured spectrum due to detector resolution and acceptance effects. In this work, we introduce a deblurring method used to restore the decay energy spectrum measured for the three-body decay of O-26. The method utilizes the Richardson-Lucy algorithm, which has proven to be successful in optics, and does not require any prior knowledge about the resonance states in the observed spectrum. It also circumvents the singularity issue by iteratively adjusting a positive definite distribution. The only inputs are the observed energy spectrum and the detector's response matrix also referred to as the Transfer Matrix (TM). We test the method's performance on a simulated spectrum using the MoNA-LISA-Sweeper setup and the associated TM. Finally, the approach is applied to the decay energy spectrum of the O-26 system measured in an experiment conducted at the National Superconducting Cyclotron Laboratory (NSCL) by the Modular Neutron Array (MoNA) Collaboration. The deblurring approach suggests three peaks in the decay energy spectrum of O-26 at 0.15, 1.5 MeV, and a broad peak between 4 and 6 MeV.