Deblurring a decay energy spectrum from a nuclear reaction

In nuclear reaction experiments, the measured decay energy spectra can give insights about the shell spectroscopy of the systems. However, it is challenging to extract the underlying physics from the measurements due to detector resolution and acceptance effects. We introduce a deblurring method, novel for nuclear physics application, that utilizes the Richardson-Lucy algorithm that has proven to be successful in optics. We demonstrate that the technique could help recover the physics from highly degraded nuclear decay energy spectrum measurements. The method does not require any prior knowledge about the resonance states in the observed spectrum, and it 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 tested the method’s performance on a simulated spectrum generated using the in-house simulation package for the MoNA-LISA-Sweeper setup and the associated TM. Finally, the approach is applied to the energy spectrum of the ²⁶O system decaying into  ²⁴O + n +n, from an experiment conducted at NSCL by the MoNA Collaboration. We demonstrate its successful performance in restoring the resonance states in the decaying systems from decay energy measurement.