Deblurring decay energy spectrum from invariant mass measurement

The 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 the measured spectrum due to detector resolution and acceptance effects. The traditional approaches rely on fitting methods such as the chi-square that require the number of resonance peaks in the spectrum to be known a priori, information that is not always accessible. Another common technique used is the inverse problem method, but it may suffer from a singularity during matrix inversion. We introduce a deblurring method that utilizes the Richardson-Lucy algorithm, which has proven to be successful in optics. 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.