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In nuclear reaction experiments, the measured decay energy spectra can giveinsights into the shell structure of decaying systems. However, extracting theunderlying physics from the measurements is challenging due to detectorresolution and acceptance effects. The Richardson-Lucy (RL) algorithm, adeblurring method that is commonly used in optics and has proven to be asuccessful technique for restoring images, was applied to our experimentalnuclear physics data. The only inputs to the method are the observed energyspectrum and the detector's response matrix also known as the transfer matrix.We demonstrate that the technique can help access information about the shellstructure of particle-unbound systems from the measured decay energy spectrumthat isn't immediately accessible via traditional approaches such as chi-squarefitting. For a similar purpose, we developed a machine learning model that usesa deep neural network (DNN) classifier to identify resonance states from themeasured decay energy spectrum. We tested the performance of both methods onsimulated data and experimental measurements. Then, we applied both algorithmsto the decay energy spectrum of $^{26}\mathrm{O} \rightarrow ^{24}\mathrm{O}$ +n + n measured via invariant mass spectroscopy. The resonance states restoredusing the RL algorithm to deblur the measured decay energy spectrum agree withthose found by the DNN classifier. Both deblurring and DNN approaches suggestthat the raw decay energy spectrum of $^{26}\mathrm{O}$ exhibits three peaks atapproximately 0.15~MeV, 1.50~MeV, and 5.00~MeV, with half-widths of 0.29~MeV,0.80~MeV, and 1.85~MeV, respectively.

Deconstructing experimental decay energy spectra: the $^{26}$O case