Unfolding the response of a zero-degree magnetic spectrometer from measurements of the resonance

The magnetic spectrometer FRagment Separator at GSI has been used to investigate the in-medium Δ -resonance excitation in peripheral heavy-ion reactions. The resolving power of this spectrometer makes it possible to disentangle the longitudinal-momentum loss induced by the excitation of the Δ resonance in the projectile residues produced in isobaric charge-exchange collisions. However, beam emittance, electromagnetic interactions of projectile and residual nuclei in the target, and the accuracy of the tracking detectors limit the final resolution. The characterization of the Δ resonance requires then to unfold the measured longitudinal-momentum distribution from the response of the spectrometer. In this work, we use an unfolding procedure based on the Richardson–Lucy method with a regularization technique to optimize the stability of the solution against statistical fluctuations. The method is validated using measurements of isobaric charge-changing collisions with a 136Xe beam at 500 A MeV.