The adopted level densities (LD) for the nuclei produced through different reaction mechanisms significantly impact the calculation of cross sections for the many reaction channels. Common LD models make simplified assumptions regarding the overall behavior of the total LD and the intrinsic spin and parity distributions of the excited states. However, very few experimental constraints are taken into account: LD at neutron separation energy coming from average resonance spacings, whenever they have been previously measured, and the sometimes subjective extrapolation of discrete levels. These, however, constrain the LD only for very specific spins, parities and excitation energies. This work aims to establish additional experimental constraints on LD through quantitative correlations between cross sections and LD. This allows for the fitting and determination of detailed structures in LD. For this we use the microscopic Hartree-Fock-Bogoliubov (HFB) LD to associate variations predicted by the model with the structure observed in double-differential spectra at low outgoing neutron energy, which is dominated by the LD input. We also use uc{56}{Fe} ($n,p$) as an example cross sections are extremely sensitive to LD. For comparison purposes we also perform calculations with the GC model. With this approach we are able to perform fits of the LD based on actual experimental data, constraining the model and ensuring its consistency. This approach can be particularly useful in extrapolating the LD to nuclei for which high-excited discrete levels and/or resonance spacings are unknown. It also predicts inelastic gamma cross sections that can significantly differ from more standard phenomenological LD.
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