The development of nuclear reaction models for the production of evaluated nuclear data has traditionally been performed by comparing measured cross sections with predictions from reaction model codes whose physical input parameters are adjusted to obtain the best agreement between measured and modeled results. To more directly probe reaction model inputs, this work introduces a forward modeling approach to experimental reaction cross-section determination, where the most important physical input parameters to reaction model calculations are obtained via ${\chi }^2$ minimization between measured and calculated observables. This was demonstrated using data collected by the Gamma Energy Neutron Energy Spectrometer for Inelastic Scattering (GENESIS) at the 88-inch cyclotron at Lawrence Berkeley National Laboratory, a detection array consisting of organic liquid scintillators and high-purity germanium (HPGe) detectors. Using a broad-spectrum neutron beam and a $99.98\%$-enriched ${}^{56}\mathrm{Fe}$ target, GENESIS was used to perform a simultaneous measurement of ${}^{56}\mathrm{Fe} \gamma$-ray production cross sections and secondary neutron energy and angle distributions. The results of the forward modeling approach to the determination of energy-differential $\gamma$-ray production cross sections for the yrast $4^{+}\to 2^{+}$ and $6^{+}\to 4^{+}$ transitions, as well as eight other off-yrast transitions, were compared against those obtained using conventional techniques, and the results are in good agreement. In addition to discrete $\gamma$-ray yield total scattered neutron energy-angular distributions as a function of incident neutron energy were also obtained using forward modeling and found to agree with evaluated data, with the exception of elastic scattering at small angles. The fitted reaction model parameters obtained through forward modeling were also used to calculate the cross section for the unobserved $(n,2n)$ reaction; excellent agreement with the current evaluation was obtained, providing a validation of the predictive capabilities of the forward model approach. This work bridges the gap between nuclear data experiment and evaluation by providing a new means for extracting inelastic neutron-scattering cross sections and neutron-induced $\gamma$-ray production data while directly probing reaction model physics.

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• Elastic scattering reactions
• Inelastic scattering reactions
• Models & methods for nuclear reactions
• Nuclear reactions
• Nuclear data analysis & compilation
• Radiation detectors
• Spectrometers & spectroscopic techniques