Background: Nuclear reactions at intermediate beam energies are often interpreted using the eikonal model. In the analysis of complex reaction probes, where few-body reaction methods are needed, the eikonal method may be used as an efficient way for describing the fragment-target reaction process.

Purpose: In this work, we perform a systematic study to test the validity of the eikonal approximation for nucleon-nucleus reactions. We also quantify uncertainties due to the nucleon optical potential on reaction observables.

Method: We inspect the validity of the eikonal model and its semiclassical correction by comparing it to exact solutions (obtained from solving the optical-model equation with a finite-differences method) for a wide range of reactions. We also study the effect of relativistic corrections, both kinematic and dynamic, by effectively incorporating the relativistic effects at intermediate energies. The uncertainties from a Bayesian global optical potential (KDUQ) are propagated to the observables of interest.

Results: Our study includes neutron and proton reactions on ${}^{27}\mathrm{Al}$, ${}^{40}\mathrm{Ca}$, ${}^{90}\mathrm{Zr}$, and ${}^{208}\mathrm{Pb}$, for a wide range of energies $E_{\mathrm{lab}}=0\text{–}400\mathrm{MeV}$. We calculate neutron-total cross sections (elastic and reactions) as well as proton-absorption cross sections as a function of beam energy, using the eikonal model, the eikonal model with a semiclassical correction, and the exact solution. We also compute angular distributions for the methods above.

Conclusions: Our results show that for the proton-absorption cross section, the eikonal model can be used down to around $60\mathrm{MeV}$ and the semiclassical correction extends its use to $30\mathrm{MeV}$. However, the validity of the eikonal model for the neutron-total cross section only goes down to $\approx 120\mathrm{MeV}$, a range extended to $\approx 50\mathrm{MeV}$ when using the semiclassical correction. We find the semiclassical correction to the eikonal model to be less effective in describing the angular distributions. The $1\sigma$ uncertainty intervals on the observables we studied is less than 5% for most of the energies considered, but increases rapidly for higher energies, namely energies outside the range of KDUQ ($E_{\mathrm{lab}}>200\mathrm{MeV}$).

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• Direct reactions
• Models & methods for nuclear reactions
• Nuclear reactions
• Cluster models