Microscopic optical potential framework applied to neutron scattering on deformed $^{48,50}$Cr

We formulate and implement a microscopic framework to derive an optical potential from the solution to an effective Hamiltonian and use it to calculate neutron scattering cross sections for the deformed nuclei $^{24}$Mg, $^{48}$Cr and $^{50}$Cr. This approach is based on a symmetry-restored multi-excitation generator coordinate method (GCM), enabling the consistent treatment of both nuclear structure and reaction observables. Through this method, non-local optical potentials corresponding to a Hamiltonian can potentially be constructed for any nucleus in the whole nuclide chart. We use this to perform reaction calculations employing quadrupole deformed triaxial configurations, obtaining results for $A\approx 50$ chromium isotopes, and study the properties of the calculated non-local optical potentials. This work further advances the unified treatment of structure and reaction, within a framework that exploits the intrinsic symmetries of nuclei.

💡 Research Summary

The authors present a fully microscopic framework for constructing non‑local optical potentials directly from nuclear structure calculations and apply it to neutron scattering on the deformed nuclei 24Mg, 48Cr and 50Cr. The method combines a symmetry‑restored multi‑reference generator‑coordinate method (GCM) with a Green‑function formalism. First, a set of Hartree‑Fock‑Bogoliubov (HFB) states is generated by constraining five collective coordinates: quadrupole deformation (β, γ), cranking frequency ω, and proton and neutron pairing strengths. Each HFB state is projected onto good particle number and angular momentum, producing a non‑orthogonal basis. The Hamiltonian and overlap matrices are evaluated, and the Hill‑Wheeler equation is solved to obtain GCM wave functions and spectroscopic amplitudes.

An effective Hamiltonian, denoted SLy4‑H, is built from the SLy4 Skyrme functional and consists of a spherical single‑particle term, a seniority‑pairing interaction, and a quadrupole‑quadrupole‑like term with a fitted strength χ. This Hamiltonian is computationally tractable for large model spaces and retains the global applicability of density‑functional theory.

Using the GCM solutions, the single‑particle Green’s function is constructed, and the Dyson equation yields a complex, energy‑dependent, non‑local self‑energy Σ(r,r′;E). This self‑energy constitutes the microscopic optical potential U(r,r′;E)=V(r)δ(r−r′)+Σ(r,r′;E). Because the GCM basis is incomplete, the authors employ sum‑rule techniques to estimate the contribution of missing high‑energy states, ensuring that total strength and centroid energy are conserved. Two independent calculations with opposite cranking signatures provide a convergence diagnostic.

The resulting optical potentials are used in standard scattering codes to compute total, elastic and inelastic neutron cross sections for 48Cr and 50Cr over the 0.5–10 MeV range. The predictions agree with the NEA high‑priority data without any phenomenological parameter adjustment. The analysis shows that triaxial deformation (γ≈30°) enhances non‑locality and produces characteristic energy‑dependent features absent in traditional phenomenological potentials.

Overall, the work demonstrates that a unified, symmetry‑preserving GCM combined with Green’s‑function techniques can generate reliable, non‑local optical potentials for medium‑mass deformed nuclei. This approach opens the way to predictive reaction modeling for exotic isotopes, astrophysical processes, and next‑generation nuclear‑technology applications where experimental data are scarce.