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

Abstract

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.

Figures (27)

• Figure 1: Comparison of spectroscopic strength as a function of energy for different calculations. i) Neutron spectroscopic factors for each GCM state $i$ of ${}^{25}\mathrm{Mg}$ plotted at $E=E^+_i-E_0$, appear above the Fermi energy $E_F=-12.78~\mathrm{MeV}$, and each ${}^{23}\mathrm{Mg}$ state $j$ plotted at $E=-(E^-_j-E_0)$ appear below, shown as orange bars; ii) the completion states shown as green bars; iii) single--particle states of ${}^{24}\mathrm{Mg}$ for the many-body mean-field $H_A$ shown with black bars. The lines are obtained by convolution with a Lorentzian, $\frac{\eta^2}{E^2+\eta^2}$ with $\eta=1.5~\mathrm{MeV}$, to approximate the resonance widths. This gives the dashed orange line for only the GCM states, and the green solid line when also including the completion states. The levels are grouped by total orbital angular momentum and total spin. An energy range of $50~\mathrm{MeV}$ is shown around the Fermi energy with two dashed blue vertical lines, corresponding the energy cutoff of $25~\mathrm{MeV}$ used in the selection of basis states used in the GCM calculation.
• Figure 2: Total neutron scattering cross section calculated for ${}^{48}\mathrm{Cr}$ for $r_x=+i$, $a=12~\mathrm{MeV}$ in solid orange, $r_x=-i$, $a=12~\mathrm{MeV}$ in solid pink, and $r_x=+i$, $a=24~\mathrm{MeV}$ in dashed purple, compared to JENDL-5 Iwamoto:23 in solid black and cross section calculated from the many--body mean--field potential $H_A$ only in dotted red.
• Figure 3: Total neutron scattering cross section calculated for ${}^{50}\mathrm{Cr}$ for $r_x=+i$, $a=12~\mathrm{MeV}$ in solid yellow, $r_x=-i$, $a=12~\mathrm{MeV}$ in solid pink, and $r_x=+i$, $a=24~\mathrm{MeV}$ in dashed purple, compared to JENDL-5 Iwamoto:23 in solid black line, ENDF/B-VIII.0 as black points Brown:18, and cross section calculated from the many--body mean--field potential only in dotted red.
• Figure 4: Differential neutron scattering cross section calculated for ${}^{50}\mathrm{Cr}$ for $r_x=+i$, $a=12~\mathrm{MeV}$ in solid yellow, $r_x=-i$, $a=12~\mathrm{MeV}$ in solid pink, and $r_x=+i$, $a=24~\mathrm{MeV}$ in dashed purple, compared to experimental results as circles Korzh:75 and squares Fedorov:75, ENDF/B-VIII.0 Brown:18 in dashdotted blue, and cross section calculated from the many--body mean--field potential only in dotted red. Laboratory energies of the neutron is shown, and angles shown are in laboratory system.
• Figure 5: Real part of the volume integral of the central part of the total optical potential per nucleon for ${}^{50}\mathrm{Cr}$ fo selected $\ell$, compared to the real part of the volume integral of the global Koning Delaroche global optical potential Koning:03.