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Ab initio optical potentials for magnesium isotopes: from stability to the island of inversion

G. H. Sargsyan, J. I. Fuentealba Bustamente, K. Beyer, Ch. Elster

Abstract

We present the first calculations of ab initio nonlocal optical potentials for $^{24,26,28}$Mg and $^{32}$Mg isotopes using the leading-order term of the spectator expansion of multiple-scattering theory. We use the structure input from the ab initio symmetry-adapted no-core shell model (SA-NCSM), which provides translationally invariant, off-shell scalar and spin-projected densities so that structure and reaction inputs are treated on equal footing with no adjustable parameters. This leading-order potential reproduces $^{24}$Mg neutron total, reaction, and elastic-scattering data at energies between 65 and 250 MeV and provides predictions for $^{26,28}$Mg and $^{32}$Mg. We compare our prediction with those from uncertainty-quantified Koning-Delaroche (KDUQ) and Weppner-Penney global optical potentials, and with the ENDF nuclear data evaluations. These comparisons highlight some of the limitations of the global models, while also validating their use in reaction modeling near the N=20 island of inversion.

Ab initio optical potentials for magnesium isotopes: from stability to the island of inversion

Abstract

We present the first calculations of ab initio nonlocal optical potentials for Mg and Mg isotopes using the leading-order term of the spectator expansion of multiple-scattering theory. We use the structure input from the ab initio symmetry-adapted no-core shell model (SA-NCSM), which provides translationally invariant, off-shell scalar and spin-projected densities so that structure and reaction inputs are treated on equal footing with no adjustable parameters. This leading-order potential reproduces Mg neutron total, reaction, and elastic-scattering data at energies between 65 and 250 MeV and provides predictions for Mg and Mg. We compare our prediction with those from uncertainty-quantified Koning-Delaroche (KDUQ) and Weppner-Penney global optical potentials, and with the ENDF nuclear data evaluations. These comparisons highlight some of the limitations of the global models, while also validating their use in reaction modeling near the N=20 island of inversion.

Paper Structure

This paper contains 9 sections, 3 equations, 13 figures.

Table of Contents

  1. Introduction
  2. Theoretical framework
  3. Symmetry-adapted no-core shell model
  4. Leading-order ab initio effective nucleon-nucleus potential
  5. Phenomenological optical potentials
  6. Results and discussion
  7. Scattering Observables for $^{24}$Mg
  8. Scattering observables for $^{26}$Mg, $^{28}$Mg, and $^{32}$Mg
  9. Summary and Outlook

Figures (13)

  • Figure 1: The total cross section for neutron scattering from $^{24}$Mg as a function of the laboratory kinetic energy for N$_{\rm max}$=6 for the $\hbar\Omega$ values 13, 15, and 17 MeV together with the predictions of KDUQ Pruitt_KDUQ2023. The experimental data are from Ref. Abfalterer:2001gw.
  • Figure 2: The differential cross section, the analyzing power $A_y$, the spin rotation function $Q$ as a function of the momentum transfer $q$ (and c.m. angle $\theta_{c.m.}$) for proton scattering from $^{24}$Mg at a 65 MeV laboratory kinetic energies as function of N$_{\rm max}$ (left) for $\hbar\Omega$=15 MeV and $\hbar\Omega$ for $N_{\rm max}$=6 (right).
  • Figure 3: The angular distribution of the differential cross section divided by the Rutherford cross section (a) and analyzing power (b) as a function of the c.m. scattering angle for elastic proton scattering from $^{24}$Mg from 65 to 250 MeV laboratory projectile energy. The band on "$N_{\rm max}$=6" calculations represents the variation of $\hbar\Omega$ between 13 and 17 MeV. The cross sections are multiplied by the powers of 10 indicated at the energies listed in the figure, while the analyzing powers are offset by -2. The data at 65 MeV are from Kato:1985zzSakaguchi:1979fpk, the data at 80 MeV from Hatanaka:1984zz, the data at 135 MeV from Schwandt:1982py, and those at 250 MeV from Hicks:1988zzb.
  • Figure 4: (a) The total reaction cross section for proton scattering from $^{24}$Mg as function of the laboratory kinetic energy for N$_\mathrm{max}$=6 and $\hbar\Omega$=13, 15, and 17 MeV together with the ENDF ENDF/B-VI, Weppner-Penney Weppner:2009qy, and KDUQ Pruitt_KDUQ2023 predictions. (b) The partial reaction cross sections as a function of the angular momentum at 65 MeV laboratory kinetic energy, as calculated for N$_\mathrm{max}$=4 and $\hbar\Omega$=15 MeV compared to the KDUQ prediction. See text for full explanation.
  • Figure 5: Comparison of the real (blue) and imaginary (orange) part of the volume integrals per nucleon for the central potentials of KDUQ (displaying 68% credible intervals) and the local-equivalent extraction of the $\textit{ab initio}$ prediction for the calculation based on $\hbar\Omega$=13 to 17 MeV and N$_{\rm max}$=6. See text for details.
  • ...and 8 more figures