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Ab initio calculations of nuclear charge radii across and beyond ${}^{132}$Sn: Putting chiral EFT nuclear interactions to the test

Pepijn Demol, Urban Vernik, Thomas Duguet, Alexander Tichai

Abstract

Charge radii are investigated along the Tin isotopic chain via ab initio Bogoliubov coupled cluster calculations at the singles and doubles level. In addition to the reproduction of absolute radii, the parabolic behavior of isotopic shifts between the N = 50 and N = 82 magic numbers and the kink through ${}^{132}$Sn are shown to provide stringent tests for state-of-the-art chiral effective field theory ($χ$EFT) inter-nucleon interactions. Indeed, none of the employed fine-tuned interactions can capture all such key characteristics. Eventually, the pronounced sensitivity of the results to the employed Hamiltonian beyond ${}^{132}$Sn provides a unique playground to pin down critical attributes of $χ$EFT inter-nucleon interactions in the future. This calls for measuring isotopic shifts both towards ${}^{100}$Sn and beyond ${}^{134}$Sn, as well as for performing high-accuracy ab initio calculations of mean-square radii in heavy open-shell nuclei by adding both triples corrections to the many-body wave function and the two-body charge density correction to the operator

Ab initio calculations of nuclear charge radii across and beyond ${}^{132}$Sn: Putting chiral EFT nuclear interactions to the test

Abstract

Charge radii are investigated along the Tin isotopic chain via ab initio Bogoliubov coupled cluster calculations at the singles and doubles level. In addition to the reproduction of absolute radii, the parabolic behavior of isotopic shifts between the N = 50 and N = 82 magic numbers and the kink through Sn are shown to provide stringent tests for state-of-the-art chiral effective field theory (EFT) inter-nucleon interactions. Indeed, none of the employed fine-tuned interactions can capture all such key characteristics. Eventually, the pronounced sensitivity of the results to the employed Hamiltonian beyond Sn provides a unique playground to pin down critical attributes of EFT inter-nucleon interactions in the future. This calls for measuring isotopic shifts both towards Sn and beyond Sn, as well as for performing high-accuracy ab initio calculations of mean-square radii in heavy open-shell nuclei by adding both triples corrections to the many-body wave function and the two-body charge density correction to the operator
Paper Structure (7 sections, 10 equations, 5 figures)

This paper contains 7 sections, 10 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Theoretical framework
  3. Absolute charge radii and isotopic shifts
  4. Kinks at $N=50, 82$ and $92$
  5. Linear and parabolic components of $\delta \langle R^2_\text{ch} \rangle$
  6. Conclusions and outlook
  7. Acknowledgements

Figures (5)

  • Figure 1: Theoretical and experimental charge radii. Hartree-Fock-Bogoliubov and BCCSD results in $^{96-150}$Sn are displayed for the 1.8/2.0 (EM), $\Delta$NNLO$_\text{GO}$ and 1.8/2.0 (EM7.5) $\chi$EFT-based Hamiltonians. Valence-space IMSGR(2) results in $^{100-132}$Sn are shown for the first two Hamiltonians Miya25privcomGustafsson2025.
  • Figure 2: Theoretical and experimental isotopic shifts. The left panel shows BCCSD results in $^{96-150}$Sn for the 1.8/2.0 (EM), $\Delta$NNLO$_\text{GO}$ and 1.8/2.0 (EM7.5) $\chi$EFT-based Hamiltonians. In the right panel, a focused view of $^{128-146}$Sn is presented, with colored bands displaying the HO frequency variation ($\hbar \omega = [10,14]$).
  • Figure 3: Differential isotopic shift (top) and two-neutron separation energies (bottom) across $^{100}$Sn (left), $^{132}$Sn (middle) and $^{142}$Sn (right). The two-neutron separation energy in $^{102}$Sn from NLEFT calculations hild25NLEFTSn is also displayed in the bottom panel.
  • Figure 4: Left panel: angular momentum of the neutron HFB valence (canonical) shell computed for the 1.8/2.0 (EM), $\Delta$NNLO$_\text{GO}$ and 1.8/2.0 (EM7.5) interactions in even-even $^{98-164}$Sn isotopes (full colored circles). Ground-state angular momentum of odd-even $^{101-131}$Sn isotopes obtained from VS-IMSRG(2) calculations based on the 1.8/2.0 (EM) and $\Delta$NNLO$_\text{GO}$ interactions (empty colored diamonds). Experimental ground-state angular momentum in odd-even $^{101-133}$Sn isotopes (full black diamonds). Right panel: change of the radial integrand between $^{132}$Sn and $^{134}$Sn in the computation of the one-body point-proton mean-square radius (Eq. \ref{['MSpointprotonradius']}).
  • Figure 5: Experimental and theoretical (quasi) parabolic component of mean-square charge radii $\delta \langle R^2_\text{ch} \rangle^{\text{A}}_{\text{res}}$ (see text for details) between $^{100}$Sn and $^{132}$Sn. Vertical bars indicate sub-shell closures predicted at the HFB level: grey full lines specify sub-shell closures commun to the three Hamiltonians whereas colored dashed and dashed-dotted lines indicate those that are interaction specific in connection with the inversion of the $3s_{1/2}$ and $2d_{3/2}$ shells for the 1.8/2.0 (EM7.5) Hamiltonian; see Fig. \ref{['fig:spin']} for more details.