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Chiral interactions and superfluidity in the calcium isotopic chain

A. Scalesi, A. Ekström, C. Forssén, G. Hagen

Abstract

We perform ab initio calculations of three-point mass differences in the odd- and even-mass $^{39-49}$Ca isotopes to probe nuclear superfluidity via empirical neutron pairing gaps. We also quantify the sensitivity of those gaps to the parameters of the interaction at mean-field level. Recent studies employing accurate chiral nuclear interactions have found these gaps to be too small. We show that experimental values can be reproduced at mean-field level by substantially increasing the attraction of the singlet $S$-wave two-nucleon contact interaction, but doing so induces an unphysical bound state of the di-neutron. The sensitivity of these predictions to the full calibration of the nuclear interaction is then studied by performing Bayesian posterior sampling in a delta-full chiral effective field theory at third chiral order. We find that pairing gaps remain largely unaffected, leaving the explanation of nuclear superfluidity as a future task for improved many-body modeling and refined interactions at higher chiral orders.

Chiral interactions and superfluidity in the calcium isotopic chain

Abstract

We perform ab initio calculations of three-point mass differences in the odd- and even-mass Ca isotopes to probe nuclear superfluidity via empirical neutron pairing gaps. We also quantify the sensitivity of those gaps to the parameters of the interaction at mean-field level. Recent studies employing accurate chiral nuclear interactions have found these gaps to be too small. We show that experimental values can be reproduced at mean-field level by substantially increasing the attraction of the singlet -wave two-nucleon contact interaction, but doing so induces an unphysical bound state of the di-neutron. The sensitivity of these predictions to the full calibration of the nuclear interaction is then studied by performing Bayesian posterior sampling in a delta-full chiral effective field theory at third chiral order. We find that pairing gaps remain largely unaffected, leaving the explanation of nuclear superfluidity as a future task for improved many-body modeling and refined interactions at higher chiral orders.
Paper Structure (4 sections, 3 equations, 2 figures, 1 table)

This paper contains 4 sections, 3 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction.
  2. Methods and results
  3. Summary and outlook.
  4. Acknowledgments.

Figures (2)

  • Figure 1: Impact of the variation of the sub-leading low-energy constant (LEC) $C_{^1S_0}$ on two-neutron shell gaps $\Delta_{2n}$ (top panel) and three-point mass differences $\Delta^{(3)}$ (bottom panel) computed with the sHFB method. Values in the legend represent the shift $\Delta C_{^1S_0}$ applied to the ${\Delta}{\rm NNLO}_{\rm GO}(394)$Jiang20 value of $C_{^1S_0} = 2.505 \times10^4\,G\eV^{-4}$ in the same unit. Experimental data (black squares) Wang21 are shown for comparison.
  • Figure 2: Posterior predictive distributions $p( \Delta_{2n}, \Delta^{(3)} \vert \mathcal{D}_\mathrm{cal}, I)$ for calcium isotopes computed with ${\Delta}{\rm NNLO}(394)$ interactions. White dots indicate the center of the distribution, thick and thin vertical lines enclose $68\%$ and $90\%$ of the probability mass, respectively. Results for the ${\Delta}{\rm NNLO}_{\rm GO}(394)$ interaction and experimental data are shown with triangle and square symbols for comparison. The hatched distributions for $\Delta_{2n}$ of $^{40,48}$Ca provide a model check as these two observables entered our likelihood calibration.