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Impact of ground-state correlations on the multipole response of nuclei: Ab initio calculations of moment operators

Andrea Porro, Achim Schwenk, Alexander Tichai

TL;DR

This paper presents an ab initio framework to extract integrated nuclear response properties by computing ground-state moments $m_0(Q_{\lambda})$ and $m_1(Q_{\lambda})$ using the in-medium similarity renormalization group (IMSRG). The authors show that ground-state correlations substantially modify the multipole response compared with mean-field or RPA, and they demonstrate improved agreement with experimental data for the isovector dipole channel, including the TRK enhancement factor, across a range of closed-shell nuclei from $^4$He to $^{78}$Ni. The method relies on transforming two-body moment operators via a unitary IMSRG flow, enabling accurate evaluation without explicit excited-state solutions, and is complemented by intrinsic sum-rule considerations and gauge invariance arguments that account for nonlocalities and two-body currents. A first valence-space IMSRG extension for open-shell nuclei is explored, highlighting both the potential and the need for further multi-reference benchmarking. Overall, the moment method provides a robust ab initio benchmark for nuclear response and offers a practical path to benchmark other state-of-the-art approaches that treat excited states explicitly.

Abstract

We develop a framework that allows to calculate integrated properties of the nuclear response from first principles. Using the ab initio in-medium similarity renormalization group (IMSRG), we calculate the expectation values of moment operators that are linked to the multipole response of nuclei. This approach is applied to the isoscalar mono- and quadrupole as well as the isovector dipole response of closed-shell nuclei from $^4$He to $^{78}$Ni for different chiral two- and three-nucleon interactions. We find that the inclusion of many-body correlations in the nuclear ground state significantly impacts the multipole response when going from the random-phase approximation to the IMSRG level. Our IMSRG calculations lead to an improved description of experimental data in $^{16}$O and $^{40}$Ca, including a good reproduction of the Thomas-Reiche-Kuhn enhancement factor. These findings highlight the utility of the moment method as a benchmark for other ab initio approaches that describe nuclear response functions through the explicit treatment of excited states.

Impact of ground-state correlations on the multipole response of nuclei: Ab initio calculations of moment operators

TL;DR

This paper presents an ab initio framework to extract integrated nuclear response properties by computing ground-state moments and using the in-medium similarity renormalization group (IMSRG). The authors show that ground-state correlations substantially modify the multipole response compared with mean-field or RPA, and they demonstrate improved agreement with experimental data for the isovector dipole channel, including the TRK enhancement factor, across a range of closed-shell nuclei from He to Ni. The method relies on transforming two-body moment operators via a unitary IMSRG flow, enabling accurate evaluation without explicit excited-state solutions, and is complemented by intrinsic sum-rule considerations and gauge invariance arguments that account for nonlocalities and two-body currents. A first valence-space IMSRG extension for open-shell nuclei is explored, highlighting both the potential and the need for further multi-reference benchmarking. Overall, the moment method provides a robust ab initio benchmark for nuclear response and offers a practical path to benchmark other state-of-the-art approaches that treat excited states explicitly.

Abstract

We develop a framework that allows to calculate integrated properties of the nuclear response from first principles. Using the ab initio in-medium similarity renormalization group (IMSRG), we calculate the expectation values of moment operators that are linked to the multipole response of nuclei. This approach is applied to the isoscalar mono- and quadrupole as well as the isovector dipole response of closed-shell nuclei from He to Ni for different chiral two- and three-nucleon interactions. We find that the inclusion of many-body correlations in the nuclear ground state significantly impacts the multipole response when going from the random-phase approximation to the IMSRG level. Our IMSRG calculations lead to an improved description of experimental data in O and Ca, including a good reproduction of the Thomas-Reiche-Kuhn enhancement factor. These findings highlight the utility of the moment method as a benchmark for other ab initio approaches that describe nuclear response functions through the explicit treatment of excited states.

Paper Structure

This paper contains 19 sections, 59 equations, 15 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Formalism
  3. Moments of the strength function
  4. Ground-state method for moments
  5. The IMSRG method
  6. Sum rules and gauge invariance
  7. Sum rules
  8. Gauge invariance and continuity equation
  9. Numerical results
  10. Computational setup
  11. Model-space convergence
  12. Interaction dependence and correlation effects
  13. Comparison to sum rules
  14. Enhancement factor of the TRK sum rule
  15. Comparison to experiment: dipole response
  16. ...and 4 more sections

Figures (15)

  • Figure 1: Convergence of $m_1$ (top panel) and $m_0$ (bottom panel) for the isovector dipole (IV1) response as a function of the model space size $e_\text{max}$ at the HF and IMSRG(2) level. For each isotope, the results with increasing $e_\text{max}$ are shown, as highlighted in the inset. The values of $m_1$ and $m_0$ are rescaled by a factor $\tfrac{A}{NZ}$ in order to show all nuclei on the same scale [see Eq. \ref{['eq:trk']}]. Results are given for the 1.8/2.0 (EM) interaction using $\hbar\omega=16$ MeV.
  • Figure 2: Convergence of the average energy $\bar{E}=m_1/m_0$ as a function of the model space size $e_\text{max}$ at the IMSRG(2) level for different multipolarities. Results are given for the 1.8/2.0 (EM) interaction using $\hbar\omega=16$ MeV.
  • Figure 3: Values of $m_1$ for the isoscalar monopole (IS0, top panels), isovector dipole (IV1, middle panels), and isoscalar quadrupole (IS2, bottom panels) response for HF/RPA (left) and IMSRG(2) (right) calculations. Results are given for four different interactions ($\Delta$NNLO$_\text{GO}$ (394) Jiang20a, 1.8/2.0 (EM) Hebeler10a, 1.8/2.0 (EM7.5) Arthuis24a, and NNLO$_\text{sat}$Ekstrom15a) for $e_\text{max}=12$ and $\hbar\omega=$16 MeV.
  • Figure 4: Relative difference between RPA and IMSRG(2) results, as defined by Eq. \ref{['eq:eps_corr']}, for $m_1$ in the IS0 (top panel), IV1 (middle panel), and IS2 (bottom panel) channels. Results are compared for four different interactions ($\Delta$NNLO$_\text{GO}$ (394) Jiang20a, 1.8/2.0 (EM) Hebeler10a, 1.8/2.0 (EM7.5) Arthuis24a, and NNLO$_\text{sat}$Ekstrom15a) for $e_\text{max}=12$ and $\hbar\omega=$16 MeV.
  • Figure 5: Ratio $m_1/m_0$ at the RPA (left panels) and IMSRG(2) level (right panel) in the IS0 (top), IV1 (middle), and IS2 (bottom) channels. Results are given for four different interactions ($\Delta$NNLO$_\text{GO}$ (394) Jiang20a, 1.8/2.0 (EM) Hebeler10a, 1.8/2.0 (EM7.5) Arthuis24a, and NNLO$_\text{sat}$Ekstrom15a) for $e_\text{max}=12$ and $\hbar\omega=$16 MeV
  • ...and 10 more figures