Ab initio calculations of monopole sum rules: From finite nuclei to infinite nuclear matter

TL;DR

This work addresses how ab initio nuclear interactions encode the isoscalar monopole response and its relation to nuclear matter incompressibility. By computing monopole-strength moments with both IMSRG and CC (and cross-checking with RPA) for NNLO_sat and ΔNNLO_GO(394) interactions, the authors connect finite-nucleus observables to the infinite-matter incompressibility K∞ via a leptodermous expansion. The study demonstrates consistent IMSRG/CC results for moments and average energies, and provides K∞ estimates that are compatible with phenomenological ranges despite some tension with pure nuclear-matter calculations. The results underscore the viability of combining moment-operator and LIT-CC approaches for ab initio descriptions of collective nuclear excitations and their implications for the nuclear EOS, while outlining paths to improve Coulomb treatment and extend to asymmetric and open-shell systems.

Abstract

We compute moments of the isoscalar monopole response of N = Z closed-shell nuclei based on chiral nucleon-nucleon plus three-nucleon interactions. We employ the random phase approximation (RPA) and two ab initio many-body approaches, the in-medium similarity renormalization group (IMSRG) and coupled-cluster theory (CC). In the IMSRG framework, the moments are obtained as ground-state expectation values, whereas in the CC approach, they are evaluated through excited-state calculations. We find good agreement between the IMSRG and CC results across all nuclei studied. RPA provides a reasonable approximation to the correlated methods if the interaction is soft. From the calculated moments, we extract average energies of the monopole response, compute finite-nucleus incompressibilities, and estimate the incompressibility of symmetric nuclear matter by a fit to a leptodermous expansion. Our extrapolated values are lower than those obtained in nuclear matter calculations with the same interactions, but the values are consistent with phenomenological ranges.

Figures (6)

• Figure 1: Values of $m_{-1}$ for the isoscalar monopole (IS0) response for RPA (left), IMSRG (middle), and CC (right) calculations. Results are given for two different interactions (NNLO$_\text{sat}$Ekstrom15a, $\Delta$NNLO$_\text{GO}$ (394) Jiang20a) for $\hbar\omega=12-16$ MeV as a function of the model space size $e_\text{max}$. Absolute values are rescaled by a factor $A^{5/3}$ in order to show all nuclei on the same scale.
• Figure 2: Values of $m_0$ for the isoscalar monopole (IS0) response for RPA (left), IMSRG (middle), and CC (right) calculations. Results are given for two different interactions (NNLO$_\text{sat}$Ekstrom15a, $\Delta$NNLO$_\text{GO}$ (394) Jiang20a) for $\hbar\omega=12-16$ MeV as a function of the model space size $e_\text{max}$. Absolute values are rescaled by a factor $A^{5/3}$ in order to show all nuclei on the same scale.
• Figure 3: Average energy $\sqrt{m_1/m_{-1}}$ for the isoscalar monopole (IS0) response for RPA (left), IMSRG (centre) and CC (right) calculations. Results are given for two different interactions (NNLO$_\text{sat}$Ekstrom15a, $\Delta$NNLO$_\text{GO}$ (394) Jiang20a) for the HO basis frequencies $\hbar\omega=12-16$ MeV as a function of the model space size $e_\text{max}$.
• Figure 4: Finite-nucleus incompressibility $K_A$ from Eq. \ref{['eq:KA']}. Calculations were performed employing the NNLO$_\text{sat}$Ekstrom15a and $\Delta$NNLO$_\text{GO}$ (394) Jiang20a interactions. Numerical values are given by the average between calculations employing different $\hbar\omega$ at $e_\text{max}$ = 14 for RPA and CC and $e_\text{max}$ = 12 for IMSRG calculations. The error bars reflect the model-space convergence of the results and are determined from the $\hbar\omega$ variation and the two largest employed $e_\text{max}$.
• Figure 5: Linear fit from Eq. \ref{['eq:extrap']} for the RPA, IMSRG, and CC points from Fig. \ref{['fig:KA_method']}. The shaded areas represent the 68% and 95% confidence level areas, while solid horizontal lines are numerical values for $K_\infty$ from nuclear matter calculations Ekstrom15aJiang20aAlp25a.