<i>Ab initio</i> calculations of monopole sum rules: From finite nuclei to infinite nuclear matter

We compute moments of the isoscalar monopole response of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>N</a:mi> <a:mo>=</a:mo> <a:mi>Z</a:mi> </a:mrow> </a:math> closed-shell nuclei based on chiral nucleon-nucleon plus three-nucleon interactions. We employ the random-phase approximation (RPA) and two 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.