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

We develop a framework that allows us to calculate integrated properties of the nuclear response from first principles. Using the 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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mmultiscripts> <a:mi>He</a:mi> <a:mprescripts/> <a:none/> <a:mn>4</a:mn> </a:mmultiscripts> </a:math> to <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mmultiscripts> <b:mi>Ni</b:mi> <b:mprescripts/> <b:none/> <b:mn>78</b:mn> </b:mmultiscripts> </b:math> 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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mmultiscripts> <c:mi mathvariant="normal">O</c:mi> <c:mprescripts/> <c:none/> <c:mn>16</c:mn> </c:mmultiscripts> </c:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mmultiscripts> <e:mi>Ca</e:mi> <e:mprescripts/> <e:none/> <e:mn>40</e:mn> </e:mmultiscripts> </e:math> , 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 approaches that describe nuclear response functions through the explicit treatment of excited states.