Ab initio description of monopole resonances in light- and medium-mass nuclei: III. Moments evaluation in ab initio PGCM calculations

TL;DR

This paper advances ab initio calculations of monopole resonances in nuclei by developing methods to compute moments of the strength distribution, analyzing angular momentum effects, and connecting results to nuclear matter properties.

Contribution

It introduces new techniques for computing monopole strength moments, assesses angular momentum projection effects, and links finite-nucleus results to nuclear matter incompressibility.

Findings

Validated methods for low-order moment calculations.

Quantified the impact of angular momentum projection.

Connected monopole centroid energies to nuclear matter incompressibility.

Abstract

The paper is the third of a series dedicated to the ab initio description of monopole giant resonances in mid-mass closed- and open-shell nuclei via the so-called projected generator coordinate method. The present focus is on the computation of the moments $m_k$ of the monopole strength distribution, which are used to quantify its centroid energy and dispersion. First, the capacity to compute low-order moments via two different methods is developed and benchmarked for the $m_1$ moment. Second, the impact of the angular momentum projection on the centroid energy and dispersion of the monopole strength is analysed before comparing the results to those obtained from consistent quasi-particle random phase approximation calculations. Next, the so-called energy weighted sum rule (EWSR) is investigated. First, the appropriate ESWR in the center-of-mass frame is derived analytically. Second, the exhaustion of the intrinsic EWSR is tested in order to quantify the (unwanted) local-gauge symmetry breaking of the presently employed chiral effective field theory ($\chi$EFT) interactions. Finally, the infinite nuclear matter incompressibility associated with the employed $\chi$EFT interactions is extracted by extrapolating the finite-nucleus incompressibility computed from the monopole centroid energy.