Moving away from singly-magic nuclei with Gorkov Green's function theory

TL;DR

This paper uses Gorkov Green's function theory with advanced Hamiltonians to calculate nuclear properties of isotopic chains around calcium, successfully reproducing many experimental trends but highlighting the need for improved correlation treatments.

Contribution

It applies Gorkov Green's function approach with state-of-the-art Hamiltonians to describe isotopic chains, revealing emergent magic numbers and limitations in current many-body truncations.

Findings

Good agreement with experimental charge radii and charge density distributions.

Emergence and evolution of neutron magic numbers N=28, 32, 34.

Systematic underestimation of pairing gaps.

Abstract

Ab initio calculations of bulk nuclear properties (ground-state energies, root mean square charge radii and charge density distributions) are presented for seven complete isotopic chains around calcium, from argon to chromium. Calculations are performed within the Gorkov self-consistent Green's function approach at second order and make use of two state-of-the-art two- plus three-nucleon Hamiltonians, $NN$+$3N\text{(lnl)}$ and NNLO$_{\text{sat}}$. An overall good agreement with available experimental data is found, in particular for differential energies (charge radii) when the former (latter) interaction is employed. Remarkably, neutron magic numbers $N=28,32,34$ emerge and evolve following experimental trends. In contrast, pairing gaps are systematically underestimated. General features of the isotopic dependence of charge radii are also reproduced, as well as charge density distributions. A deterioration of the theoretical description is observed for certain nuclei and ascribed to the inefficient account of (static) quadrupole correlation in the present many-body truncation scheme. In order to resolve these limitations, we advocate the extension of the formalism towards incorporating breaking of rotational symmetry or, alternatively, performing a stochastic sampling of the self-energy.