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

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, N N +3N (lnl) and NNLOsat. 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.

Investigation of the ground-state spin inversion in the neutron-rich Cl47,49 isotopes

“…In addition, full-space ab initio calculations within the Gorkov self-consistent Green's function approach [29,37] were performed. This technique has been recently applied to specific examples [15,[74][75][76], as well as systematic surveys [77,78] in the medium-mass region of the nuclear chart. One specificity of Green's function techniques is the ability to access the spectroscopy of odd-even nuclei [29], which makes it particularly suited to the present case.…”

“…It combines a N 3 LO two-body force with N 2 LO three-body operators. It has been shown to provide a very good description of (total and differential) groundstate energies and excitation spectra in the calcium region [77,78]. All GGF calculations were performed in a spherical harmonic-oscillator basis, including up to 14 major shells (e max = 13).…”

“…By interaction. The iterative character of the GGF solution (as opposed to the full diagonalization performed in valence-space calculations), the collective nature of these states, and the not-optimal account of quadrupole correlations [78] make the resolution of this low-lying spectrum particularly challenging for the current GGF implementation. FIG.…”

Nuclear Charge Radii of the Nickel Isotopes $^{58-68,70}$Ni

“…The long-term goal of nuclear physics is thus to develop a universal framework to consistently describe atomic nuclei across the entire nuclear chart. Research in recent years has led to remarkable advances in nuclear manybody methods [1][2][3][4][5][6][7] as well as in the development of nuclear forces based on chiral effective field theory (EFT), rooted in symmetries of QCD and based on pion ex-changes and short-ranged interactions [8][9][10]. A significant theoretical effort has been dedicated to the description of electromagnetic properties such as nuclear charge radii R c .…”

“…In the present work, the values of R 2 p = 0.709 fm 2 [42, 43] and R 2 n = −0.106 fm 2 [44] were used. We employ the following two-plus three-nucleon (3N) interactions from chiral EFT: (i) NNLO sat [45], which gives a good description of charge radii in light and mid-mass isotopes but somewhat underbinds finite nuclei [1,2,7,12,15,46,47]; (ii) 1.8/2.0(EM) [6,48,49], and (iii) N N +3N (lnl) [46], which reproduce groundstate and excitation energies throughout the mediumand heavy mass region, but generally underpredict absolute charge radii [6,7,50]. The present work addresses a long sequence of charge radii along the Ni isotopic chain for the first time with three ab initio techniques, using these three nuclear interactions.…”