Trends of Neutron Skins and Radii of Mirror Nuclei from First Principles

S. J. Novario, D. Lonardoni, S. Gandolfi, and G. Hagen

Phys. Rev. Lett. 130, 032501 – Published 19 January 2023

Abstract

The neutron skin of atomic nuclei impacts the structure of neutron-rich nuclei, the equation of state of nucleonic matter, and the size of neutron stars. Here we predict the neutron skin of selected light- and medium-mass nuclei using coupled-cluster theory and the auxiliary field diffusion Monte Carlo method with two- and three-nucleon forces from chiral effective field theory. We find a linear correlation between the neutron skin and the isospin asymmetry in agreement with the liquid-drop model and compare with data. We also extract the linear relationship that describes the difference between neutron and proton radii of mirror nuclei and quantify the effect of charge symmetry breaking terms in the nuclear Hamiltonian. Our results for the mirror-difference charge radii and binding energies per nucleon agree with existing data.

Received 2 December 2021
Revised 4 April 2022
Accepted 13 December 2022

DOI:https://doi.org/10.1103/PhysRevLett.130.032501

Physics Subject Headings (PhySH)

Nuclear charge distribution Nuclear many-body theory Nuclear matter in neutron stars Nuclear structure & decays

Nuclear Physics

Authors & Affiliations

S. J. Novario ¹, D. Lonardoni ^1,*, S. Gandolfi ¹, and G. Hagen^2,3

¹Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
²Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
³Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA

^*Present address: XCP-2, Eulerian Codes Group, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.

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Issue

Vol. 130, Iss. 3 — 20 January 2023

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Images

Figure 1
Neutron skin thickness plotted against the isospin asymmetry from ab initio calculations. Coupled-cluster results of nuclei with $14 \leq A \leq 56$ using the $Δ N^{2} {LO}_{GO} (394)$ , $Δ N^{2} {LO}_{GO} (450)$ , and $N^{2} {LO}_{sat} (450)$ interactions are shown as solid blue circles, empty orange squares, and right-filled red triangles, respectively. Left-filled green triangles represent auxiliary field diffusion Monte Carlo results for $6 \leq A \leq 18$ using the $N^{2} {LO}_{E 1}$ local chiral interaction. The linear regression is printed in the bottom right with $1 σ$ uncertainty, and the $1 σ$ , $2 σ$ , and $3 σ$ confidence levels are shown as gray bands. Select nuclei are labeled.
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Figure 2
Coulomb-subtracted neutron skin thickness ( $Δ R_{np}^{*} = Δ R_{np} + Z A^{- 1 / 3} \times 0.0033 fm$ ) plotted against the isospin asymmetry from available experimental data. Solid green diamonds are the results extracted from antiprotonic x-ray data [90, 91] and open blue pentagons are from proton scattering [92, 93]. These data are accompanied by linear fits shown as green and blue bands, respectively, and both relations are printed in the bottom right ( $Δ R_{np}^{* <}$ and $Δ R_{np}^{* >}$ ). The right-filled blue star and the left-filled red star are the values for ${}^{208}{Pb}$ from PREX-I [8] and PREX-II [9], respectively. The open cross is the value for ${}^{48}{Ca}$ from CREX [10]. These experimental data are compared with our ab initio results, shown as dashed black lines from the $1 σ$ limits of a linear regression.
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Figure 3
Coulomb-subtracted mirror neutron skin thickness $Δ R_{np}^{* mirror} / A = (Δ R_{np}^{mirror} + Z A^{- 1 / 3} \times 0.0033 fm) / A$ plotted against the isospin asymmetry. The data markers are the same as those in Fig. 1. The experimental data for ${}^{16}O$ ( ${}^{18}{Ne}$ ), ${}^{40}{Ca}$ , and ${}^{54}{Ni}$ are extracted from Refs. [24, 90, 91, 92, 96]. The linear regression is printed in the bottom right with $1 σ$ uncertainty, and the $1 σ$ , $2 σ$ , and $3 σ$ confidence levels are shown as gray bands. Selected nuclei are labeled.
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Figure 4
Top panel: Mirror-difference charge radii plotted against the isospin asymmetry compared with experiment. The data markers are the same as those in Fig. 1. The linear regression of our data is printed in the bottom left with $1 σ$ uncertainty, and the $1 σ$ , $2 σ$ , and $3 σ$ confidence levels are shown as gray bands. Selected neutron-deficient nuclei are labeled. Experimental data are shown as open white diamonds, taken from Ref. [24] except for those of ${}^{36}{Ca}$ [18] and ${}^{54}{Ni}$ [96]. Bottom panel: Mirror-difference binding energy per nucleon $Δ (BE / A)$ as a function of the Coulomb asymmetry. Experimental data are taken from Ref. [88].
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