Matter radii from interaction cross sections using microscopic nuclear densities

Abstract

Understanding how nuclear size evolves with the number of protons and neutrons tests our models of strongly interacting matter. The nuclear charge (and proton) radii accessible through electromagnetic probes carry fundamental information on the saturation density and nuclear correlations. The radii of the neutron distribution are more difficult to measure, but they are important for our understanding of the isovector properties of nuclei that depend on the proton-to-neutron asymmetry, and on extended nucleonic matter in neutron stars. Interaction cross sections offer one of the few direct experimental windows into the neutron radii of nuclei far from stability, but translating these measurements into reliable structural information requires an integrated theoretical framework that links structure and reactions with a rigorous treatment of uncertainty. In this work, we compute interaction cross sections by using uncertainty-quantified proton and neutron distributions obtained in the self-consistent nuclear Density Functional Theory (DFT) with the Fayans energy density functional. The resulting densities are used in a modernized Glauber reaction framework, which features the refit of nucleon-nucleon profile functions. Applying this pipeline to the existing data on the calcium isotopic chain, we find no evidence for the dramatic neutron swelling reported earlier. While focusing here on the Ca chain, the methodology proposed in this work is applicable to interaction cross section measurements across the nuclear chart and is well-suited for new experiments currently planned at leading rare isotope facilities.

Figures (2)

• Figure 1: Comparison of experimental interaction cross sectionsTanaka2020 (black error bars, including both statistical and systematic errors) with theoretical predictions obtained using the MOL approach, densities predicted with the Fayans EDF, and profile function calibrated to $^{42-48}$Ca data. The dark-shaded red band corresponds to the 1$\sigma$ uncertainties $d\sigma^{struct}$ associated with the EDF calculations of nuclear densities. The gray band corresponds to the same calculations, except that we use a profile function from the literatureRay1979. The light-shaded red band also includes the uncertainties associated with the $NN$ cross sections $d\sigma^{NN}$, that are used in the definition of the profile functions (see Methods). The uncertainties $d\sigma^{struct}$ and $d\sigma^{NN}$ are considered independent. The blue bands correspond to parametric uncertainties related to the calibration of the profile function's free parameters.
• Figure 2: Theoretical predictions for (a) interaction cross sections, (b) matter radii, (c) charge radii and (d) neutron skins (defined as differences between neutron and proton radii). The distribution delimited by the solid red line and the red-shaded distribution correspond respectively to the theoretical calculations that pass the $\chi^2$-test at the 3$\sigma$ and 2$\sigma$ confidence levels (no theoretical calculations pass the $\chi^2$-test at the 1$\sigma$ confidence level). This $\chi^2$-test is performed on measurements of the interaction cross sections for the whole Calcium chainTanaka2020 (black error bars in panel (a)). The error bars in panel (b) and (d) correspond to matter radii and neutron skins that were extracted in the initial analysisTanaka2020 of these interactions cross sections data. The charge radii data are taken fromGarcia_Ruiz2016.