Nuclear charge radii of silicon isotopes

Abstract

The nuclear charge radius of $^{32}$Si was determined using collinear laser spectroscopy. The experimental result was confronted with ab initio nuclear lattice effective field theory, valence-space in-medium similarity renormalization group, and mean field calculations, highlighting important achievements and challenges of modern many-body methods. The charge radius of $^{32}$Si completes the radii of the mirror pair $^{32}$Ar - $^{32}$Si, whose difference was correlated to the slope $L$ of the symmetry energy in the nuclear equation of state. Our result suggests $L \leq 60$\,MeV, which agrees with complementary observables.

Figures (5)

• Figure 1: Normalized resonance spectra of $^{28,29,30,32}$Si. Inelastic collisions during the charge exchange process led to slightly asymmetric line shapes and were considered in the fit function Klose.2012. The frequency is relative to the centroid of $^{28}$Si.
• Figure 2: Experimental and theoretical differential mean square charge radii of Si. Only the nuclear lattice calculation provided an uncertainty which is plotted as a gray band. Together with the DFT calculations using the SVmin functional, the lattice results agree with the experimental results.
• Figure 3: $\Delta R_\textnormal{ch}(^{32}\textnormal{Ar}-^{32}\textnormal{Si}$) as a function of $L$. The experimental $1\sigma$ constraint of $\Delta R_\textnormal{ch}$ is indicated by the horizontal dashed lines. The solid circles are the results of Skyrme EDF, and the crosses are for the CODF calculations. The overlapping area, highlighted in gray, shows our constraint for $L\leq 60$ MeV. It is in good agreement with the result from the $^{54}$Ni-$^{54}$Fe pair Pineda.2021, with the findings from the electric dipole polarizability $\alpha_\textnormal{D}$Roca-Maza.2015, the neutron star merger GW 170817 Raithel.2019 but smaller than the PREX II result Reed.2021. Please note that those are only plotted as reference on the $L$ axis and are not correlated to $\Delta R_\textnormal{ch}$. From our theoretical calculations on the lattice and from VS-IMSRG calculations with the EM$1.8\_2.0$ and $\Delta$N$^2$LO$_{\rm{GO}}$ interaction, we deduced $\Delta R_\textnormal{ch}$ and related those with corresponding calculations for $L$Elhatisari:2022qfrHagen.2016PhysRevC.102.054301.
• Figure 4: Schematic of the BECOLA beamline. In the radio-frequency-quadrupole trap (RFQ) the beam was cooled and extracted as a continuous beam. Laser and ion beams were superimposed and aligned through two 3-mm apertures at 2.1 m distance. The beam was neutralized through charge-exchange reactions with Na vapor. Fluorescence light was collected by an elliptical mirror set and guided to a photo-multiplier tube (PMT) outside the vacuum chamber. Further ion optics for beam deflection and collimation are not shown.
• Figure 5: Experimentally and theoretically determined root-mean square charge radii $R$ of Si. The band of orange lines show the results for $R$ obtained with the 12 Skyrme EDF points colored orange in \ref{['fig:DeltaR_L']} that correspond to an assumed $^{208}$Pb neutron skin of 0.16 fm.