Proton Distribution Radii of ${}^{16–24}\mathrm{O}$: Signatures of New Shell Closures and Neutron Skin

The root mean square radii of the proton density distribution in ${}^{16–24}\mathrm{O}$ derived from measurements of charge changing cross sections with a carbon target at $\sim 900A\mathrm{MeV}$ together with the matter radii portray thick neutron skin for ${}^{22–24}\mathrm{O}$ despite ${}^{22,24}\mathrm{O}$ being doubly magic. Imprints of the shell closures at $N=14$ and 16 are reflected in local minima of their proton radii that provide evidence for the tensor interaction causing them. The radii agree with ab initio calculations employing the chiral ${\mathrm{NNLO}}_{\mathrm{sat}}$ interaction, though skin thickness predictions are challenged. Shell model predictions agree well with the data.

Figure 1

(a) Schematic view of the experiment setup at the FRS with detector arrangement at the final focus F4. (b) Particle identification before C target at F4. (c) $Z$ identification using the MUSIC detector behind the C target. The red and blue histogram shows data without and with C target.

Figure 2

(a) $R_p^{\mathrm{ex}}$ (solid circles), blue open squares show $R_p^{e^{-}}$. (b) $R_m^{\mathrm{ex}}$ (Table 1) ${\sigma }_I$ from Ref. [12] (open circles), Ref. [11] (solid circles). The curves show predictions with coupled cluster theory for ${\mathrm{NNLO}}_{\mathrm{sat}}$ interaction (red curves). The dotted curves represent the $\pm 3\%$ uncertainty of the theory. The predictions with ${\mathrm{NNLO}}_{\mathrm{sat}}$ interaction and the IMSRG model are shown by the star symbols. The pink squares show shell model predictions. The green bars and dashed lines show mean field results.

Figure 3

Neutron skin thickness data from $R_p^{\mathrm{ex}}$ and $R_m^{\mathrm{ex}}$ filled circles. The red solid (dotted) curves represent the predictions ($\pm 3\%$ uncertainty) from coupled cluster theory using the ${\mathrm{NNLO}}_{\mathrm{sat}}$ interaction. The star symbols represent predictions from the IMSRG calculations. The pink filled squares are shell model results. Green bars show mean-field results.