Proton Radii of ${}^{12–17}\mathrm{B}$ Define a Thick Neutron Surface in ${}^{17}\mathrm{B}$

The first determination of radii of point proton distribution (proton radii) of ${}^{12–17}\mathrm{B}$ from charge-changing cross sections (${\sigma }_{\mathrm{CC}}$) measurements at the FRS, GSI, Darmstadt is reported. The proton radii are deduced from a finite-range Glauber model analysis of the ${\sigma }_{\mathrm{CC}}$. The radii show an increase from ${}^{13}\mathrm{B}$ to ${}^{17}\mathrm{B}$ and are consistent with predictions from the antisymmetrized molecular dynamics model for the neutron-rich nuclei. The measurements show the existence of a thick neutron surface with neutron-proton radius difference of 0.51(0.11) fm in ${}^{17}\mathrm{B}$.

Figure 1

(a) Schematic view of the experiment setup at the FRS with detector arrangement at the final focus F4. Identification spectrum of (b) ${}^{17}\mathrm{B}$ before reaction target and (c) $Z=5$ after reaction target.

Figure 2

The filled triangles for ${}^{13–17}\mathrm{B}$ are measured ${\sigma }_{\mathrm{CC}}$. The open triangles for ${}^{10,11}\mathrm{B}$ are the measured cross sections. The filled triangles for ${}^{10–11}\mathrm{B}$ are ${\sigma }_{\mathrm{CC}}^{\text{corr}}$. The open square is the weighted average value of ${\sigma }_{\mathrm{CC}}$ calculated using the proton radius of ${}^{10}\mathrm{B}$ from Refs. [40, 41, 42]. The filled circles (green) are ${\sigma }_{\mathrm{CC}}^{\text{scaled}}$ using $f_{\mathrm{av}}^{\mathrm{all}}$ (see text). The open circles are ${\sigma }_{\mathrm{CC}}$ using AMD model densities.

Figure 3

The filled triangles for ${}^{12–17}\mathrm{B}$ are proton radii extracted from ${\sigma }_{\mathrm{CC}}^{\mathrm{ex}}$ through a Glauber model analysis with harmonic oscillator density. The open squares are proton radii determined from measured charge radii from Refs. [40, 41, 42]. The filled square for ${}^{10}\mathrm{B}$ is the weighted average of the open squares. The filled square for ${}^{11}\mathrm{B}$ is the radius derived from the measured charge radius from Ref. [43]. The open circles are $r_m^{\mathrm{ex}}$. The $\text{solid}/\text{dashed}$ lines are $r_p^{\mathrm{AMD}}/r_m^{\mathrm{AMD}}$.