Charge-changing cross sections of ${}^{30}\mathrm{Ne}$, ${}^{32,33}\mathrm{Na}$ with a proton target

The total charge-changing, charge pick-up, and partial charge-changing cross sections of very neutron-rich nuclei (${}^{30}\mathrm{Ne}$, ${}^{32,33}\mathrm{Na}$) with a proton target have been measured at ∼240$A$ MeV for the first time. We introduced the phenomenological correction factor in Glauber-model calculations for the total charge-changing cross sections with the proton target, and applied it to deduce the proton radii of these nuclei. For ${}^{30}\mathrm{Ne}$ and ${}^{32}\mathrm{Na}$, the neutron skin thicknesses of the nuclei were deduced by comparing the proton radii with the matter radii deduced from the interaction cross-section measurements. A significant thick neutron-skin has been observed for the nuclei. We also found that the charge pick-up cross sections are much larger than those in the systematics of stable nuclei.

Figure 1

Experimental setup in the zero-degree spectrometer (ZDS) at the RI-beam factory (RIBF) at the end of the Big-RIPS.

Figure 2

Typical particle-identification spectrum for ${}^{32}\mathrm{Na}$ before a solid hydrogen target (SHT). The solid square shows the gate for selecting the events of ${}^{32}\mathrm{Na}$.

Figure 3

(a) Typical Δ$E$ spectrum for ${}^{32}\mathrm{Na}$ measured by a stack of Si detectors located after the solid hydrogen target (SHT). Peaks for $Z$ = 9, 10, 11, and 12 are clearly seen. (b) Same spectrum, but without SHT.

Figure 4

Neutron skin thicknesses$\left(r_{\mathrm{n}}-r_{\mathrm{p}}\right)$ for Na isotopes as a function of the difference of the proton and neutron separation energies $\left(S_{\mathrm{p}}-S_{\mathrm{n}}\right)$ calculated from the mass evaluated in AME2012 [19]. Neutron skin thicknesses marked by the open circles obtained from Ref. [16] and the closed circle from the present study (${}^{32}\mathrm{Na}$).

Figure 5

Experimental partial charge-changing cross sections vs. charge changing Δ$Z$ for ${}^{30}\mathrm{Ne}$ (closed circle), ${}^{32}\mathrm{Na}$ (closed square), and ${}^{33}\mathrm{Na}$ (closed triangle), respectively.