Swelling of Doubly Magic ${}^{48}\mathrm{Ca}$ Core in Ca Isotopes beyond $N=28$

Interaction cross sections for ${}^{42–51}\mathrm{Ca}$ on a carbon target at $280\mathrm{MeV}/\mathrm{nucleon}$ have been measured for the first time. The neutron number dependence of derived root-mean-square matter radii shows a significant increase beyond the neutron magic number $N=28$. Furthermore, this enhancement of matter radii is much larger than that of the previously measured charge radii, indicating a novel growth in neutron skin thickness. A simple examination based on the Fermi-type distribution, and mean field calculations point out that this anomalous enhancement of the nuclear size beyond $N=28$ results from an enlargement of the core by a sudden increase in the surface diffuseness of the neutron density distribution, which implies the swelling of the bare ${}^{48}\mathrm{Ca}$ core in Ca isotopes beyond $N=28$.

Figure 1

Particle-identification plots for ${}^{48}\mathrm{Ca}$. (a) Incident particles including ${}^{48}\mathrm{Ca}$ before the reaction target. (b) Corresponding outgoing particles after the reaction target with the selection of incoming ${}^{48}\mathrm{Ca}$ indicated by the ellipse in (a).

Figure 2

Neutron number dependence of $⟨r^2{⟩}_m^{1/2}$ and $⟨r^2{⟩}_p^{1/2}$ [7] for Ca isotopes. The present results are represented by closed circles. The present error bars neglect model ambiguity in deriving matter radii from the ${\sigma }_I$ data. The existing experimental results of $⟨r^2{⟩}_m^{1/2}$ deduced from proton elastic scattering (p,p) [16, 22] are plotted as open triangles [16] and open squares [22], respectively. The experimental results of $⟨r^2{⟩}_p^{1/2}$ measured using the isotope-shift (IS) method [7] are represented by crosses. The examinations by SPM and 2 pF function are also indicated by the open diamond connected by the solid line and the dashed line with the green band, respectively.

Figure 3

Neutron number dependence of $\mathrm{\Delta }{r}_{np}$ for Ca isotopes. The present results are represented by filled circles, and the existing experimental results deduced from electric dipole polarizability ${\alpha }_D$ [34] and those from proton elastic scattering (p,p) [22] are represented by the rectangle and by open squares, respectively. The present error bars neglect model ambiguity in deriving matter radii from the ${\sigma }_I$ data. The dashed and dashed-and-dotted lines are the results of the chi-square fitting to the data below and above $N=28$.