Electric Dipole Polarizability of ${}^{48}\mathrm{Ca}$ and Implications for the Neutron Skin

The electric dipole strength distribution in ${}^{48}\mathrm{Ca}$ between 5 and 25 MeV has been determined at RCNP, Osaka from proton inelastic scattering experiments at forward angles. Combined with photoabsorption data at higher excitation energy, this enables the first extraction of the electric dipole polarizability ${\alpha }_{\mathit{D}}({}^{48}\mathrm{Ca})=2.07(22){\mathrm{fm}}^3$. Remarkably, the dipole response of ${}^{48}\mathrm{Ca}$ is found to be very similar to that of ${}^{40}\mathrm{Ca}$, consistent with a small neutron skin in ${}^{48}\mathrm{Ca}$. The experimental results are in good agreement with ab initio calculations based on chiral effective field theory interactions and with state-of-the-art density-functional calculations, implying a neutron skin in ${}^{48}\mathrm{Ca}$ of 0.14–0.20 fm.

Figure 1

(a) Spectra of the ${}^{48}\mathrm{Ca}$$(p,p^{\prime })$ reaction at $E_0=295\mathrm{MeV}$ and scattering angles ${\mathrm{\Theta }}_{\mathrm{lab}}=0.4°$ (blue) and 2.4° (green). (b) Example of the decomposition for the spectrum at ${\mathrm{\Theta }}_{\mathrm{lab}}=0.4°$. Green histogram: contribution from isoscalar giant resonances subtracted prior to the MDA. Blue histogram: $E1$ part from the MDA. Red histogram: nuclear background from the MDA.

Figure 2

Comparison of $B(E1)$ strength distributions in ${}^{48}\mathrm{Ca}$, deduced from Ref. [50] (squares), Ref. [51] (triangles), and from the present Letter (circles).

Figure 3

(a) Photoabsorption cross sections in ${}^{48}\mathrm{Ca}$ (present Letter, circles) compared with ${}^{40}\mathrm{Ca}$ (Ref. [53, 54], squares). (b) ${}^{40}\mathrm{Ca}$ data shifted by $-0.87\mathrm{MeV}$ (Eq. (2). (c) Cross sections of the $(p,p^{\prime })$ reaction at $E_0=295\mathrm{MeV}$ and scattering angle ${\mathrm{\Theta }}_{\mathrm{lab}}=0.4°$ for ${}^{48}\mathrm{Ca}$ (circles) and ${}^{40}\mathrm{Ca}$ (squares), the latter shifted by $-0.87\mathrm{MeV}$.

Figure 4

(a) Combined photoabsorption cross sections in ${}^{48}\mathrm{Ca}$ from the present Letter (blue circles) for $E_X\le 25\mathrm{MeV}$ and from Ref. [53] (red squares) for $25\le E_{\mathrm{X}}\le 60\mathrm{MeV}$. (b) Running sum of the electric dipole polarizability in comparison to $\chi \mathrm{EFT}$ predictions, where the gray band is based on a set of two- plus three-nucleon interactions [17] and includes a partial uncertainty estimate from the many-body method.

Figure 5

Experimental electric dipole polarizability in ${}^{48}\mathrm{Ca}$ (blue band) and predictions from $\chi \mathrm{EFT}$ (green triangles) and EDFs (red squares, for details on the functionals see [17], error bars from Ref. [66]). The green and black bars indicate the $\chi \mathrm{EFT}$ prediction selected to reproduce the ${}^{48}\mathrm{Ca}$ charge radius [17] and the range of ${\alpha }_D$ predictions [14] from EDFs providing a consistent description of polarizabilities in ${}^{68}\mathrm{Ni}$ [39], ${}^{120}\mathrm{Sn}$ [37], and ${}^{208}\mathrm{Pb}$ [36], respectively.