Difference in proton radii of mirror nuclei as a possible surrogate for the neutron skin

It has recently been suggested that differences in the charge radii of mirror nuclei are proportional to the neutron-skin thickness of neutron-rich nuclei and to the slope of the symmetry energy $L$ [Brown, Phys. Rev. Lett. 119, 122502 (2017)]. The determination of the neutron skin has important implications for nuclear physics and astrophysics. Although the use of electroweak probes provides a largely model-independent determination of the neutron skin, the experimental challenges are enormous. Thus, the possibility that differences in the charge radii of mirror nuclei may be used as a surrogate for the neutron skin is a welcome alternative. To test the validity of this assumption we perform calculations based on a set of relativistic energy density functionals that span a wide region of values of $L$. Our results confirm that the difference in charge radii between various neutron-deficient nickel isotopes and their corresponding mirror nuclei is indeed strongly correlated to both the neutron-skin thickness and $L$. Moreover, given that various neutron-star properties are also sensitive to $L$, a data-to-data relation emerges between the difference in charge radii of mirror nuclei and the radius of low-mass neutron stars.

Figure 1

(a) Data-to-data relations between the neutron-skin thickness of ${}^{48}\mathrm{Ca}$ and the difference in proton radii between a few neutron-deficient nickel isotopes and their corresponding mirror nuclei along the $A=50$, 52, and 54 isobars. Numbers in parentheses represent the correlation coefficients; numbers next to the lines, linear regression slopes. (b) Same as (a), but for the neutron-skin thickness of ${}^{208}\mathrm{Pb}$.

Figure 2

(a) Difference in proton radii along the $A=50$, 52, and 54 isobars as a function of the slope of the symmetry energy at saturation density. Numbers in parentheses represent correlation coefficients. (b) Same as (a), but as a function of the slope of the symmetry energy at the lower density of 0.10 fm.

Figure 3

Stellar radii for neutron stars with masses of $M_{★}=0.8M_{\odot },1.0M_{\odot },1.2M_{\odot }$, and $1.4M_{\odot }$ as a function of the difference in proton radii between ${}^{50}\mathrm{Ni}$ and ${}^{50}\mathrm{Ti}$. Here $r$ is the correlation coefficient deduced from a linear regression.