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The proton density polarization in ${\rm ^{48}Ca}$ by the eight neutrons added on the ${\rm ^{40}Ca}$ core is discussed. We adopt the proton density distributions determined by electron scattering and the neutron density distributions determined by proton elastic scattering in ${\rm ^{40}Ca}$ and ${\rm ^{48}Ca}$. As a measure of the proton density polarization effect due to the neutrons, a ratio $R$ of the peak values of the neutron density difference $\Delta\rho_{n,{\rm peak}}$ between ${\rm ^{48}Ca}$ and ${\rm ^{40}Ca}$ to the proton one $\Delta\rho_{p,{\rm peak}}$ is introduced and compared with the Hartree–Fock and Hartree calculations by non-relativistic and relativistic energy density functionals (EDFs), respectively. The value $R$ shows clear correlations with the symmetry energy parameters $J$ and $L$, but not with the isoscalar incompressibility $K_\infty$. The experimental value $R$ can be reproduced by theoretical calculations using the EDFs with $L=25$–50 MeV.

Proton density polarization of the doubly magic 40Ca core in 48Ca and EoS parameters