T. Hashimoto$^1$, A. M. Krumbholtz$^2$, P. G. Reinhard$^3$, A. Tamii$^4$, P. von Neumann-Cosel$^2$ for RCNP E282 and E316 collaboration
$^1$Rare Isotope Project, Institute for Basic Science, Korea
$^2$Institute fur Kernphysik, Technische Universitat Darmstadt, Germany
$^3$Institute of Theoretical Physik II, Universitat Erlanen-Nurnberg, Germany
$^4$Research Center for Nuclear Physics, Osaka University, Japan

Abstract
Nuclear Equation of State (EOS) is one of hot topics of nuclear physics. It describes the energy and density dependence of nuclear matter and thus has wide impact on nuclear physics and astrophysics. Although the EOS of symmetric nuclear matter is relatively well constrained, one of the neutron-rich matter is poorly determined experimentally. Therefore, our knowledge of the symmetry energy is still quite limited.

The neutron skin formation in nuclei with neutron excess is governed by the symmetry energy. A linear correlation between the neutron skin thickness and the slope parameter, L, is predicted by studies of self-consistent energy density functionals (EDFs). The most studied case is $^{208}$Pb. However the neutron skin thickness has delivered from many experiments, EDFs are needed to translate the result into parameters of the symmetry energy in any case.

The isovector properties of EDFs are poorly determined by the typical set of data used to fix parameters of interaction. A particularly useful experimental observable to constrain the large theoretical uncertainties is the electric dipole polarizability of nuclei ($\alpha_{D}$). All EDFs agree on a strong correlation of the dipole polarizability with the neutron skin and L, but the predictions for a given $\alpha_{D}$ differ considerably. While the result for $^{208}$Pb already exclude many results based on Skyrme interactions, modern Skyrme-Hartree-Fock and relativistic models can be brought into agreement by changing the magnitude of the symmetry energy, which can be varied over a certain range of values without detonating the quality of the fit determining the interaction parameters. Experimental information on $\alpha_{D}$ in other nuclei is therefore of high interest to further constrain the iosvector part of the EDF interaction.

We measured the electric dipole responce in $^{120}$Sn between 5 and 22 MeV with polarized proton scattering based on a polarization transfer analysis. Combined with photoabsorption data a dipole polarizability is extracted for $^{120}$Sn. The correlation with the polarizability of $^{208}$Pb serves as a test of EDFs. The majority of models based on Skryrme interaction can describe the data while relativistic approaches fail. The accuracy of the experimental results provide important constraints on the static isovector properties of EDFs used to predict symmetry energy parameters and the neutron skin thickness.