Spin-Dipole Strengths and Neutron Skin Thickness of \({}^{{90}}\)Zr, \({}^{{132}}\)Sn, \({}^{{208}}\)Pb

The strength distributions of charge exchange spin-dipole excitations are calculated in the continuum quasiparticle random-phase approximation based on the Fayans density functional with modified isovector part. An impact of the isovector parameter \(h_{2}^{-}\) of the DF3-f functional on the strength functions of charge-exchange spin-dipole excitations (\(0^{-}\), \(1^{-}\), \(2^{-}\)) are studied for \({}^{208}\)Pb, \({}^{132}\)Sn and \({}^{90}\)Zr. The sum rules are calculated using both ground state radii and direct integration of the total SD strength distributions. A comparison with the experimental SD sum rule in \({}^{90}\)Zr gives one a possibility to check previously estimated \(h_{2}^{-}\) values which described well the recent combined estimate for \(\Delta R_{np}\) in \({}^{208}\)Pb and corresponding equation of state parameters – symmetry energy \(J_{0}=J(\rho_{0})\) and a slope parameter \(L_{0}=L(\rho_{0})\).