  Charge exchange spin-dipole (SD) excitations of $^{90}$Zr and $^{208}$Pb are
studied by using a Skyrme
  Hartree-Fock(HF) + Random Phase approximation (RPA). The calculated
spin-dipole strength distributions are compared with experimental data obtained
by $^{90}$Zr (p,n) $^{90}$Nb and $^{90}$Zr (n,p) $^{90}$ Nb reactions. The
model-independent SD sum rule values of various Skyrme interactions are studied
in comparison with the experimental values in order to determine the neutron
skin thickness of $^{90}$Zr. The pressure of the neutron matter equation of
state (EOS) and the nuclear matter symmetry energy are discussed in terms of
the neutron skin thickness and peak energies of SD strength distributions.
