  A consistent folding model analysis of the ($\Delta S=0, \Delta T=1$) charge
exchange \pn reaction measured with $^{48}$Ca, $^{90}$Zr, $^{120}$Sn and
$^{208}$Pb targets at the proton energies of 35 and 45 MeV is done within a
two-channel coupling formalism. The nuclear ground state densities given by the
Hartree-Fock-Bogoljubov formalism and the density dependent CDM3Y6 interaction
were used as inputs for the folding calculation of the nucleon optical
potential and \pn form factor. To have an accurate isospin dependence of the
interaction, a complex isovector density dependence of the CDM3Y6 interaction
has been carefully calibrated against the microscopic Brueckner-Hatree-Fock
calculation by Jeukenne, Lejeune and Mahaux before being used as folding input.
Since the isovector coupling was used to explicitly link the isovector part of
the nucleon optical potential to the cross section of \pn reaction exciting the
0$^+$ isobaric analog states in $^{48}$Sc, $^{90}$Nb, $^{120}$Sb and
$^{208}$Bi, the newly parameterized isovector density dependence could be well
tested in the folding model analysis of the \pn reaction. The isospin- and
density dependent CDM3Y6 interaction was further used in the Hartree-Fock
calculation of asymmetric nuclear matter, and a realistic estimation of the
nuclear symmetry energy has been made.
