  Differential cross sections of ($p,n$) and ($^3$He,$t$) charge-exchange
reactions leading to the excitation of the isobaric analog state (IAS) of the
target nucleus are calculated with the distorted wave Born approximation. The
$G$-matrix double-folding method is employed to determine the nucleus-nucleus
optical potential within the framework of the Lane model. $G$-matrices are
obtained from a Brueckner-Hartree-Fock calculation using the Argonne Av18
nucleon-nucleon potential. Target densities have been taken from
Skyrme-Hartree-Fock calculations which predict values for the neutron skin
thickness of heavy nuclei compatible with current existing data. Calculations
are compared with experimental data of the reactions ($p,n$)IAS on $^{14}$C at
$E_{lab}=135$ MeV and $^{48}$Ca at $E_{lab}=134$ MeV and $E_{lab}=160$ MeV, and
($^3$He,$t$)IAS on $^{58}$Ni, $^{90}$Zr and $^{208}$Pb at $E_{lab}=420$ MeV.
Experimental results are well described without the necessity of any rescaling
of the strength of the optical potential. A clear improvement in the
description of the differential cross sections for the ($^3$He,$t$)IAS
reactions on $^{58}$Ni and $^{90}$Zr targets is found when the neutron excess
density is used to determine the transition densities. Our results show that
the density and isospin dependences of the $G$-matrices play a non-negligible
role in the description of the experimental data.

Nuclear Theory