Excitation of isobaric analog states from (p,n) and (He3,t) charge-exchange reactions within the G -matrix folding method

Differential cross sections of $(p,n)$ and $(^{3}\mathrm{He},t)$ 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 $(p,n)\mathrm{IAS}$ on $^{14}\mathrm{C}$ at ${E}_{\mathrm{lab}}=135$ MeV and $^{48}\mathrm{Ca}$ at ${E}_{\mathrm{lab}}=134$ MeV and ${E}_{\mathrm{lab}}=160$ MeV, and $(^{3}\mathrm{He},t)\mathrm{IAS}$ on $^{58}\mathrm{Ni},$ $^{90}\mathrm{Zr},$ and $^{208}\mathrm{Pb}$ at ${E}_{\mathrm{lab}}=420$ 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 $(^{3}\mathrm{He},t)\mathrm{IAS}$ reactions on $^{58}\mathrm{Ni}$ and $^{90}\mathrm{Zr}$ 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.