Coulomb and nuclear inelastic excitations and the optical potential for heavy ions

We present a simple, exact numerical method of obtaining the complex, $l$-dependent potentials $\Delta U_l\mathrm{}\left(r\right)\mathrm{}$ induced in the elastic channel by coupling to inelastic channels. For ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ + ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$ at 72 MeV, we consider pure Coulomb coupling and find that a simple power law absorption or the imaginary $l$-dependent polarization potentials of Baltz et al. gives good agreement with coupled channel cross sections out to 100°. For larger angles a more accurate representation of the polarization potentials for the low partial waves is required, both real and imaginary parts being significant. We also examine the ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ system at 68 MeV including a number of excited levels in both projectile and target. Here, nuclear coupling is dominant. The strength of the imaginary part of $\Delta U_l$ is found to vary quadratically with deformation length and inversely with excitation energy for excitations above about 5 MeV. The states above 8 MeV lead to a real potential of strength comparable to the imaginary in the surface region. The effect on the cross sections is discussed.