A study of local approximation for polarization potentials

We discuss the derivation of an equivalent $\mathit{\text{l}}$-independent polarization potential for use in the optical Schr"{o}dinger equation that describes the elastic scattering of heavy ions. Three diffferent methods are used for this purpose. Application of our theory to the low energy scattering of the halo nucleus ${}^{11}$Li from a ${}^{12}$C target is made. It is found that the notion of $\mathit{\text{l}}$-independent polarization potential has some validity but can not be a good substitute for the $\mathit{\text{l}}$-dependent local equivalent Feshbach polarization potential.