  We discuss the derivation of an equivalent \textit{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 \textit{l}-independent polarization potential has some validity
but can not be a good substitute for the \textit{l}-dependent local equivalent
Feshbach polarization potential.
