This study investigates the fusion and scattering of nuclei at energies spanning the Coulomb barrier. The coupling of the relative motion of the nuclei to internal degrees of freedom can be thought to give rise to a distribution of potential barriers. ¶ Two new methods to extract representations of these potential barrier distributions are suggested using the eigen-channel model. The new techniques are based on measurements of quasi-elastic and elastic backscattering excitation functions, from which the representations are extracted by differentiation. A third method utilizing transfer excitation functions is introduced using qualitative arguments. The techniques are investigated experimentally for the reactions 16O + 92Zr, 144,154Sm, 186W and 208Pb. The results are compared with barrier distribution representations obtained from fusion data. The methods are further explored using the systems 40Ca + 90,96Zr and 32S + 208Pb, for which scattering and fusion excitation functions have been measured. The new barrier distribution representations are consistent with the one from fusion. They are direct evidence of the effects of the internal degrees of freedom on channels other than the fusion channel. ¶ ...