Inversion formula for the internucleus potential using sub-barrier fusion cross sections

Subject to the assumption that sub-barrier fusion is described by an effective one-dimensional energy-independent local potential barrier, the Jeffreys-Wentzel-Kramers-Brillouin approximation for the fusion cross sections is inverted to determine this effective potential. Potential barriers, with their associated experimental errors, are presented for ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$+${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$+${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, and the assumption of a local effective potential is shown to be inadequate for ${}_{}{}^{64}{}_{}{}^{}\mathrm{Ni}$+${}_{}{}^{64}{}_{}{}^{}\mathrm{Ni}$.