Molecular geometry in fullerene ${\mathrm{C}}_{60}$: A direct determination of the bond-length difference ${\mathit{d}}_{\mathrm{C}–\mathrm{C}}$-${\mathit{d}}_{\mathrm{C}=\mathrm{C}}$

The molecular structure factor of fullerene ${\mathrm{C}}_{60}$ has recently been determined with a high accuracy using neutron scattering over a large momentum-transfer range. The two bond lengths ${\mathit{d}}_{\mathrm{C}–\mathrm{C}}$ and ${\mathit{d}}_{\mathrm{C}=\mathrm{C}}$ have been measured with a precision of ${10}^{\mathrm{-}3}$ Å. As the temperature is lowered from 295 K down to 4 K, the single bond is elongated and the double bond shortened, but the radius of the sphere remains almost unchanged. Unfortunately, the covariance matrix obtained from the fit shows that the two lengths are strongly correlated; this means that any error made on the determination of one bond length is compensated by an opposite error on the other bond length without significantly increasing the ${\mathrm{\chi }}^2$ and, thus, the exactness of the reported temperature effect could be argued against. We present in this paper an alternative way of processing the data which allows us to remove almost completely the coupling, using an appropriate change of variables. The temperature effect is confirmed and resolved with a better accuracy.