  Cross sections of $^{120}$Sn($\alpha$,$\alpha$)$^{120}$Sn elastic scattering
have been extracted from the $\alpha$ particle beam contamination of a recent
$^{120}$Sn($^6$He,$^6$He)$^{120}$Sn experiment. Both reactions are analyzed
using systematic double folding potentials in the real part and smoothly
varying Woods-Saxon potentials in the imaginary part. The potential extracted
from the $^{120}$Sn($^6$He,$^6$He)$^{120}$Sn data may be used as the basis for
the construction of a simple global $^6$He optical potential. The comparison of
the $^6$He and $\alpha$ data shows that the halo nature of the $^6$He nucleus
leads to a clear signature in the reflexion coefficients $\eta_L$: the relevant
angular momenta $L$ with $\eta_L \gg 0$ and $\eta_L \ll 1$ are shifted to
larger $L$ with a broader distribution. This signature is not present in the
$\alpha$ scattering data and can thus be used as a new criterion for the
definition of a halo nucleus.
