  The root mean square radii of $^{20}$Ne in the short-lived excited states
were experimentally deduced for the first time from the analyses of
$\alpha$+$^{20}$Ne diffraction scattering. Differential cross sections of the
elastic and inelastic $\alpha$+$^{20}$Ne scattering in the incident energy
range from a few MeV/nucleon up to 100 MeV/nucleon were analyzed by the
modified diffraction model. No significant radius enhancement for the members
of K$^{\pi}$ = 0$_{1}^{+}$ and K$^{\pi}$ = 2$^{-}$ bands in comparison with the
ground state was observed. At the same time 20 % radius enhancement was
obtained for the K$^{\pi}$ = 0$_{1}^{-}$ band members. Moreover, for the
0$_{2}^{+}$ state located above $\alpha$-emission threshold increased radius
was observed. This result can speak in favor of possible $\alpha$-condensate
structure of the 0$_{2}^{+}$ state and can be considered as a possible analog
of the famous 7.65-MeV 0$_{2}^{+}$ Hoyle state of $^{12}$C.
