  We perform the first quantitative analysis of the reaction cross sections of
$^{28-32}$Ne by $^{12}$C at 240 MeV/nucleon, using the double-folding model
(DFM) with the Melbourne $g$-matrix and the deformed projectile density
calculated by the antisymmetrized molecular dynamics (AMD). To describe the
tail of the last neutron of $^{31}$Ne, we adopt the resonating group method
(RGM) combined with AMD. The theoretical prediction excellently reproduce the
measured cross sections of $^{28-32}$Ne with no adjustable parameters. The
ground state properties of $^{31}$Ne, i.e., strong deformation and a halo
structure with spin-parity $3/2_{}^-$, are clarified.
