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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 densitycalculated by the antisymmetrized molecular dynamics (AMD). To describe thetail of the last neutron of $^{31}$Ne, we adopt the resonating group method(RGM) combined with AMD. The theoretical prediction excellently reproduce themeasured cross sections of $^{28-32}$Ne with no adjustable parameters. Theground state properties of $^{31}$Ne, i.e., strong deformation and a halostructure with spin-parity $3/2_{}^-$, are clarified.

Determination of the structure of $^{31}$Ne by full-microscopic framework