α+C12inelastic angular distribution and nuclear size ofC12(02+)

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We analyze the inelastic scattering of \ensuremath{\alpha} particles on $^{12}\mathrm{C}$ exciting the ${0}_{2}^{+}$ state at incident energies of ${E}_{\ensuremath{\alpha}}=139\text{\ensuremath{-}}240$ MeV using \ensuremath{\alpha}-condensate model wave functions, and investigate the effect of the nuclear radius of $^{12}\mathrm{C}$(${0}_{2}^{+}$) on the inelastic angular distribution. It is found that the oscillation pattern in inelastic angular distribution is sensitive to the extension of the transition density rather than the nuclear radius of the excited state, although the absolute value of the inelastic differential cross section is sensitive to the nuclear radius of $^{12}\mathrm{C}$(${0}_{2}^{+}$).