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In the reactions Be ^{9 }(α, 2α)He ^{5 } and C ^{12 }(α, 2α)Be ^{8 } at 28 MeV, the single and summed energy spectra of emitted alpha-particles have been measured at several pairs of angle in order to investigate the quasi-free collision between incident alpha-particles and alpha-clusters in Be ^{9 } and C ^{12 }. The summed energy spectrum of the alpha-particles from the reaction Be ^{9 }(α, 2α)He ^{5 } shows a peak corresponding to the ground state of He ^{5 } at the angles at which the emitted particles come from the collision between incident alpha-particles and nearly zero-momentum alpha-clusters in Be ^{9 }. The momentum spread of the alpha-cluster in Be ^{9 } coupled with He ^{5 } (ground state) is estimated to be 0.3 fm ^{-1 } from the angular correlation of the peak in the summed energy spectrum, and the probability of finding an alpha-cluster in this state is 0.12, if a plane wave impulse approximation is assumed. In the reaction C ^{12 }(α, 2α)Be ^{8 }_{g'nd }, the yield has a minimum at the angles expected from the quasi-free collision between incident alpha-particles and nearly zero-momentum alpha-clusters in C ^{12 }. The state in which an alpha-cluster is bound to Be ^{8 } (ground state) in C ^{12 } seems to be very different from that for Be ^{9 }.

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