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The mechanism of the Coulomb breakup reactions of the nuclei withneutron-halo structure is investigated in detail. A time-dependentSchr\"odinger equation for the halo neutron is numerically solved by treatingthe Coulomb field of a target as an external field. The momentum distributionand the post-acceleration effect of the final fragments are discussed in afully quantum mechanical way to clarify the limitation of the intuitive picturebased on the classical mechanics. The theory is applied to the Coulomb breakupreaction of $^{11}$Be + $^{208}$Pb. The breakup mechanism is found to bedifferent between the channels of $j^{\pi}=\frac{1}{2}^{-}$ and$\frac{3}{2}^{-}$, reflecting the underlying structure of $^{11}$Be. Thecalculated result reproduces the energy spectrum of the breakup fragmentsreasonably well, but explains only about a half of the observed longitudinalmomentum difference.Comment: 15 pages,revtex, 9 figures (available upon request

Coulomb breakup mechanism of neutron-halo nuclei in a time-dependent method