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Recently a tachyon DBI action is proposed for describing the non-coincident D$_p$-brane-anti-D$_p$-brane system. For brane separation larger than $\sqrt{2\pi^2\alpha'}$, the tachyon potential has both false and true vacuums. We shall show that due to the non-standard form of the kinetic term in the effective action, the thin wall approximation for calculating the bubble nucleation rate gives a result which is independent of the brane separation.
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