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The negatively charged and long-lived X^- may form a Coulomb bound state (A X) with a nucleus A and may affect the big-bang nucleosynthesis through catalyzed fusion process. We calculate a production cross section of Li6 from the catalyzed fusion (He4 X^-) + d \\to Li6 + X^- by solving the Schr\\\"{o}dinger equation exactly for three-body system of He4, d, and X. 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