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The Q value of the (76)Ge double beta decay has been determined by measuring the masses of (76)Ge and (76)Se in a Penning trap using neon- and fluorinelike ions. The obtained masses are 75.921 402 758(96) u and 75.919 213 795(81) u, respectively. The systematic errors of these two determinations are nearly equal, and therefore, the remaining systematic uncertainty of the Q value is drastically reduced. A Q value of 2 039.006(50) keV was obtained improving the accuracy of the accepted value by a factor of 6.

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