We report new measurements of the cross sections for the production of D Dbar final states at the psi(3770) resonance. Our data sample consists of an integrated luminosity of 2.93/fb of e+e- annihilation data produced by the BEPCII collider and collected and analyzed with the BESIII detector. We exclusively reconstruct three D0 and six D+ hadronic decay modes and use the ratio of the yield of fully reconstructed D Dbar events (double tags) to the yield of all reconstructed D or Dbar mesons (single tags) to determine the number of D0 D0bar and D+D- events, benefiting from the cancellation of many systematic uncertainties. Combining these yields with an independent determination of the integrated luminosity of the data sample, we find the cross sections to be sigma(e+e- --> D0 D0bar)=(3.615 +- 0.010 +- 0.038) nb and sigma(e+e- --> D+D-)=(2.830 +- 0.011 +- 0.026) nb, where the uncertainties are statistical and systematic, respectively.
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