The aCORN experiment measures the neutron decay electron-antineutrino correlation ($a$-coefficient) using a novel method based on an asymmetry in proton time-of-flight for events where the beta electron and recoil proton are detected in delayed coincidence. We report the data analysis and result from the second run at the NIST Center for Neutron Research, using the high-flux cold neutron beam on the new NG-C neutron guide end position: $a = -0.10758 pm 0.00136 (mbox{stat}) pm 0.00148 (mbox{sys})$. This is consistent within uncertainties with the result from the first aCORN run on the NG-6 cold neutron beam. Combining the two aCORN runs we obtain $a = -0.10782 pm 0.00124 (mbox{stat}) pm 0.00133 (mbox{sys})$, which has an overall relative standard uncertainty of 1.7 %. The corresponding result for the ratio of weak coupling constants $lambda = G_A/G_V$ is $lambda = -1.2796pm 0.0062$.
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