The decays $J/psito pbar{p}$ and $J/psito nbar{n}$ have been investigated with a sample of 225.2 million $J/psi$ events collected with the BESIII detector at the BEPCII $e^+e^-$ collider. The branching fractions are determined to be $mathcal{B}(J/psito pbar{p})=(2.112pm0.004pm0.031)times10^{-3}$ and $mathcal{B}(J/psito nbar{n})=(2.07pm0.01pm0.17)times10^{-3}$. Distributions of the angle $theta$ between the proton or anti-neutron and the beam direction are well described by the form $1+alphacos^2theta$, and we find $alpha=0.595pm0.012pm0.015$ for $J/psito pbar{p}$ and $alpha=0.50pm0.04pm0.21$ for $J/psito nbar{n}$. Our branching-fraction results suggest a large phase angle between the strong and electromagnetic amplitudes describing the $J/psito Nbar{N}$ decay.
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