  We observe the decay $\psi(3686) \to n \bar{n}$ for the first time and
measure $\psi(3686) \to p \bar{p}$ with improved accuracy by using $1.07\times
10^8$ $\psi(3686)$ events collected with the BESIII detector. The measured
branching fractions are $\mathcal{B}(\psi(3686) \to n \bar{n}) = (3.06 \pm 0.06
\pm 0.14)\times 10^{-4}$ and $\mathcal{B}(\psi(3686) \to p \bar{p}) = (3.05 \pm
0.02 \pm 0.12) \times 10^{-4}$. Here, the first uncertainties are statistical
and the second ones systematic. With the hypothesis that the polar angular
distributions of the neutron and proton in the center-of-mass system obey
$1+\alpha \cos^2\theta$, we determine the $\alpha$ parameters to be
$\alpha_{n\bar{n}} = 0.68 \pm 0.12 \pm 0.11$ and $\alpha_{p\bar{p}} = 1.03 \pm
0.06 \pm 0.03$ for $\psi(3686)\to n\bar{n}$ and $\psi(3686)\to p\bar{p}$,
respectively.
