  The strong forces between nucleons and between nucleons and antinucleons are
fundamental to the visible universe. Whereas the interactions between nucleons
($pp$, $pn$, $nn$) and those between nucleons and antiproton ($p\bar{p}$,
$n\bar{p}$) have been extensively studied, the interactions between nucleons
and antineutron ($p\bar{n}$, $n\bar{n}$) are not well understood, due to lack
of data, limited by scarcity of suitable antineutron sources. Here we point out
and investigate a new high-quality source: antineutrons produced in $J/\psi$
decays at rest into $p\pi^-\bar{n}$. By tagging $p$ and $\pi^-$, the flux and
momentum of the antineutron can be determined precisely. With 10 billion
$J/\psi$ events produced in $e^+e^-$ annihilation in BESIII, and orders of
magnitude more in the super $J/\psi$ factory, the decay $J/\psi\to
p\pi^-\bar{n}$ serves as an ideal antineutron source, enabling unprecedented
precision-study of antineutron interactions with a wide range of targets. We
also discuss an analogous possibility of using $J/\psi$ decays as an abundant
high-quality source of $\Lambda, \Sigma$ and $\Xi$ hyperons and their
antiparticles. These novel high-statistics sources of baryons and antibaryons
with precisely known kinematics open fresh opportunities for applications in
particle and nuclear physics, including antinucleon-nucleon interaction,
nonvalence $s\bar{s}$ component of the nucleon, (anti)hyperon-nucleon
interaction, OZI violation, (multi-strange) hypernuclei, exotic light hadron
spectroscopy and many others.
