  Cross-section distributions are calculated for the reaction $e^+ e^-
\rightarrow J/\psi\rightarrow \bar{\Lambda}(\rightarrow \bar{p}\pi^+)
\Lambda(\rightarrow p\pi^-)$, and related annihilation reactions mediated by
vector mesons. The hyperon-decay distributions depend on a number of structure
functions that are bilinear in the, possibly complex, psionic form factors
$G_M^\psi$ and $G_E^\psi$ of the Lambda hyperon. The relative size and relative
phase of these form factors can be uniquely determined from the unpolarized
joint-decay distributions of the Lambda and anti-Lambda hyperons. Also the
decay-asymmetry parameters of Lambda and anti-Lambda hyperons can be
determined.
