  Two types of pseudoscalar quarkonium electromagnetic decay processes, i.e.
decay to a lepton pair, and to a lepton pair plus a photon (Dalitz decay), are
analyzed at the leading order in NRQCD expansion. The former type of processes,
highly suppressed in the Standard Model, have been hoped to act as the
sensitive probes of the possible new physics. The latter type of processes
generally possess much greater decay rates than the former, owing to several
conspiring factors. The recently launched BES-III program, with $10^8$ $\eta_c$
samples to be anticipated in the coming years, may be able to observe the
Dalitz decays $\eta_c\to e^+e^-\gamma$ and $\eta_c\to \mu^+\mu^-\gamma$, which
have branching ratios of order $10^{-6}$. When the radiated photon becomes very
soft, the Dalitz decay events will be experimentally tagged as the exclusive
lepton pair events. It is found that, those quasi-two-body events that arise
from $\eta_c\to e^+ e^-\gamma$ with photon energy less than the minimum
sensitivity of the electromagnetic calorimeter, can vastly outnumber the
literal $\eta_c\to e^+ e^-$ events, however this amplification is still not
dramatic enough for the BES-III experiment to establish these events.
Consequently, the expectation of looking for new physics signature in the
$\eta_c\to l^+l^-$ channel is obscured, unless the contamination from $\eta_c
\to l^+l^-\gamma$ has been taken into account carefully.
