  We use the greatly improved optical linewidths provided by highly enriched
$^{28}$Si to study a photoluminescence line near 1017 meV previously observed
in the luminescence spectrum of natural Si diffused with Mg, and suggested to
result from the recombination of an isoelectronic bound exciton localized at a
Mg-pair center. In $^{28}$Si this no-phonon line is found to be comprised of
five components whose relative intensities closely match the relative
abundances of Mg-pairs formed by random combinations of the three stable
isotopes of Mg, thus confirming the Mg-pair hypothesis. We further present the
results of temperature dependence studies of this center that reveal unusual
and as yet unexplained behaviour.
