  We revisit the upper limits on the abundance of unstable massive relic
particles provided by the success of Big-Bang Nucleosynthesis calculations. We
use the cosmic microwave background data to constrain the baryon-to-photon
ratio, and incorporate an extensively updated compilation of cross sections
into a new calculation of the network of reactions induced by electromagnetic
showers that create and destroy the light elements deuterium, he3, he4, li6 and
li7. We derive analytic approximations that complement and check the full
numerical calculations. Considerations of the abundances of he4 and li6 exclude
exceptional regions of parameter space that would otherwise have been permitted
by deuterium alone. We illustrate our results by applying them to massive
gravitinos. If they weigh ~100 GeV, their primordial abundance should have been
below about 10^{-13} of the total entropy. This would imply an upper limit on
the reheating temperature of a few times 10^7 GeV, which could be a potential
difficulty for some models of inflation. We discuss possible ways of evading
this problem.
