  We revisit the Boltzmann equation governing the spectrum of energetic
particles originating from the decay of massive progenitors during the process
of thermalization. We assume that these decays occur when the background
temperature $T$ is much less than the mass $M$ of the progenitor. We pay
special attention to the IR cutoff provided by the thermal bath, and include
the suppression resulting from the interference of multiple scattering
reactions (LPM effect). We solve the resulting integral equation numerically,
and construct an accurate analytical fit of the solutions.
