  Fully microscopic many-body models based on inputs from first principle
density functional theory are used to calculate the carrier losses due to
radiative- and Auger-recombinations in bulk tellurium. It is shown that Auger
processes dominate the losses for carrier densities in the range typical for
applications as lasers. The Auger loss depends crucially on the energetic
position of the $H_6$ valence bands. At cryogenic temperatures of 50$\,$K
(100$\,$K) the Auger coefficient, $C$, varies by about six (three) orders of
magnitude within the range of published distances between these bands and the
valence bandedge. Values for $C$ at the high and low end of these ranges are
found if the distance is smaller or larger than the bandgap, respectively. At
room temperature the sensitivity is reduced to about a factor of four with $C$
values ranging between $0.4$ and $1.6\times 10^{-27}$cm$^6$s$^{-1}$. Here,
radiative losses dominate for carrier densities up to about $10^{16}/$cm$^3$
with a loss coefficient $B\approx 10^{-11}$cm$^3$s$^{-1}$. The radiative losses
are about two to three times lower than in typical bulk III-V materials for
comparable wavelengths.
