The equations describing the polarization and temporal shapes of the superr
adiance pulses formed in gaseous media on the transitions between degenerat
e levels are obtained with an account of first-order atom-atom correlations
. In these equations, unlike the semiclassical case, the initial conditions
are well defined by the characteristics of the excitation pulse. The numer
ical calculations of the superradiance pulse temporal shapes are carried ou
t for some transitions with small values of the level angular momenta. Such
calculations showed no qualitative difference with the results of semiclas
sical approximation except the case of symmetric excitation, when the two p
olarization components of superradiance are equal. In this latter case the
superradiance pulse remains fully unpolarized, while in a semiclassical app
roach it is considered to be fully polarized, its polarization varying rand
omly from pulse to pulse. The results of the calculations indicate that in
case of arbitrary values of the level angular momenta the coherent superrad
iance pulse cannot depopulate the excited level totally, some part of the e
xcited atoms (e.g., about 20 per cent in case of transitions 3/2 --> 3/2) i
s depopulated in cause of incoherent spontaneous emission.