Deviation from Maxwell distribution in granular gases with constant restitution coefficient

We analyze the velocity distribution function of force-free granular gases in the regime of homogeneous cooling when deviations from the Maxwellian di stribution may be accounted only by the leading term in the Sonine polynomi al expansion, quantified by the second coefficient a,. We go beyond the lin ear approximation for a(2) and find three different values (three roots) fo r this coefficient which correspond to a scaling solution of the Boltzmann equation. The stability analysis performed showed, however, that among thes e three roots only one corresponds to a stable scaling solution. This is ve ry close to at, obtained in previous studies in a linear with respect to ae approximation.