  We theoretically examine the effect of carrier-carrier scattering processes
(electron-hole and electron-electron) on the intraband radiation absorption and
their contribution to the net dynamic conductivity in optically or electrically
pumped graphene. We demonstrate that the radiation absorption assisted by the
carrier-carrier scattering can be stronger than the Drude absorption due to the
carrier scattering on disorder. Since the intraband absorption of radiation
effectively competes with its interband amplification, this can substantially
affect the conditions of the negative dynamic conductivity in the pumped
graphene and, hence, the interband terahertz and infrared lasing. We find the
threshold values of the frequency and quasi-Fermi energy of nonequilibrium
carriers corresponding to the onset of negative dynamic conductivity. The
obtained results show that the effect of carrier-carrier scattering shifts the
threshold frequency of the radiation amplification in pumped graphene to higher
values. In particular, the negative dynamic conductivity is attainable at the
frequencies above 6 THz in graphene on SiO2 substrates at room temperature. The
threshold frequency can be decreased to markedly lower values in graphene
structures with high-k substrates due to screening of the carrier-carrier
scattering, particularly at lower temperatures.
