We study the effects of adding the Coulomb interactions to the harmonic oscillator (HO) approximation of the heavy parton propagating through the quark-gluon plasma (the extension to QCD of the Molliere theory). We explicitly find the expression for the transverse momentum distribution of the gluon radiation of the heavy quark propagating in the quark gluon plasma in the framework of the Moliere theory, taking into account the BDMPSZ radiation in the harmonic oscillator (HO) approximation, and the Coulomb logarithms described by the additional logarithmic terms in the effective potential. We show that these Coulomb logarithms significantly influence the HO distribution, derived in the BDMPSZ works, especially for the small transverse momenta, filling the dead cone, and reducing the dead cone suppression of the heavy quark radiation (dead cone effect). In addition we study the effect of the phase space constraints on the heavy quark energy loss, and argue that taking into account of both the phase space constraints and of the Coulomb gluons reduces the dependence of the heavy quark energy loss on its mas in the HO approximation.
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