  The splitting processes of bremsstrahlung and pair production in a medium are
coherent over large distances in the very high energy limit, which leads to a
suppression known as the Landau-Pomeranchuk-Migdal (LPM) effect. In this paper,
we continue study of the case when the coherence lengths of two consecutive
splitting processes overlap (which is important for understanding corrections
to standard treatments of the LPM effect in QCD), avoiding soft-gluon
approximations. In particular, this paper completes the calculation of the rate
for real double gluon bremsstrahlung from an initial gluon with various
simplifying assumptions (thick media; $\hat q$ approximation; and large $N_c$)
by now including processes involving 4-gluon vertices.
