  We revisit the calculation of the medium-induced gluon radiative spectrum and
propose a novel expansion scheme that encompasses the two known analytic
limits: i) the high frequency regime dominated by a single hard scattering that
corresponds to the leading order in the standard opacity expansion, ii) the low
frequency regime that is dominated by multiple soft scatterings. Our approach
is based on expanding around the harmonic oscillator instead of vacuum in the
leading logarithmic approximation. We compute the first two orders in this
improved opacity expansion and show that they account for the aforementioned
limits.
