  Interactions of charged leptons with nuclei and the naive tree-level
kinematics of these processes are affected by radiation of photons induced by
the QED nuclear medium. We evaluate cross-section modifications at leading
orders of the number of correlated interactions inside the nucleus, known as
the opacity expansion. We derive results for soft and collinear types of the
bremsstrahlung at the first three orders in opacity and generalize them to
higher orders. We present the leading in opacity energy spectra of soft and
collinear photons and radiative energy loss inside the nucleus for experiments
with lepton kinematics in the GeV energy range. At leading power of the Glauber
soft-collinear effective field theory, the soft radiation is further resummed
to all orders both in opacity and in the electromagnetic coupling constant. We
find that the soft and collinear medium-induced radiation is vacuumlike, and
additional corrections are power suppressed. Despite the negligible
modification to the induced photon spectra, the nuclear medium-induced
radiation sizably affects the broadening of charged leptons in the direction
orthogonal to their propagation.
