  We describe a model for photon absorption by superconducting tunnel junctions
in which the full energy dependence of all the quasiparticle dynamic processes
is included. The model supersedes the well-known Rothwarf-Taylor approach,
which becomes inadequate for a description of the small gap structures that are
currently being developed for improved detector resolution and responsivity. In
these junctions relaxation of excited quasiparticles is intrinsically slow so
that the energy distribution remains very broad throughout the whole detection
process. By solving the energy-dependent kinetic equations describing the
distributions, we are able to model the temporal and spectral evolution of the
distribution of quasiparticles initially generated in the photo-absorption
process. Good agreement is obtained between the theory and experiment.
