  Non-resonant fusion cross-sections significantly higher than corresponding
theoretical predictions are observed in low-energy experiments with deuterated
matrix target. Models based on thermal effects, electron screening, or
quantum-effect dispersion relations have been proposed to explain these
anomalous results: none of them appears to satisfactory reproduce the
experiments. Velocity distributions are fundamental for the reaction rates and
deviations from the Maxwellian limit could play a central role in explaining
the enhancement. We examine two effects: an increase of the tail of the target
Deuteron momentum distribution due to the Galitskii-Yakimets quantum
uncertainty effect, which broadens the energy-momentum relation; and spatial
fluctuations of the Debye-H\"{u}ckel radius leading to an effective increase of
electron screening. Either effect leads to larger reaction rates especially
large at energies below a few keV, reducing the discrepancy between
observations and theoretical expectations.
