Following the interaction of superintense, short pulse lasers and plasmas, ions can be accelerated to velocities sufficient to drive nuclear fusion reactions, in particular, by the process of Coulomb explosion of clusters [T. Ditmire, Nature (London) 398, 491 (1999)]]. We show here how short bursts of neutrons can be produced using a jet of low-density deuterated methane clusters. Ion velocity distributions were simultaneously measured by a Thomson parabola mass spectrometer, demonstrating deuteron energies up to 120 keV. We show that, in such conditions, nuclear fusion will occur not only in the hot plasma core, but also in the cold outer region by collision processes.