  In this work we explore the possibility that the motion of the deuterium ions
emitted from Coulomb cluster explosions is chaotic enough to resemble
thermalization. We analyze the process of nuclear fusion reactions driven by
laser-cluster interactions in experiments conducted at the Texas Petawatt laser
facility using a mixture of D2+3He and CD4+3He cluster targets. When clusters
explode by Coulomb repulsion, the emission of the energetic ions is nearly
isotropic. In the framework of cluster Coulomb explosions, we analyze the
energy distributions of the ions using a Maxwell- Boltzmann (MB) distribution,
a shifted MB distribution (sMB) and the energy distribution derived from a
log-normal (LN) size distribution of clusters. We show that the first two
distributions reproduce well the experimentally measured ion energy
distributions and the number of fusions from d-d and d-3He reactions. The LN
distribution is a good representation of the ion kinetic energy distribution
well up to high momenta where the noise becomes dominant, but overestimates
both the neutron and the proton yields. If the parameters of the LN
distributions are chosen to reproduce the fusion yields correctly, the
experimentally measured high energy ion spectrum is not well represented. We
conclude that the ion kinetic energy distribution is highly chaotic and
practically not distinguishable from a thermalized one.
