  Experimental results for sub-barrier nuclear fusion reactions show cross
section enhancements with respect to bare nuclei which are generally larger
than those expected according to electron screening calculations. We point out
that energy spread of target or projectile nuclei is a mechanism which
generally provides fusion enhancement. We present a general formula for
calculating the enhancement factor and we provide quantitative estimate for
effects due to thermal motion, vibrations inside atomic, molecular or crystal
system, and due to finite beam energy width. All these effects are marginal at
the energies which are presently measurable, however they have to be considered
in future experiments at still lower energies. This study allows to exclude
several effects as possible explanation of the observed anomalous fusion
enhancements, which remain a mistery.
