Fusion rate enhancement due to energy spread of colliding nuclei

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 that generally provides fusion enhancement. We present a general formula for calculating the enhancement factor and 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 that are presently measurable; however, they have to be considered in future experiments at still lower energies. This study allows us to exclude several effects as a possible explanation of the observed anomalous fusion enhancements, which remain a mystery.