The Bochum experimental enhancement of the d+d fusion rate in a deuterated metal matrix at low incident energies is explained by the quantum broadening of the momentum-energy dispersion relation and consequent modification of the highmomentum tail of the distribution function from an exponential to a power-law.

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This study concerns a situation when measurements of the nonresonant cross-section of nuclear reactions appear highly dependent on the environment in which the particles interact. An appealing example discussed in the paper is the interaction of a deuteron beam with a target of deuterated metal Ta. In these experiments, the reaction cross section for d(d,p)t was shown to be orders of magnitude greater than what the conventional model predicts for the low-energy particles. In this paper we take into account the influence of quantum effects due to the Heisenberg uncertainty principle for particles in a non-ideal medium elastically interacting with the medium particles.In order to calculate the nuclear reaction rate in the non-ideal environment we apply both the Monte Carlo technique and approximate analytical calculation of the Feynman diagram using nonrelativistic kinetic Green's functions in the medium which correspond to the generalized energy and momentum distribution functions of interacting particles. We show a possibility to reduce the 12-fold integral corresponding to this diagram to a fivefold integral. This can significantly speed up the computation and control accuracy. Our calculations show that quantum effects significantly influence reaction rates such as p + 7 Be, 3 He + 4 He, p + 7 Li, and 12 C + 12 C. The new reaction rates may be much higher than the classical ones for the interior of the Sun and supernova stars. The possibility to observe the theoretical predictions under laboratory conditions is discussed.