This paper shows that an exact calculation for transition probability can make some systems deviate seriously from Fermi’s golden rule. The paper also shows that the corresponding exact calculation of the phonon-induced hopping rate for a deuteron in the Pd–D system plus many-body electron screening, proposed by Ichimaru, can explain experimental factors observed in the Pd–D system. It also predicts that the perfect and low dimensional forms of the Pd lattice are very important factors for the phonon-induced hopping rate enhancement of deuterons in the Pd–D system.

This paper shows that exact calculation for transition probability can make some systems deviate from Fermi golden rule seriously. This paper also shows that the corresponding exact calculation of hopping rate induced by phonons for deuteron in Pd-D system with the many-body electron screening, proposed by Ichimaru, can explain the experimental fact observed in Pd-D system, and predicts that perfection and low-dimension of Pd lattice are very important for the phonon-induced hopping rate enhancement in Pd-D system.

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