Attractive d-d interaction via phonon exchange in deuterated Pd

Phonon exchange between two quasi free, slow deuterons moving in a host lattice (e.g. Pd) partly filled with localized deuterons leads to an interaction potential between them. The spherically symmetric parts of the potential produced by acoustic and optical modes are given. It is found that the leading term results from optical phonon exchange and that it becomes attractive for small distances as the deuteron-density fraction u = nd/nion, the deuteron over metal ion number density increases. The value of the potential for zero separation of the particles is given as a function of their equal kinetic energy E at different values of u. Numerical results obtained for the Gamow factor are also given. The connection of the results with the recently observed enhancements of fusion rates of d + d reactions in deuterated metals is also discussed.