Theoretical Framework for Anomalous Heat and He from Low Energy Nuclear Reactions in Transition Metal Systems

During the First Annual Cold Fusion Conference (ICCF1), Julian Schwinger stated that "In the very low energy cold fusion, one deals essentially with a single state, described by a single-wave function, all parts of which are coherent. A separation into two independent, incoherent factors is not possible, and all considerations based on such a factorization are not relevant." In the paper, we provide some background information that can be used to understand, in basic terms, the origin of this intuitive idea. In particular, the usual picture of nuclear physics, which assumes that the wave function can be separated into two factors (one that couples to nuclear processes, and a second factor that couples to electromagnetic processes), holds for the dominant nuclear fusion reactions. But this approximation fails to describe deuteron (D) +D -> He fusion, which is dominated by electromagnetic effects. A second idea, also alluded to by Schwinger at ICCF1, is that coupling can occur between nuclear processes associated with this “single wave function” to atomic processes associated with a lattice. In the paper, we point out that the origin of these forms of coupling can be explained through known coherent effects (associated with broken gauge symmetry) that allow for momentum to be shared at many locations simultaneously. In particular, although at high values of momentum p, that occur when individual D’s collide at a point (for example), a particle possessing charge q, mass m, and velocity v approximately obeys p=mv, the precise relationship involves the vector potential (A) associated with the local electromagnetic field; i.e., mv=p-e/cA, where c is the speed of light. As a consequence, in more general situations, involving many particles, mv and p can both be small in value, at many locations, but they can be coupled non-locally, through changes in A. For this reason, nuclear and electromagnetic interactions can become coupled non-locally. Using general expressions, based on conventional many-body physics, we quantify these effects and show that the usual assumption that a high energy gamma ray be released in D +D -> He can be modified in such a way that all of the energy of the reaction can become dissipated through processes that have characteristic time scales that are consistent with those that are found in normal chemistry.