Florian Metzler, Camden Hunt, Peter L Hagelstein and Nicola Galvanetto: Known mechanisms that increase nuclear fusion rates in the solid state (preprint, PDF)

The authors of the paper say there are three separate mechanisms for cold fusion. Each on its own is too small an effect, but all 3 together could just make it work. Cascading multiple such mechanisms could lead to an overall enhancement of 40 orders of magnitude or more. Take it all together, they say, and these effects can enhance the fusion rate in materials enough for it to produce net energy. They also outline ways to test these individual mechanisms to learn more about them, most importantly by using specific materials that have controlled amounts of traces of other elements in them.

1. The first mechanism in the atomic range. Remember that the problem with nuclear fusion is the electric repulsion between the nuclei. Now imagine you could put a thin slice of negative electric charge between them, then the nuclei wouldn’t notice each other as they get closer. Something similar could happen in solid-state lattice, near defects, where the electron wave-functions become focused and form a sort of shield between the deuterium nuclei. In the paper they write that this can enhance the fusion rate by a whopping 25 orders of magnitude.

2. The second mechanism they discuss is nuclear resonance between several of the nuclei that you want to fuse. This can be triggered for example with the pulsed lasers that I mentioned earlier. They say that the reason this works is that it causes a deformation of the nuclei that effectively lowers the energy you need to make them approach. Unfortunately, creating this resonance eats up energy similar to what would be released during the fusion. They conjecture, however, that similar resonances could exist at lower energy and estimate that this could lead to an “enhancement of 7 orders of magnitude" of fusion probability.

3. The third mechanism they discuss in the paper is that the presence of the larger nuclei in the material facilitates the fusion of the smaller nuclei by aiding a quantum tunneling process. This superficially makes sense because we know that nuclei can aid quantum processes that are otherwise impossible. For example, an electron can normally not just emit a photon. However, put the electron in the vicinity of an atomic nuclei, and that process can happen thanks to momentum exchange with the nucleus. For cold fusion they say something similar takes place. The small nuclei that you want to fuse can temporarily borrow energy from the surrounding nuclei, fuse, and then give that energy back. They estimate that this could lead to “an increase [of fusion rates] upwards of 30 orders of magnitude”.

Actually the speed of cold fusion has to be increased only by some 8 orders of magnitude (from range of 1.44 MeV for pair of free protons to range of eV) for being able to run. This target thus isn't so unattainable. See for instance What Happens if You Focus a 5W Laser With a Giant Magnifying Glass? Most of us know, we can not heat objects with focusing of sunlight to the temperature higher than this one of Sun surface. But how it applies to monochromatic laser instead of black body radiation governed with Planck law? The thermodynamics of collisions within metal lattices is similar: the thermodynamic temperature and energy of transition can not be easily applied for them, once these collisions become low-dimensional and coherent.

Here I'm explaining that hot fusion runs on random collisions coming from all possible directions in an equal way. But head-2-head collisions of atoms inside of metal lattices are collinear - which is from statistical perspective of hot fusion as low probable arrangement as the probability that collision of two atoms at the room temperature overcomes Coulomb barrier.

Go figure, how these two extremely low probabilities can cancel out mutually... See also:

Freak waves are a mechanical analogy of laser light not just in their negative thermodynamic time arrow and temperature. They also arise in similar mechanism to lasing, as they drain energy from their environment instead of scattering it into an outside. So that the rogue waves may serve as a water surface analogy of various overunity devices.. The cold fusion therefore may run like solid state phonon laser on coherent collisions within metal lattices.