Cold fusion/Theory/Electron catalysis
Proposal developed by Vernon Nemitz, see Cold Nuclear Fusion: A Hypothesis (Wikisource) for details.
This proposal starts with several different facts, and tries to tie them together into a coherent explanation. It notes that in a metal such as palladium, many electrons are "loose" in the sense that they are free to roam throughout the body of the metal (see w:Conduction band). It also notes that hydrogen and palladium have very similar w:Electronegativity, which implies that hydrogen should be able to form an w:Alloy with palladium. One logical consequence would be the breakup of hydrogen molecules into loose electrons that join the conduction band, and bare deuterons, which could explain hydrogen's extraordinary ability to permeate solid palladium metal, almost as if the metal wasn't there.
Other relevant facts concern the w:Virtual particles that are found everywhere, and, more specifically, the role of virtual w:Pions in ordinary nuclear fusion. Also, the w:Uncertainty_principle plays a very important role in allowing large numbers of loose conduction-band electrons to very closely and semi-simultaneously (because of their uncertainty-in-location) approach bare deuterons.
The idea that many loose electrons can very closely approach a bare deuteron is important because a normal "orbiting" electron does so only rarely--and a single orbiting electron spends too little time exactly-in-between two deuterons, to shield their mutual electrostatic repulsion (while a w:Muon can spend enough time there; see w:Muon-catalyzed fusion). Basically, multiple loose electrons can do the job of an orbiting muon.
One way of looking at it is to note that two separate deuterons have electric charges that attract electrons, and the place where the attraction is greatest is exactly in-between the two deuterons. Any single electron can only exist there momentarily (it is a fairly fast-moving particle), but if many loose conduction-band electrons are available, then every time one leaves that spot, another can immediately take its place (can actually be said to already be there, thanks to Uncertainty). Not to mention that since there are two electric charges attracting electrons, there can even be two at a time in-between the deuterons. And it only takes one to shield the two deuterons' mutual repulsion (as proved by the existence of muon catalyzed fusion).
The preceding can explain how two deuterons can approach each other closely enough for them to begin the process of fusing, especially because as long as the deuterons are separate particles, loose non-orbiting conduction-band electrons can still become (per Uncertainty) located in-between them. However, this explanation for how two deuterons can approach each other is not the same thing as "encouragement" for them to approach each other. This is a significant difference with muon catalysis, because in that event the muon orbits one deuteron, and has enough mass to drag the deuteron it orbits closer to a second deuteron. Loose electrons are neither in orbit nor have sufficient mass. All they can do is allow the deuterons to closely approach each other, should they happen to be, at random, on a collision course. This in turn may explain why so much deuterium needs to be "loaded" into the palladium (typically 80% or more as many deuterium atoms as there are palladium atoms) before significant quantities of heat begins to appear --a sheer quantity of bare deuterons is needed to balance the low probability that any two of them will randomly very closely approach each other.
If two deuterons begin the process of fusing, then virtual pions, some of which are electrically charged, start traversing the space between the two deuterons. These pions travel at nearly the speed of light and can cross the distance in something like a trillionth of a trillionth of a second. While it is well known that pions can interact with neutrons and protrons via the w:Strong force, it is a logical certainty that any electrically charged pions can also interact electrostatically with electrons.
So, what happens when a virtual pion moving nearly at light-speed runs into one of those electrons that is helping to cancel out the electric repulsion of the two deuterons? Any pion has about 250 times the mass of an electron; if the pion is electrically charged, then it is not difficult to envision the electron being "kicked" severely. And, the "bookkeeping" of these events will require that any energy imparted to the electron must happen at the expense of the overall fusion reaction.
But that's just the beginning, because as mentioned, as soon as one electron leaves the scene (by whatever means), another loose conduction-band electron can practically instantly take its place. And if the overall fusing of the two deuterons takes a mere trillionth of a second to be done-and-over, that is still enough time for a trillion virtual pions to pass in-between them, many of them kicking electrons that get in their way.
The electron-catalysis proposal basically states that so much energy can be imparted to so many electrons that the overall fusion reaction can take the simple form of D+D->4He. Note that this can only happen if a great many conduction-band electrons are available, so, in "co-deposition" experiments that involve extremely thin layers of metal, sometimes not-enough energy can be imparted to electrons, and therefore in those experiments the more-conventional deuteron-fusion reactions can occur.
Finally, low levels of w:X-rays have been observed in cold fusion experiments. Electron catalysis can easily explain that, since high-speed electrons moving through solid metal very often generate X-rays. More, since palladium is not particularly transparent to X-rays, only those which are produced near the surface of the metal can escape to be observed (thus low levels). All the rest of the X-rays simply get absorbed inside the palladium, becoming heat.