First of all, let me remind why electron's magnetic dipole moment seems important from the point of view of fusion - I think the most crucial are back-scattering (on nucleus) type of electron trajectories due to the resulting Lorentz force, like (from simulation):
If you imagine that there is another proton approaching from the direction of this trajectory, electron can remain between the two nuclei, screening the Coulomb barrier and finally leading e.g. to p-e-p fusion into deuteron.
This is kind of nonstandard ("dual") Lorenz force: for magnetic dipole (electron) traveling in electric field (of nucleus)
- one of many EM dualities ( https://en.wikipedia.org/wiki/Duality_( ... _magnetism
It would have exactly the opposite sign if the nucleus would be the magnetic dipole (in fact it is, but thousand times weaker).
To see it, for a moment make a boost so that electron stays and nucleus travels - in magnetic field of electron's magnetic moment, so Lorentz force acts on the proton ... but due to 3rd Newton law opposite force acts on the electron.
Here is a more formal derivation:
I have managed to contact Eganova, but only got materials in Russian and couldn't find the details for the claims from the citation above.
The big problem with Sun is that it is believed that the core has only ~15MK, what gives ~1.4keV thermal energy per dof ... while for fusion we need to take e.g. protons to ~1fm, what needs >1MeV energy ... the temperature is thousand times too low.
The standard Gamov's explanation is quantum tunneling, but this is kind of magical explanation: proton teleports through energy barrier ... electron's assistance might bring a nonmagical understanding: help of electron maintaining trajectory between two nuclei, screening the Coulomb barrier and so making fusion much more probable - this "molecular fusion" of Gryzinski and Eganova, where dependence on temperature is far more nontrivial: such electron trajectories need stability, made more difficult while increasing temperature.
Regarding arguments for fusion inside our planet, the strongest I have seen concern tritium production in volcanoes - it quickly decays to He3 and amount produced in fission is nearly negligible - some volcanoes produce like 10000x more tritium than standard ways could explain:http://lenr-canr.org/acrobat/JonesSEgeofusiona.pdf
Also, in some rocks there are found helium concentration up to 7% ( https://en.wikipedia.org/wiki/Helium
) - could you imagine getting such concentrations from alpha decay only?
ps. nice animation about 1-10 electron atoms in free-fall atomic model: https://www.youtube.com/watch?v=P2IsIkSn5bk
my slides: https://dl.dropboxusercontent.com/u/124 ... efall2.pdf
Gryzinski's papers (3000+ citations): https://scholar.google.pl/scholar?hl=en&q=gryzinski