**Imagine zero velocity situation: two protons and electron in the middle between them ( p ---- e ---- p ).**

The Coulomb force says that electron-proton attraction is four times stronger than proton-proton repulsion.

So this simple 3 body system should collapse – down to fusion into deuteron.

This trivial example suggests that electron could be very helpful in overcoming Coulomb barrier for LENR.

What is wrong with this picture? That it requires” classical” trajectory of electron, while we are expected to consider the quantum picture: with electron smeared into a probability density cloud – making such electron assisted fusion practically improbable.

So the main question here is: can we consider a trajectory of electron? For example averaging to the quantum probability distribution.

There are many arguments that we can, for example equivalent dBB interpretation: that inserting psi = rho * exp(iS) to Schrodinger equation, we get continuity equation for the density (rho) and “classical” Hamilton-Jacobi equation for action S, with h-order correction/perturbation: of interaction with the pilot wave.

Great intuition about this picture provides e.g. “classical-quantum” Couder experiments , getting for example interference: the corpuscle travels one paths, while its “pilot” wave travels multiple waves, influencing trajectory of the corpuscle (e.g.

So imagine there is some (semi-classical) trajectory of electron’s corpuscle inside atoms, piloted by its wave, averaging to Schrodinger’s probability cloud.

What trajectories should we expect? The first answer is Sommerfeld-Bohr’s elliptic trajectories. However, the ground hydrogen has zero angular momentum: we should degenerate the ellipse into a line: a free-fall trajectory.

What is missing in Bohr-Sommerfeld is taking electron’s magnetic dipole moment into consideration – it is corrected in the free-fall atomic model of Gryzinski.

This correction, classical spin-orbit interaction, has large influence on the free-falling trajectories.There appear also backscattering trajectories: when electron turns 180 degrees – allowing it to jump a few times between two nuclei, screening the Coulomb repulsion. And so Gryzinski has a note in Nature about cold fusion in 1989.

Gryzinski's papers (~30 from Phys. Rev. type of journals, ~3000 total citations): https://scholar.google.pl/scholar?hl=en&q=gryzinski

Wikipedia article: http://en.wikipedia.org/wiki/Free-fall_atomic_model

Slides about free-fall atomic model: https://www.dropbox.com/s/38xidhztpe9zxsr/freefall2.pdf

Simple simulations in Mathematica: http://demonstrations.wolfram.com/KeplerProblemWithClassicalSpinOrbitInteraction/

What do you think about it?

update: simulations of atoms with electron's magnetic dipoles taken into consideration (classical spin-orbit interaction):

update: gentle introduction to Maximal Entropy Random Walk - https://en.wikipedia.org/wiki/Maximal_Entropy_Random_Walk

2017 paper about its connection with QM: https://arxiv.org/pdf/0910.2724v2.pdf

showing why standard diffusion models are only approximation (of the Jaynes maximum uncertainty principle required by statistical physics models), and that **doing diffusion right there is no longer disagreement with thermodynamical predictions of QM (Anderson localization)**: