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An example of a metal that can hold a lot of hydrogen is palladium. The hydrogen atoms (protons) in the metal lattice are positive and the electrons are negative. When a large electric potential is applied across the lattice, the protons flux in one direction and the electrons in the other. Is it possible to increase the probability of electron capture (neutron production) by applying a large electric potential across a metal hydride, and if so at what potential/current? And what would be the effect of the lattice elements (e.g. palladium atoms) on this probability?

I would appreciate if anybody has suggestions about where I could find information on this subject.

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It depends a little on what you mean by "extreme" electric current, but the answer is probably no. The energy scales are wrong.

Electric current in a metal is a sub-electron-volt process: a potential difference of much less than a volt can displace electrons all the way through a piece of metal.

The weak interaction is a keV- or MeV-scale process. And that's only the "residual" weak interaction that is responsible for slow processes like electron capture. If you want to materially alter the cross section for a weak interaction process like electron capture on a proton, you'd need the electron-proton system to exchange an energy comparable to the mass of the W boson: hundreds of GeV. This is enough energy to break apart the palladium nucleus, let alone a solid palladium crystal at room temperature. I suppose you could characterize the transmutation of a solid palladium crystal into a radioactive slag of lighter nuclei by a 100 GeV electron beam as "an extreme electric current," but the comparison feels a little forced.

For what it's worth electron capture is most likely to involve the $1s$ or $2s$ electrons, which remain bound to the nucleus in metals and don't participate in current flow.

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Even if the hosting lattice is destroyed, is there a voltage potential that could give electrons and protons(hydrogen) enough energy for electron capture? (i.e. not from an external beam) And would the lattice elements affect the energy requirement by some sort of guiding of the electrons/protons? – Cedric Eveleigh Feb 6 at 16:31
    
The electric potential required is billions of volts; in the presence of such a potential, you'll develop a beam whether you intend to or not. – rob Feb 7 at 17:52

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