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I know about photoelectric field, but it's about an E&M waves (photons). How about external electric\Coulombic\static field (virtual photons)? Can it turn the electron away from atom?

I wonder, it's one of "double standards" of physics. In the hand, electron can leave atom, only when atom is excited, i.e. incoming photon's energy equals $\Delta E$, and, as I understood, greater then work function. This is only one case, when electron can lose atom right? But in the other hand, I doubt that, if external electric field will be greater, then atom's, electrons won't leave the atom.

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it is possible to remove electrons from an object by applying an extremely large electrostatic field gradient on it, as for instance when the object is a sharp point and a large planar electrode is moved very close to it. this is called cold-cathode emission.

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