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Electron capture is a kind of decay by which a nuclear transformation takes place. Below is an example of it.

$$ _{29} ^{64} \text{Cu} + e^- \rightarrow _{28}^{64} \text{Ni} $$

Of course, nucleus being positively charged and electron being negatively charged, there is an attraction between them, but electron generally don't fall in the nucleus. I am unable to understand that exactly how does nucleus is able to capture electron, using which interaction or force? Uncertainty principle won't allow electron in nucleus, though it is being captured. Exactly how?

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Electron capture occurs via a weak nuclear reaction. The electron itself ceases to exist; instead a neutron and neutrino appear. It is a reversed reaction of the neutron weak decay, if you like.

A bound electron wave function is not zero in the nucleus. There is a finite probability to find an electron within the nucleus volume. So they can interact and they do interact.

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Just to clarify, there's also a proton from the old nucleus involved that ceases to exist in the reaction, right? –  b_jonas Dec 27 '12 at 16:39
    
@b_jonas: Yes, it disappears too. –  Vladimir Kalitvianski Dec 27 '12 at 16:44

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