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

$$ _{29} ^{64} \text{Cu} + e^- \to\ {}_{28}^{64} \text{Ni} + {\nu}_e$$

Of course, with the nucleus being positively charged and electron being negatively charged, there is an attraction between them, but electrons generally don't fall into the nucleus. I am unable to understand exactly how is the nucleus able to capture electron; using which interaction or force? The uncertainty principle won't allow an electron in the 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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    $\begingroup$ Just to clarify, there's also a proton from the old nucleus involved that ceases to exist in the reaction, right? $\endgroup$
    – b_jonas
    Commented Dec 27, 2012 at 16:39
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    $\begingroup$ @b_jonas: Yes, it disappears too. $\endgroup$
    – Vladimir Kalitvianski
    Commented Dec 27, 2012 at 16:44
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    $\begingroup$ The reason electron capture can happen is because S states have an orbital that overlaps the nucleus, i.e. there is a probability for a proton to be superposed on an electron and the weak interaction can take over, if the energetics allows it, i.e. enough energy to allow a proton instead of a neutron . (64 neuclei before and after) $\endgroup$
    – anna v
    Commented Apr 3, 2017 at 11:51
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    $\begingroup$ Indeed, electrons in $s$ wave orbitals have a contact density at the nucleus. This is also responsible for NMR (nuclear magnetic resonance) shifts and other hyperfine effects. $\endgroup$
    – user137289
    Commented May 7, 2018 at 11:11
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Well during electron capture an electron around the nucleus that was just floating around falls in. The reason the electron does not react with proton in normal cases is because the weak force is extremely weak. An electron in the nucleus will interact if the weak force somehow participates. It is for the most part rare, but can happen. Especially, if the nucleus does not have enough energy to undergo Beta+ decay.

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