Electron capture: swallowing your own electron

Same result as beta-plus (a proton becomes a neutron, $Z$ down by 1), by another route: the nucleus absorbs one of its own electrons.

1. How can an electron get into the nucleus?

Electrons don’t orbit like little planets. Each one is a cloud of probability: thick where you’d likely find it, thin where you wouldn’t. The innermost electrons (the K shell) have clouds densest right at the center — they pass straight through the nucleus. In iron, a K electron is inside the nucleus roughly one-hundred-millionth of the time. Nothing has to throw it in. It’s already partly there.

2. The reaction

Step through it for iron-55. While the electron overlaps a proton, the weak force lets them trade a $W$ boson: the up quark becomes a down quark and the electron becomes a neutrino.

Step through electron capture (iron-55)

Step 1An iron-55 atom: 26 protons, 29 neutrons and 26 electrons. The nucleus is proton-heavy but only has 0.23 MeV to spare, nowhere near the 1.022 MeV that β⁺ needs. So it uses the other route.

Step 2One of the two innermost (K-shell) electrons. Its cloud overlaps the nucleus, so at any moment there's a small chance it's "inside." Nothing pushes it there.

Step 3While the electron overlaps a proton, the weak force can act. The up quark and the electron trade a W boson: the up quark becomes a down quark (proton → neutron) and the electron becomes a neutrino. Charge: +⅔ − 1 = −⅓ ✓

Step 4Only one particle leaves: the neutrino. Since there's nothing to split the energy with, it always comes out with the same energy (≈0.23 MeV), unlike the spread in β decay. The nucleus is now manganese-55 (25 p, 30 n), which is stable.

Step 5The atom now has a hole in its innermost shell. An electron from farther out drops into it and releases the energy difference as an X-ray (5.9 keV for manganese). Sometimes that energy instead kicks another electron out of the atom (an "Auger electron").

Step 6The atom lost one proton and one electron, so it's still electrically neutral, just an ordinary manganese atom. Since the neutrino escapes undetected, the X-rays and Auger electrons are the only signs that anything happened.

$u + e^- \to d + \nu \qquad p + e^- \to n + \nu$ ${}^{55}_{26}\mathrm{Fe} + e^- \to {}^{55}_{25}\mathrm{Mn} + \nu$

Iron-55 has only $0.23\ \mathrm{MeV}$ to spare — nowhere near the $1.022\ \mathrm{MeV}$ beta-plus needs — so it uses this route. Because there is nothing to split the energy with, the neutrino always comes out with the same energy, unlike the spread in beta decay.

The quark diagram, with the electron coming in from below and only a neutrino leaving:

3. The visible sign

The atom now has a hole in its innermost shell. An electron from farther out drops in and releases the difference as an X-ray ( $5.9\ \mathrm{keV}$ for manganese). Sometimes that energy kicks another electron out instead (an Auger electron). Since the neutrino escapes undetected, those X-rays are the only sign anything happened.

	Beta-plus	Electron capture
Inside	$p \to n$	$p \to n$
Comes out	$e^+ + \nu$ , sharing energy	just $\nu$ , fixed energy
Needs	$> 1.022\ \mathrm{MeV}$	any $> 0$
Signal	two $511\ \mathrm{keV}$ gammas	X-rays from refilled shell
Favored in	light nuclei, lots of spare energy	heavy nuclei, low-energy cases

Because it needs electrons, chemistry can nudge it: beryllium-7’s half-life changes ~0.1% with bonding, and fully stripped Be-7 with no electrons cannot decay at all. Many nuclei go more than one way: potassium-40 mostly does beta-minus but ~11% of the time captures to argon-40 — where nearly all Earth’s atmospheric argon came from.

Next: half-life — the math of how fast.