β⁺Chapter 5 of 9
Beta-plus (β⁺) decay: a proton turns into a neutron
The mirror image of β⁻. An up quark becomes a down quark, and instead of an electron the nucleus emits its antimatter twin, a positron, along with a neutrino.
quark levelu → d + e⁺ + ν
nucleon levelp → n + e⁺ + ν
example189F → 188O + e⁺ + ν (half-life 110 min)
Step through a β⁺ decay (fluorine-18)
Step 1Fluorine-18: 9 protons, 9 neutrons. The only stable fluorine has 10 neutrons, so this one is proton-heavy.
Step 2Zoom into one proton: two up quarks and a down quark.
Step 3The weak force turns an up quark into a down quark, emitting a W⁺. The charge balances: +⅔ = −⅓ + (+1).
Step 4The W⁺ immediately becomes a positron (e⁺) and a neutrino (ν), both created on the spot from released energy.
Step 5The positron and neutrino fly off, sharing up to 0.63 MeV. The proton is now a neutron (u d d). With 8 protons the nucleus is oxygen-18, which is stable.
Step 6The positron is antimatter. Within about a millimeter of tissue it slows down and meets an ordinary electron, and both are destroyed. Their combined mass becomes two gamma rays of exactly 511 keV flying in opposite directions. PET scanners detect these back-to-back pairs to pinpoint where F-18 (attached to sugar) collects in the body.
The catch: a lone proton can never do this
A neutron is heavier than a proton, so a free proton turning into a neutron would be making mass from nothing. Free protons are stable, which is lucky, since every hydrogen atom is one.
Inside a proton-heavy nucleus the whole nucleus pays. The top proton drops onto a lower neutron rung, and the new nucleus is so much more tightly bound that the total energy goes down, even though that one particle got heavier.
β⁺ only works if the parent atom is at least 1.022 MeV (twice an electron's mass) heavier than the daughter atom. That covers creating the positron, plus one leftover electron the atom has to shed now that it has one fewer proton. F-18 has 1.656 MeV, which leaves up to 0.634 MeV of motion. A nucleus with less than 1.022 MeV to spare can't emit a positron, so it uses electron capture instead (next part).
The quark diagram
| Rule | Before (u) | After (d + e⁺ + ν) | So… |
|---|---|---|---|
| Charge | +⅔ | −⅓ + 1 + 0 = +⅔ ✓ | created particle must be positive → positron |
| Lepton count | 0 | −1 + 1 = 0 ✓ | an anti-electron (−1) forces a regular neutrino (+1) |