A neutron turns into a proton, and to balance the books it emits an electron and a ghost — the neutrino Pauli was forced to invent. The electron does not come out at a single energy: it comes out at any energy from zero to the endpoint, because it shares the release with the neutrino. That smear was the clue. Rendered, not quoted.
source Fermi, E. — Versuch einer Theorie der β-Strahlen. I, Z. Phys. 88, 161–177 (1934) · DOI 10.1007/BF01351864 · first complete theory of beta decay with the neutrino.
Beta-minus: a bound neutron decays.
n → p + e− + ν̄e
Also beta-plus p → n + e+ + νe (Z→Z−1, needs parent heavier by ≥ 2mec²) and electron capture. The neutrino is the third body that makes the electron spectrum continuous.
A neutron becomes a proton. The direction is not free — beta decay slides the nucleus down the mass parabola toward the valley of stability, the minimum of the-semi-empirical-mass-formula. If Z sits below the stable Z for that A, beta-minus climbs it up; if above, beta-plus/EC brings it down.
amber The smooth SEMF misplaces odd-odd nuclei: it wrongly favours ¹⁴C over ¹⁴N, though ¹⁴C really does beta-decay up to ¹⁴N. The pairing exceptions are the reason the isobar chosen here for the live check is even-A, Z-clean.
Fermi 1934 gave the weak coupling that sets the rate; Weizsäcker 1935 gave the landscape it rolls down.
Live re-check of the two load-bearing invariants: the spectrum is continuous (three bodies) and spin is conserved (odd fermion count). Press TAMPER in window 6 and this flips.
A parent nuclide (Z, A) and its decay Q-value. Example loaded: ¹⁴C (Z=6, A=14), Qβ− = 0.156 MeV.
The electron energy spectrum N(E) ∝ pe Etot (Q − E)² — the shared-energy shape. Fixed line if the neutrino is dropped.
Proven at boot by a fail-loud selfcheck (tolerance 1e−6 on the RK4 decay integral):
"Energy is simply not conserved in the individual beta decay." — the honest 1930 reading of the data, before the neutrino. The electron came out with less than the full Q and no missing partner was ever seen.
The wall was real: a two-body decay must give a fixed electron energy. The observed smear looked like a violation of the most sacred law in physics. Fermi's answer was not to break conservation but to add an invisible, near-massless, weakly-coupled body that carries the rest.
The electron leaves the nucleus pre-formed, like an alpha. → No. It is created at the instant of decay by the weak interaction, same as a photon is created when an atom radiates.
The beta electron has a single, sharp energy. → Continuous, 0 to Q. The share not taken by the electron leaves with the antineutrino.
Any nuclide can beta-plus decay if you wait. → Only if the parent is heavier than the daughter by at least 2mec² = 1.022 MeV; otherwise only electron capture is open.
The disclosed planted void: drop the neutrino. Force a two-body decay n → p + e−. The electron energy collapses to a single fixed line and spin can no longer balance (two half-integers cannot sum to a half-integer). The Witness in window 7 catches it live.