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Physics 1934

Attempt at a Theory of β-Rays

Enrico Fermi

A new, feeble force turns a neutron into a proton — and makes Pauli's neutrino real.

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In depth · the introduction

Some atoms fling out an electron carrying the wrong amount of energy every single time. To balance the books, Fermi invented a new force of nature — and a nearly invisible particle to carry off the rest.

The big idea

In one kind of radioactivity, called β decay, a neutron inside the nucleus turns into a proton and shoots out a high-speed electron. The trouble was the energy: the electron came out with a different amount each time, anywhere from almost nothing up to a fixed maximum. If the electron were the only thing leaving, it should always carry the same energy — so where was the rest going?

Fermi's answer had two parts. First, a third particle leaves too: a tiny, neutral, almost ghostly one that Wolfgang Pauli had proposed and Fermi named the neutrino. The electron and the neutrino split the energy between them, so the electron's share varies. Second, the whole process is driven by a previously unknown force — far weaker than electricity or magnetism — that lets a neutron flip into a proton. Fermi wrote down the rules of that force and used them to predict, correctly, the exact spread of electron energies.

How it came about

The puzzle was old and serious. Some physicists, including Niels Bohr, were ready to give up the sacred law of energy conservation to explain it. In December 1930 Pauli floated a daring escape in a letter he addressed, half-joking, to the 'Dear radioactive ladies and gentlemen' at a physics meeting: perhaps an unseen particle carried off the missing energy. He thought it almost too reckless to publish.

Fermi, working in Rome with his young team — the 'Via Panisperna boys' — took the idea seriously and built it into a full theory over the winter of 1933–34. He gave the particle its name and its mathematics. When he sent a short account to the journal Nature, it was rejected as 'too remote from reality to be of interest to the reader.' Stung, he published in German and Italian instead — and turned toward experiment, work that would win him the 1938 Nobel Prize. The neutrino itself was not detected until 1956, more than twenty years later.

Why it mattered

Fermi's theory was the first description of the weak force, which sits alongside gravity, electromagnetism and the strong nuclear force as one of the four fundamental interactions. It rescued the law of energy conservation, made the neutrino a real, calculable particle rather than a desperate guess, and handed physicists a recipe — a 'contact' coupling between particles — that became the model for how all forces are described in modern physics.

A way to picture it

Imagine you and a silent, invisible partner must split a fixed sum of money, but no one records who gets what. Count only your share over many rounds and it looks random — sometimes you get almost all of it, sometimes almost none. That is the continuous β spectrum: the electron and the neutrino divide a fixed energy, and we see only the electron's portion. If there were no hidden partner — a simple two-body split — you would get exactly the same amount every time, a single sharp value. The fact that we don't is the fingerprint of the neutrino. Use the tool below to switch the neutrino on and off and watch the single line spread into a smear.

An interactive plot of the electron energies from β decay. With the neutrino switched on, the energies spread into a smooth curve from zero up to a maximum; switched off, they collapse to one sharp line. Sliders change the maximum energy and the nuclear charge, which tilts the curve.

Where it sits

Fermi's theory grew out of the new quantum mechanics — especially Dirac's 1928 theory of how light is emitted and absorbed, which gave Fermi his template. It opened a road that ran straight through the rest of the century: the discovery that this force breaks mirror symmetry, its unification with electromagnetism into the 'electroweak' theory, and finally the Higgs boson found in 2012, which gives the weak force its short range. The neutrino Fermi named is now studied in vast detectors and is one of the most abundant particles in the universe.

The original document
Original source text
Enrico Fermi · Zeitschrift für Physik 88 (1934): 161–177 · in German
Fermi's paper sets out to do for β decay what the new quantum theory had done for the emission of light: build a quantitative theory of how a radioactive nucleus throws out an electron. Its argument moves in four steps, mapped below.
1 · The neutrino and the analogy with radiation
Following Pauli's 1930 conjecture, Fermi assumes a light, neutral, spin-½ particle — which he calls the neutrino — is emitted alongside the electron. He insists that neither the electron nor the neutrino exists inside the nucleus beforehand; both are created at the instant of decay, exactly as a photon is created when an atom drops to a lower energy level.
2 · The interaction and the transition rate
By analogy with Dirac's radiation theory, Fermi writes an interaction localized at a single point: a term that converts a neutron into a proton while creating the electron–neutrino pair, multiplied by one new coupling constant. First-order perturbation theory (the rule now called Fermi's golden rule) turns this into a probability of decay per unit time.
3 · The shape of the β spectrum
Counting the available final states of the emitted pair fixes how the decay energy is shared. For an allowed transition the number of electrons of a given energy follows a definite curve, rising from zero, peaking, and falling to an endpoint set by the total decay energy; a Coulomb correction (the Fermi function) bends the curve near zero energy. This is the paper's central, testable prediction — and it explained the long-standing puzzle of the continuous β spectrum.
4 · Lifetimes and selection rules
From the same expression Fermi reads off the decay rate, and hence the relation between a nucleus's β-decay energy and its half-life. He sorts transitions into 'allowed' and 'forbidden' according to how much angular momentum the leptons carry off, extracting the strength of the new interaction from the measured rates.
[ … ]
The equations themselves — the interaction Hamiltonian, the matrix elements, the spectrum formula and the lifetime integral — are not reproduced here. Follow the source links for the full German text and Wilson's English translation.