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Sandbox Physics

P001 · Polarized beta decay

Weak Decay & the Broken Mirror

Why does reversing the nuclear spin reverse the preferred electron direction? Polarized cobalt nuclei emit more beta electrons against their spin. Reversing the spin reverses that preference. The correlation between spin and emission direction changes under spatial inversion, revealing parity violation in the weak decay.

Turn the nuclear spin and watch electrons favour the opposite direction. Reverse the polarization, warm the source or rotate the spin across the detectors to compare the two counting rates.

Interactive modelWeak Decay & the Broken Mirror
Right detector fraction00
Left detector fraction00
Right–left asymmetry00
Electron speed / light speed00
A simulated angular sample
Expected detector fractions

Blue bars: 2,400 simulated electrons. Gold curve: the angular model. Detector fractions are predictions for two identical acceptance cones.

Model and scientific sources

An allowed pure Gamow–Teller model for the dominant cobalt-60 branch, at one selected electron kinetic energy. The spin direction is an axial vector. Full spatial inversion reverses the electron momentum and leaves the spin unchanged. Reversing the polarization is an experimental control, not a mirror operation. The source is pointlike, the detectors have equal efficiency, and scattering, magnetic bending, recoil-order corrections and the electron energy spectrum are omitted. The particles are enlarged and time is slowed.

dPdcos⁡θ=1+APβcos⁡θ2,A=−1\frac{dP}{d\cos\theta}=\frac{1+A P\beta\cos\theta}{2},\qquad A=-1

Physics tutorial

A preferred direction in beta decay

BackgroundWu and her collaborators cooled cobalt-60 nuclei until their spins partially aligned. Electrons emerged more often opposite the spin direction.

Why it mattersA mirror reverses a velocity but leaves a spin direction unchanged. A preference between those two directions therefore tests a symmetry of the decay law.

Start with the essentials

Focus question
Why do the two identical detectors count different fractions?
One-sentence intuition
The weak decay probability depends on the angle between electron momentum and nuclear spin.

Core mathematical model

Angular probability at one electron energy

dPdu=1+APβu2,u=cos⁡θ,A=−1\frac{dP}{du}=\frac{1+A P\beta u}{2},\qquad u=\cos\theta,\quad A=-1

The angle is measured from the spin axis. Nuclear polarization sets how well the spins align; the electron speed is expressed as a fraction of light speed.

Two equal acceptance cones

f±=1−cos⁡α2±APβcos⁡ϕ4sin⁡2αf_{\pm}=\frac{1-\cos\alpha}{2}\pm\frac{A P\beta\cos\phi}{4}\sin^2\alpha

Each detector accepts a cone of half-angle alpha. Phi is the angle between the spin axis and the right detector. The two signs select right and left.

Common difficulties

Spin reversal and a mirror

Typical misconceptionTurning the spin around makes a mirror image of the experiment.

Better mental modelSpin reversal is a control that exchanges the preferred detector. A mirror reverses electron momentum while preserving spin, which is an axial vector.

Run the experiment

  1. 01

    Reverse the polarization

    Choose Reverse the polarization.

    What to observe: The favoured detector swaps sides while both acceptance cones remain fixed.
  2. 02

    Lose the alignment

    Choose Warm, disordered source.

    What to observe: The sample becomes symmetric and both detectors receive the same expected fraction.
  3. 03

    Rotate the source spin

    Drag the gold arrow until it points across the detector axis.

    What to observe: The detectors balance even though the electron distribution still favours the direction opposite the spin.
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