Concept

Weak interaction — where it appears

The fundamental interaction responsible for beta decay and for neutrino processes, carried by the W and Z bosons. It is short-ranged and feeble at low energies, and it is the only interaction that treats a spinning particle and its mirror image differently.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

The same law, across twenty-eight decades. The mean free path 1/nσ against cross-section, for a target density of 6.83·10³⁰ targets per cubic metre — solid lead. It is a straight line of slope minus one, because there is only one thing in the law. At 10⁻²⁸ m² the path is 1.46 mm; at 10⁻⁴⁷ m² the path is 1.55 light-years. Nothing about the physics changes between those ends. Only the area does.

How far a neutrino gets

A mean free path is one over the number density times the cross-section, and nothing else. Change only the cross-section — by twenty-eight powers of ten — and the same arithmetic that gives a molecule seventy nanometres in air gives a neutrino a light-year of solid lead.

astrophysics · Kinetic theory

The rectangle a spin tilts. The laboratory energy of the pion from a tau into a pion and a neutrino moving at 0.8 of the speed of light, for samples of 60,000 decays whose parents have αP = +1, 0, −1 along their line of flight. Every sample fills the same interval, 313 to 2667 MeV: the edges are set by the masses and the speed, and they do not move. Inside that interval an unpolarised sample is flat and a polarised one is tilted, its height at each energy 1 + αP times the cosine of the rest-frame angle that energy corresponds to. Reading the slope back from each sample gives +0.993, −0.010, −1.006, each with a standard error near 0.006. A parent spinning along its flight throws the pion forwards in its own frame, and the boost turns forwards into more energetic, so the tilt of an energy spectrum measures a polarisation without any angle being measured at all.

The slope a spin leaves in a spectrum

An unpolarised parent decaying in flight gives its products a rectangle of energies. Give the parent a spin along its line of flight and the rectangle tilts, while its two edges stay exactly where they were. The tilt is the polarisation, it can be read without ever seeing which way the parent was going — and which variable it is read from decides how many decays the reading costs.

relativity · Relativistic dynamics

The parabola that decides which way a nucleus decays

A weak decay turns a neutron into a proton or a proton into a neutron and leaves the number of nucleons alone, so it moves a nucleus sideways among its isobars. Whether it can happen, and in which direction, is settled by weighing: a decay goes wherever the atom ends up lighter, by any amount at all, except that emitting a positron needs two electron masses more. Laid out against proton number, the masses of a family of isobars fall on a parabola — or, for an even number of nucleons, on two — and the shape of that parabola is why potassium-40 decays both ways and germanium-76 can only take two steps at once.

relativity · Mass-energy

Named alongside it

The objects these essays reach for when they reach for this one.

Neutrino Angular distribution Attenuation Beaming Beta decay Binding energy Cross-section Decay Double beta decay Electron capture Four-momentum Kinematics

All concepts