Nature of Particles and Their Interactions

Lessons

Senior 6 · Physics

Nature of Particles and Their Interactions

5 lessons

Lesson 2 of 5

Antiparticles and Antimatter

25 min

A track that curved the wrong way

In 1932 Carl Anderson was photographing cosmic-ray tracks in a cloud chamber placed in a strong magnetic field, with a lead plate across the middle. One track had exactly the curvature of an electron, but it bent the opposite way. It was an electron with a POSITIVE charge. Four years earlier the British physicist Paul Dirac had combined quantum mechanics with relativity and found that his equation for the electron had a second set of solutions, describing a particle of the same mass and opposite charge. Anderson had found it: the positron, the first known particle of antimatter.

Every particle has an antiparticle

Every particle has an antiparticle with the same mass, spin and lifetime, but opposite charge and opposite values of the other "charges" you will meet in Lesson 4 (baryon number, lepton number, strangeness). An antiparticle is usually written with a bar: the antiproton $\bar{\mathrm{p}}$ ( $\bar{\mathrm{u}}\bar{\mathrm{u}}\bar{\mathrm{d}}$ ), the antineutron $\bar{\mathrm{n}}$ , the electron antineutrino $\bar{\nu}_e$ . The charged leptons are written by charge instead: the positron is $\mathrm{e^+}$ , the antimuon $μ^{+} \mu^+$ .

Particle	Antiparticle	Same	Opposite
electron $\mathrm{e^-}$	positron $\mathrm{e^+}$	mass 0.511 MeV, spin $\frac{1}{2}$	charge; lepton number
proton p (uud)	antiproton $\bar{\mathrm{p}}$ ( $\bar{\mathrm{u}}\bar{\mathrm{u}}\bar{\mathrm{d}}$ )	mass 938.27 MeV	charge; baryon number
neutron n (udd)	antineutron $\bar{\mathrm{n}}$ ( $\bar{\mathrm{u}}\bar{\mathrm{d}}\bar{\mathrm{d}}$ )	mass, zero charge	baryon number; quark content
$π^{+} \pi^+$ ( $\mathrm{u}\bar{\mathrm{d}}$ )	$π^{-} \pi^-$ ( $\mathrm{d}\bar{\mathrm{u}}$ )	mass 139.57 MeV	charge
photon $\gamma$	itself	everything	nothing

A few neutral particles, such as the photon, the $\pi^0$ and the Z boson, are their own antiparticles. The neutron is NOT: it is neutral, but its quarks have antiquark partners, so $\bar{\mathrm{n}}$ is a different particle. The antiproton was first made at Berkeley in 1955; atoms of antihydrogen (an antiproton with a positron) have been made and trapped at CERN, where in 2023 the ALPHA experiment showed that antihydrogen falls under gravity just as ordinary matter does.

Definition

An antiparticle has the same mass, spin and lifetime as its particle, but the opposite charge and opposite quantum numbers. Antimatter is matter made of antiparticles. Pair production is the creation of a particle and its antiparticle from energy; annihilation is the conversion of a particle and its antiparticle into energy, usually photons. Example: $\mathrm{e^-} + \mathrm{e^+} \rightarrow \gamma + \gamma$ .

Pair production: energy becomes matter

A gamma-ray photon passing close to a nucleus can disappear and create an electron–positron pair:

\gamma \rightarrow \mathrm{e^-} + \mathrm{e^+}

Charge is conserved ( $0 = - 1 + 1$ ), and so is lepton number, because one lepton and one antilepton are made. Energy conservation sets a threshold: the photon must supply at least the rest energy of both particles,

hf_{\min} = 2m_ec^2 = 2 \times 0.511\,\mathrm{MeV} = 1.022\,\mathrm{MeV}

Any extra energy becomes the kinetic energy of the pair. Why must there be a nucleus nearby? A photon of energy $E$ carries momentum $\frac{E}{c}$ . If the pair were made in empty space, they would need the same total momentum $\frac{E}{c}$ and total energy $E$ ; but for any particles with mass, total energy is always MORE than (total momentum) $\times c$ . Both laws cannot be met at once. A nearby nucleus recoils and takes up the spare momentum, with almost no energy because it is so heavy.

Figure 2.1: Pair production in a bubble or cloud chamber. The photon leaves no track; the two charged particles curve in opposite directions.

Worked example 1: the threshold for pair production

Find (a) the minimum photon energy for electron–positron pair production and (b) the longest wavelength that can do it. (c) A 3.00 MeV photon produces a pair. What total kinetic energy do the particles share? ( $hc = 1.240 \times 10^{-6}\,\mathrm{eV\,m}$ .)

Solution

(a) $E_{\min} = 2m_ec^2 = 2 \times 0.511 = 1.022\,\mathrm{MeV}$ .

(b) $\lambda_{\max} = \frac{hc}{E_{\min}} = \frac{1.240 \times 10^{-6}\,\mathrm{eV\,m}}{1.022 \times 10^{6}\,\mathrm{eV}} = 1.21 \times 10^{-12}\,\mathrm{m}$ : a gamma ray.

(c) $E_k = 3.00 - 1.022 = 1.98\,\mathrm{MeV}$ , shared between the electron and the positron (the nucleus takes a negligible amount).

Annihilation: matter becomes energy

A positron cannot last long in ordinary matter. It slows down and meets an electron, and the two annihilate, their whole mass turning into photons. If they are nearly at rest, the total momentum is zero, so they cannot produce a single photon (which always carries momentum). They produce two photons flying in exactly opposite directions, each with energy $m_ec^2 = 0.511\,\mathrm{MeV}$ :

\mathrm{e^-} + \mathrm{e^+} \rightarrow \gamma + \gamma

Figure 2.2: (a) Annihilation. (b) Its use in positron emission tomography (PET).

Application: PET scans. A patient is given a sugar-like compound labelled with a positron emitter such as fluorine-18 (half-life about 110 minutes). Tissues that use a lot of sugar, such as active tumours, collect it. Each positron annihilates within a millimetre or so, and a ring of detectors records the two back-to-back photons at the same instant. A computer builds up an image from millions of such lines. Medical imaging is treated fully in Unit 8.

Worked example 2: photons from annihilation

(a) An electron and a positron annihilate at rest. Find the energy and wavelength of each photon. (b) A proton and an antiproton annihilate at rest. What is the least total energy released?

Solution

(a) Momentum conservation gives two photons of equal energy, back to back: each has $E = m_ec^2 = 0.511\,\mathrm{MeV}$ , and $\lambda = \frac{hc}{E} = \frac{1.240 \times 10^{-6}}{0.511 \times 10^{6}} = 2.43 \times 10^{-12}\,\mathrm{m}$ .

(b) $E = 2m_pc^2 = 2 \times 938.27 = 1876.5\,\mathrm{MeV}$ , about 1.88 GeV. (In practice proton–antiproton annihilation usually produces several pions rather than two photons, because the quarks and antiquarks rearrange.)

Worked example 3: energy from a small mass of antimatter

Estimate the energy released if 1.0 μg of antihydrogen annihilated completely with 1.0 μg of hydrogen, and compare it with a 100 W lamp.

Solution

All the mass is converted: $E = mc^2 = (2.0 \times 10^{-9}\,\mathrm{kg})(3.00 \times 10^{8})^2 = 1.8 \times 10^{8}\,\mathrm{J}$ . A 100 W lamp would take $\frac{1.8 \times 10^{8}}{100} = 1.8 \times 10^{6}\,\mathrm{s}$ , about 21 days, to use this much energy.

This is no energy source, however: making antimatter takes far more energy than it gives back, and CERN produces only billionths of a gram per year.

Where is all the antimatter?

The laws of physics treat matter and antimatter almost identically, and the Big Bang should have made them in equal amounts. Yet the universe we see is made of matter: there are no antimatter stars or galaxies, which would light up where they touched ordinary matter. Tiny differences between the behaviour of particles and antiparticles have been measured, but they are too small to explain the imbalance. Why any matter survived is one of the big open questions in physics.

Warning

Common mistakes. (1) Saying pair production can happen in empty space: a nucleus (or another particle) must take up momentum. (2) Using $m_{e} c^{2}$ as the threshold instead of $2 m_{e} c^{2}$ : TWO particles must be made. (3) Saying annihilation at rest gives ONE photon of 1.022 MeV: momentum conservation requires at least two photons, each 0.511 MeV. (4) Thinking a neutral particle is always its own antiparticle: the neutron has a distinct antiparticle, the antineutron. (In this course the neutrinos are also treated as having antiparticles; whether a neutrino is its own antiparticle is still being tested.)

Tip

Remember the 1.022 / 0.511 pair: a photon needs at least 1.022 MeV to make an electron–positron pair, and an electron–positron pair at rest gives back two photons of 0.511 MeV each. For protons, replace 0.511 by 938.3.

Antimatter Explained, Episode 1 (CERN). Watch how antiparticles were predicted and discovered, and how CERN makes and traps antimatter today.

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Practice

State two properties that a particle and its antiparticle share and two that are opposite.
Write the quark content of the antiproton and of the $π^{-} \pi^-$ , and check their charges.
Find the minimum energy and maximum wavelength of a photon that can produce a muon–antimuon pair ( $m_\mu c^2 = 105.66\,\mathrm{MeV}$ ).
A photon of wavelength $4.0 \times 10^{-13}\,\mathrm{m}$ produces an electron–positron pair. Find the total kinetic energy of the pair.
Explain why electron–positron annihilation at rest cannot produce just one photon.
In a PET scan, two photons are detected at the same instant by detectors on opposite sides of the ring. What can you conclude about where the annihilation happened?
In a bubble chamber photograph, two tracks start from the same point and curl in opposite directions, with no track leading to that point. Explain what has happened.
Umutoni says: "The neutron has no charge, so it must be its own antiparticle, like the photon." Evaluate her statement.

Show answersHide answers

Same: mass, spin, lifetime. Opposite: charge, baryon number, lepton number, strangeness.
$\bar{\mathrm{p}} = \bar{\mathrm{u}}\bar{\mathrm{u}}\bar{\mathrm{d}}$ : $-\frac{2}{3} - \frac{2}{3} + \frac{1}{3} = -1$ . $\pi^- = \mathrm{d}\bar{\mathrm{u}}$ : $-\frac{1}{3} - \frac{2}{3} = -1$ .
$E_{\min} = 2 \times 105.66 = 211.3\,\mathrm{MeV}$ ; $\lambda_{\max} = \frac{1.240 \times 10^{-6}}{211.3 \times 10^{6}} = 5.87 \times 10^{-15}\,\mathrm{m}$ .
$E = \frac{1.240 \times 10^{-6}}{4.0 \times 10^{-13}} = 3.10\,\mathrm{MeV}$ ; $E_k = 3.10 - 1.022 = 2.08\,\mathrm{MeV}$ .
The total momentum before is zero. A single photon always carries momentum $\frac{E}{c} \neq 0$ , so momentum would not be conserved. Two photons with equal and opposite momenta give zero total.
It happened somewhere on the straight line joining the two detectors. Many such lines crossing at one place locate the source.
A neutral particle (a photon, leaving no track) produced an electron–positron pair near a nucleus. Opposite charges curve in opposite directions in the magnetic field.
Wrong. Having zero charge is not enough. The neutron (udd) has baryon number +1; the antineutron ( $\bar{\mathrm{u}}\bar{\mathrm{d}}\bar{\mathrm{d}}$ ) has baryon number −1 and opposite quark content, so it is a different particle, and a neutron and antineutron can annihilate.

Key points

An antiparticle has the same mass, spin and lifetime, and opposite charge and quantum numbers.
Pair production: $\gamma \rightarrow \mathrm{e^-} + \mathrm{e^+}$ , needs $hf \ge 2m_ec^2 = 1.022\,\mathrm{MeV}$ and a nearby nucleus.
Annihilation at rest: $\mathrm{e^-} + \mathrm{e^+} \rightarrow 2\gamma$ , each 0.511 MeV, back to back; used in PET.
The universe is made almost entirely of matter; why is still unknown.

Sources and credits

11.2: Introduction to Particle Physics, from University Physics Volume 3 by Samuel J. Ling, Jeff Sanny and William Moebs, OpenStax, hosted by LibreTexts, licensed under CC BY 4.0. Adapted by Ganzaa.
Particle data: Review of Particle Physics, Summary Tables, Particle Data Group, 2026.
Photo: PositronDiscovery.jpg by Carl D. Anderson, from "The Positive Electron", Physical Review 43 (1933), Wikimedia Commons, public domain.
Video: Antimatter Explained - Ep. 1, CERN, embedded from YouTube.

The two diagrams, the worked examples and the practice exercises are written by Ganzaa.

1A track that curved the wrong way

2Every particle has an antiparticle

3Pair production: energy becomes matter

4Annihilation: matter becomes energy

5Where is all the antimatter?

A track that curved the wrong way

Every particle has an antiparticle

Pair production: energy becomes matter

Annihilation: matter becomes energy

Where is all the antimatter?