Third Lecture: the Discovery of Antimatter

HC 209H: Discovery of Fundamental Particles and Interactions Third Lecture: The Discovery of Antimatter

Chris Potter

University of Oregon

HC 209H: Third Lecture – p.1/10 Dirac and the Anti-Electron (Positron)

Erwin Schrodinger (1887-1961), an Austrian physicist, applied the classical expression for kinetic energy, = 1 2 Ek 2 mv , to non-relativistic quantum mechanical systems like the atom. Paul Dirac (1902-1984), a Swiss/English physicist, extended this in 1928 to Einstein’s relativistic expression E2 = p2c2 + m2c4, or = 2 + 1 2 + ··· E mc 2 mv . In order to make this work, Dirac found he had to use matrices of numbers for observable quantities, like momentum and energy, rather than ordinary numbers. Dirac also found that he got two solutions for the energy of an electron e−: one positive and the other negative. In 1931 he interpreted the negative solution as belonging to an anti-electron (or positron e+) with equal mass but opposite charge. Immediately afterward, experimental physicists were on the lookout in their cloud chambers... Paul Dirac (Credit: Wikipedia)

HC 209H: Third Lecture – p.2/10 Charged Particles in Magnetic Fields

Just as planets are held in circular orbits by a gravitational ﬁeld, so charged particles can be held in orbits by a magnetic ﬁeld. Suppose the particle has charge q, velocity v and mass m. We set the magnetic force qvB equal to the centripetal force mv2/R:

= mv2 qvB R

Solving, we get the momentum p = qBR (since p = mv). For a constant B, large p particles have large orbital radii while small p particles have small radii. If a known constant magnetic ﬁeld B is applied and the particle path can be made visible, the orbit radius R can be measured. For B coming out of the page, the orbit is clockwise for q > 0 and counter-clockwise for q < 0. Once the orbit radius R is known, the particle’s momentum can be The magnetic ﬁeld B is coming out calculated. of the page (Credit: Wikipedia)

HC 209H: Third Lecture – p.3/10 Reversing the Magnetic Field

Positive charges orbit clockwise, negative Positive charges orbit counter-clockwise, charges counterclockwise. negative charges clockwise.

HC 209H: Third Lecture – p.4/10 Cloud Chambers: Seeing Fundamental Particles

A Basic Cloud Chamber - Click Me! (Credit: Wikipedia)

Charles Wilson (1869-1959), a Scottish physicist also at the Cavendish Lab with Thompson, Rutherford and Chadwick, invented the cloud chamber. The trails of tiny charged particles traversing a cloud chamber can be made visible when they ionize (eject electrons from) nearby atoms. The ions form nuclei for condensation of cooled vapor ready to condense on a condensation nucleus. This is precisely what happens in jet contrails: jets too high above to see are made visible by the contrails they leave behind. HC 209H: Third Lecture – p.5/10 Discovery of the Positron

Carl Anderson (1905-1991), an American physicist at Caltech, discovered positrons in 1932 with a cloud chamber bathed in a magnetic ﬁeld B. Cosmic rays are protons or heavy nuclei expelled from exploding stars many years ago which happen to collide with Earth. Cosmic rays collide with atoms in our atmosphere and create high energy photons γ. The photons then produce electron-positron pairs γ → e+e−. The positron enters a cloud chamber at the time a picture is taken. Credit: Wikipedia

HC 209H: Third Lecture – p.6/10 Anderson’s Experimental Setup

The magnetic field B is into the page, not out of the page as in slide 3. Does the particle come from above or below? A 6mm lead plate, in the middle of the photograph, slows the particle, reducing its momentum. The orbital radius R is larger below than above, so it comes from below since p = qBR. Therefore the particle has q > 0. But the only known charged particles in 1932 were e− and p. ⊗ B Could it be the positron e+? In his paper, Anderson listed five possible interpretations of the track. Credit: Wikipedia HC 209H: Third Lecture – p.7/10 Anderson’s Scientific Argument

Interpretation 1. The track is one electron e−. But the electron gains energy after traversing the lead plate. But this runs counter to established scientiﬁc understanding of electrons in matter (“completely untenable”). Therefore the particle is not an electron. Interpretation 2. The track is two electrons 2e−. Two electrons 2e− have been simultaneously photographed while lining up perfectly, one with higher momentum than the other. But the probability for this to happen is practically zero. Therefore it is not two electrons. Interpretation 3. The track is the proton p. But if the particle was a proton with this momentum then it would travel less than 5cm since protons lose energy to nuclear interactions. But the particle clearly travels more than 5cm. Therefore it is not a proton. Interpretation 4. The track is one electron e− and one positron e+. The pair is created by a photon γ pair producing γ → e+e− in the lead plate. But in this case there is also a positron e+. Interpretation 5. The track is the positron e+.

HC 209H: Third Lecture – p.8/10 Particles and Anti-Particles

Anti-particles were ﬁrst predicted by Paul Dirac in 1931 when he attempted a relativistic quantum mechanics. Anti-particles have the same mass but opposite charge. Known matter particles in 1935:

Light (q,m) Heavy (q,m) Interaction (q,m) e− (-1,0.5 MeV/c2) p (+1,938 MeV/c2) γ (0,0) ν (0,0) n (0,940 MeV/c2)

Their anti-particles discovered afterward:

Light (q,m) Heavy (q,m) Interaction (q,m) e+ (+1,0.5 MeV/c2) p¯ (-1,938 MeV/c2) γ (0,0) ν¯ (0,0) n¯ (0,940 MeV/c2)

The anti-electron e+ was discovered in 1932 with cosmic rays in a cloud chamber. The anti-proton p¯ was discovered in 1955 with an accelerator and a bubble chamber. The anti-neutron n¯ was discovered in 1957 in the same accelerator experiment. The anti-neutrino ν¯ was discovered in 1956 using a nuclear reactor as an intense source of anti-neutrinos in the reaction ν¯ + p → n + e+. HC 209H: Third Lecture – p.9/10 Worksheet 3 Preparation

Matter-Antimatter Annihilation When matter particles and antimatter particles get close enough, they annihilate into pure energy. If p = 0, the energy released is twice the rest energy of the particle. The stable hydrogen anti-atom, made up of an anti-proton p¯ nucleus with an orbiting positron e+, was recently created at CERN. (Link to CERN Article) In principle, complex molecules and even lifeforms (like you) made up entirely of anti-particles could function precisely as their particle versions do. Energy, time and power. Power P =∆E/∆t is the time rate of energy production. The unit of power in the SI system of units is the Watt, a Joule per second: W=1J/s. To calculate the amount of time ∆t required to produce an amount of energy ∆E assuming power P , use ∆t =∆E/P . Carl Anderson’s positron track. Only charged particles experience a force due to a magnetic ﬁeld B. Charged particles lose energy when passing through matter. They do not gain it. Protons lose energy in matter far faster than electrons because they experience the nuclear force, and lose energy to nuclear interactions, while electrons do not.

HC 209H: Third Lecture – p.10/10