Matter – Antimatter Creation and Annihilation

Matter – Antimatter Creation and Annihilation

E=MC2At the beginning of the 20th century, the notion of mass underwent a radical revision. Mass lost its absoluteness. One of the striking results of Einstein’s theory of relativity is that mass and energy are equivalent and convertible one into the other. Equivalence of the mass and energy is described by Einstein’s famous formula E = mc2. In words, energy equals mass multiplied by the speed of light squared.

In special theory of relativity certain types of matter may be created or destroyed, but in all of these processes, the mass and energy associated with such matter remains unchanged in quantity. As a result of the conservation of lepton and baryon numbers,  antimatter (antiparticles) can be created out of energy, but only if a particle counterpart for every antiparticle is created as well. It will be demonstrated in the following sections.

Matter – Antimatter Creation

Matter and Antimatter - ComparisonMatter – Antimatter creation occurs naturally in high-energy processes involving cosmic rays, and also in high-energy experiments in accelerators in Earth. High-energy cosmic rays impacting Earth’s atmosphere (or any other matter in the Solar System) produce minute quantities of antiparticles in the resulting particle jets, which are immediately annihilated by contact with nearby matter. The presence of the resulting antimatter is detectable by the two gamma rays (with 511 keV) produced every time positrons annihilate with nearby matter.

Antimatter creation is also very common in nuclear decay of many isotopes. Let assume a decay of potassium-40. Naturally occurring potassium is composed of three isotopes, of which 40K is radioactive. Traces of 40K are found in all potassium, and it is the most common radioisotope in the human body40K is a radioactive isotope of potassium which has a very long half-life of 1.251×109 years and undergoes both types of beta decay.

  • About 89.28% of the time (10.72% is by electron capture), it decays to calcium-40 (40Ca) with emission of a beta particle (β, an electron) with a maximum energy of 1.33 MeV and an antineutrino, which is an antiparticle to the neutrino.
  • Very rarely (0.001% of the time) it will decay to 40Ar by emitting a positron (β+) and a neutrino.

Another very interesting source of antimatter is, in fact, a nuclear reactorNuclear reactors are the major source of human-generated antineutrinos. This is due to the fact that antineutrinos are produced in a negative beta decay. In a nuclear reactor occurs especially the βdecay, because the common feature of the fission fragments is an excess of neutrons. Please note that billions of solar neutrinos per second pass (mostly without any interaction) through every square centimeter (~6×1010) on the Earth’s surface and antineutrino radiation is by no means dangerous.

Finally, the fact is that antimatter is much more common, than it may seem.

In January 2011, research by the American Astronomical Society discovered antimatter (positrons) originating above thunderstorm clouds.  It is suggested that these positrons are formed in terrestrial gamma-ray flashes (TGF). These positrons are produced in gamma-ray flashes created by electrons accelerated by strong electric fields in the clouds. TGFs are brief bursts occurring inside thunderstorms and associated with lightning. The streams of positrons and electrons collide higher in the atmosphere to generate more gamma rays. About 500 TGFs may occur every day worldwide, but mostly go undetected.

 
Electron - Positron Pair Production
Pair production in chamberIn general, pair production is a phenomenon of nature where energy is direct converted to matter. The phenomenon of pair production can be view two different ways. One way is as a particle and antiparticle and the other is as a particle and a hole. The first way can be represented by formation of electron and positron, from a packet of electromagnetic energy (high energy photon – gamma ray) traveling through matter.  It is one of the possible ways in which gamma rays interact with matter. At high energies this interaction dominates. In order for electron-positron pair production to occur, the electromagnetic energy of the photon must be above a threshold energy, which is equivalent to the rest mass of two electrons. The threshold energy (the total rest mass of produced particles) for electron-positron pair production is equal to 1.02MeV (2 x 0.511MeV) because the rest mass of a single electron is equivalent to 0.511MeV of energy.If the original photon’s energy is greater than 1.02MeV, any energy above 1.02MeV is according to the conservation law split between the kinetic energy of motion of the two particles.
Pair production in nuclear field and electron field.
Cross section of pair production in nuclear field and electron field.

The presence of an electric field of a heavy atom such as lead or uranium is essential in order to satisfy conservation of momentum and energy. In order to satisfy both conservation of momentum and energy, the atomic nucleus must receive some momentum. Therefore a photon pair production in free space cannot occur.Moreover, the positron is the anti-particle of the electron, so when a positron comes to rest, it interacts with another electron, resulting in the annihilation of the both particles and the complete conversion of their rest mass back to pure energy (according to the E=mc2formula) in the form of two oppositely directed 0.511 MeV gamma rays (photons). The pair production phenomenon is therefore connected with creation and destruction of matter in one reaction.

 
Nuclear Reactor as the Antineutrinos Source
Fission fragment yields
Fission fragment yield for different nuclei. The most probable fragment masses are around mass 95 (Krypton) and 137 (Barium).

Nuclear reactors are the major source of human-generated antineutrinos. This is due to the fact that antineutrinos are produced in a negative betadecay. In a nuclear reactor occurs especially the βdecay, because the common feature of the fission fragments is an excess of neutrons (see Nuclear Stability). An unstable fission fragment with the excess of neutrons undergoes β decay, where the neutron is converted into a proton, an electron, and an electron antineutrino. The existence of emission of antineutrinos and their very low cross-section for any interaction leads to very interesting phenomenon.

Energy from Uranium Fission
Energy from Uranium Fission

Roughly about 5% (or about 12 MeV of 207 MeV) of released energy per one fission is radiated away from reactor in the form of antineutrinos. For a typical nuclear reactor with a thermal power of 3000 MWth (~1000MWe of electrical power), the total power produced is in fact higher, approximately 3150 MW, of which 150 MW is radiated away into space as antineutrino radiation. This amount of energy is forever lost, since antineutrinos are able to penetrate all reactor materials without any interaction. In fact, a common statement in physics texts is that the mean free path of a neutrino is approximately a light-year of lead. Moreover, a neutrino of moderate energy can easily penetrate a thousand light-years of lead (according to the J. B. Griffiths).

Please note that billions of solar neutrinos per second pass (mostly without any interaction) through every square centimeter (~6×1010) on the Earth’s surface and antineutrino radiation is by no means dangerous.

Example – Amount of antineutrinos produced:

Stable nuclei with most likely mass number A from U-235 fission are _{40}^{94}\textrm{Zr} and _{58}^{140}\textrm{Ce}. These nuclei have together 98 protons and 136 neutrons, while fission fragments (parent nuclei) have together 92 protons and 142 neutrons. This means after each U-235 fission the fission fragments must undergo on average 6 negative beta decays (6 neutrons must decay to 6 protons) and therefore 6 antineutrinos must be produced per each fission. The typical nuclear reactor therefore produces approximately 6 x 1020 antineutrinos per second(~200 MeV/fission; ~6 antineutrinos/fission; 3000 MWth; 9.375 x 1019 fissions/sec).

beta decay
Beta decay of C-14 nucleus.

Matter – Antimatter Annihilation

positron annihilation
When a positron (antimatter particle) comes to rest, it interacts with an electron, resulting in the annihilation of the both particles and the complete conversion of their rest mass to pure energy in the form of two oppositely directed 0.511 MeV photons.

As was written, a particle and its antiparticle have the same mass as one another, but opposite electric charge, and other differences in quantum numbers. That means a proton has positive charge while an antiproton has negative charge and therefore they attract each other. A collision between any particle and its antiparticle partner is known to lead to their mutual annihilation. Since matter and antimatter carry an immense amount of energy (due to E = mc2), their mutual annihilation is associated with production of intense photons (gamma rays), neutrinos, and sometimes less-massive particle–antiparticle pairs.

One of best known processes is electron-positron annihilation. Electron–positron annihilation occurs when a negatively charged electron and a positively charged positron collide.When a low-energy electron annihilates a low-energy positron (antiparticle of electron), they can only produce two or more photons (gamma rays). The production of only one photon is forbidden because of conservation of linear momentum and total energy. The production of another particle is also forbidden because of both particles (electron-positron) together do not carry enough mass-energy to produce heavier particles. When an electron and a positron collide, they annihilate resulting in the complete conversion of their rest mass to pure energy (according to the E=mc2 formula) in the form of two oppositely directed 0.511 MeV gamma rays (photons).

e + e+ → γ + γ (2x 0.511 MeV)

This process must satisfy a number of conservation laws, including:

  • Conservation of electric charge. The net charge before and after is zero.
  • Conservation of linear momentum and total energy. T
  • Conservation of angular momentum.
 
References:
Nuclear and Reactor Physics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
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  9. Paul Reuss, Neutron Physics. EDP Sciences, 2008. ISBN: 978-2759800414.

Advanced Reactor Physics:

  1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
  2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
  3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2. 
  4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

See above:

Antimatter