Nuclear Reactions

The interaction between nuclear radiation and matter is called a "nuclear reaction" (although gamma rays can also interact with the electrons of an atom through photoatomic reactions). Nuclear reactions are described by specifying the type of the incident radiation, the nuclear target, the products of the reaction, the probability that the reaction will take place, which is called the "cross section," and the distributions in energy and angle of the reaction products.

Nuclear Radiation Types

There are several different kinds of "radiation," including nuclear particles, that can cause nuclear reactions:
  • Gamma Rays (γ): Energetic photons (same as light). The term "gamma ray" is usually for photons produced in the nucleus, and the term "X-ray" is usually for photons produced by electronic transitions in the atom. X-rays usually have lower energies than gamma rays. Gamma rays can penetrate deeply into matter, especially for high energies; therefore, they can be useful for medical radiation therapy, and they can be harmful when people are exposed by accident.

  • Neutrons (n): Neutrons are one of the basic components of the nuclei of atoms (protons being the other). They are neutral particles, and they can penetrate through materials easily. As was the case for gamma rays, this makes them both useful and dangerous. Neutrons can induce nuclear reactions readily, and they are products of many reactions. They are especially important as the mediator of the "chain reaction," which makes both nuclear power and nuclear weapons possible.

  • Protons (p): Protons are the other main component of the nuclei of atoms (with neutrons). They have about the same mass as neutrons, but they have a positive charge of one unit. As a result, they interact strongly with the electrons in normal matter, and they have shorter ranges than neutrons of similar energy. Beams of energetic protons can be produced by accelerators, and they have been used for medical radiotherapy and to produce intense pulses of neutrons for studies of materials. Modern ideas for intense proton beams produced by accelerators include the production of tritium to refresh thermonuclear weapons (APT), the burning of radioactive wastes (ATW), the conversion of excess weapons plutonium (ABC), or the production of nuclear power in a safe and environmentally favorable way.

  • Light ions (d,t, 3He, α): Deuterons (d) and tritons (t) consist of one proton and one or two neutrons, respectively. They are "isotopes" of hydrogen. Similarly, 3He and the alpha particle (α) are isotopes of helium with two protons and one or two neutrons, respectively. The light ions with charge 2 interact with matter so strongly that most natural alphas won't penetrate your skin or a piece of paper, but alpha-emitting radioactive materials can be dangerous if they get inside the body. The light ions are interesting because of their importance in fusion reactions in weapons, fusion power experiments, and astrophysical situations (stars, supernovas, the Big Bang).

  • Heavy ions: Projectiles heavier than the alpha particle can be produced and made energetic with accelerators. They are used in scientific research and in several practical applications.
Most of the nuclear reaction data available from this WWW site are neutron data because of their technological importance.

What is an eV, KeV, or MeV?

Throughout the nuclear data field, you will see the energies of nuclear particles expressed in "electron volts," or eV. Quite often, you will see KeV (1000 eV), MeV (one million eV), or even GeV (109 eV). An electron volt is the energy acquired by a charged particle with unit charge (e.g., an electron or a proton) when it falls through a potential difference of one volt. It is equal to 1.60207x10-12 erg.

Some interesting energies expressed in this way include thermal neutrons at room temperature (average energy of .0253 eV), neutrons produced by fission (around 2 MeV), neutrons produced by the d-t fusion reaction (14 MeV), and protons used in medical radiotherapy (up to 200 MeV).

Targets for Nuclear Reactions

The most interesting targets for nuclear radiations (including particles) are atomic nuclei, although charged particles do react with atomic electrons (slowing down, stopping power). Nuclei are usually named by giving the name of the element they belong to, or the number of protons that they contain, together with the total number of protons and neutrons in the nucleus. Thus, you might see 27Al, Al-27, 208Pb, or 20882. Sometimes a nuclide as either target or reaction product may exist in a compartively long-lived excited state called an "isomer." Isomers are often denoted by adding the suffix "m", e.g., Pm-148m. In many experiments and practical nuclear devices, the target might be an element, which contains some combination of the various stable isotopes. As an example, Cu-nat, or natCu, contains 69% 63Cu and 31% 65Cu.

For more information on nuclei, isotopes, and isomers, see our discussion of nuclear structure.

Products of Nuclear Reactions

The products of nuclear reactions normally consists of gamma rays, some of the light particles (n, p, d, t, 3He, α), and heavier "residual nucleus." Therefore, we can define a nuclear reaction by specifying the projectile, target, and products in forms like the following:

n + 6Li = 7Li + γ

The gammas aren't always given explicitly in these notations.

In these cases, the residual nucleus is another stable isotope; however, sometimes it is unstable and decays with some "half life" into other products. For example, the (n,&gamma') reaction on 27Al produces 28Al, which decays to 28Si by emitting a negative beta particle with a half life of 2.25 minutes.

Sometimes the break up of the residual is so fast that it doesn't make sense to show it explicitly. Therefore, we write


and omit the unstable 8Be from the notation.

In writing out these reactions, it is important to preserve the charge (Z) and mass number (A). In the beryllium example the charge and mass before the reaction are 4 and 10. The two neutrons and two alpha particles remaining after the reaction also total up to Z and A values of 4 and 10.

The various libraries of evaluated nuclear reaction data normally use some standard set of identifiers to define reactions. As an example, the ENDF system uses MT=102 for the (n,&gammma;) reaction and MT=16 for the (n,2n) reaction.

Cross Sections: What the Heck is a Barn?

The probability that a nuclear reaction will take place is measured in units of "barns," where 1 barn equals 10-24 cm2. This is a unit of area. You can visualize a target material as an array of little disks. Larger disks would be easy to hit (large cross section, large reaction probability), and smaller disks would be hard to hit. Folklore has it that this term was invented when there were still lots of farm boys in physics; an atom with a large cross section would be "as easy to hit as the side of a barn." Early compilations of nuclear cross sections were called "Barn Books," and the National Nuclear Data Center still uses a barn as an icon ( take a visit).

As an example of a nuclear cross section, the following figure shows the fission cross section for U-235, the reaction that is responsible for generating a good fraction of the world's electricity.

U-235 fission cross section graph

This is an example of an exothermic reaction--it releases energy. Note that the cross section is very large at low energies. This is where most of the reactions take place in a power reactor. The complex structure at intermediate energies is from "resonances." These are characteristic energies where the nucleus is easy to excite, much the same as the characteristic vibration frequencies of a guitar string.

Endothermic reactions require energy to proceed; therefore, they can only be induced by incident particles that already have high energy. The minimum amount of energy required to induce such a reaction is called the "threshold" energy. Reaction thresholds are typically in the MeV range and higher. Below the threshold, the cross section disappears like the smile of the Chesire Cat. Clearly, the geometric analogy for reaction probabilities can't be followed too far!

For an easy way to look up the reaction thresholds or the amount of energy used or released by nuclear reactions (the reaction Q value), try our qtool.

Product Distributions in Energy and Angle

When a particle, such as a neutron or a proton, passes close to a target nucleus, it can "scatter," changing its direction of travel and its kinetic energy. The scattering can be "elastic" or "inelastic". In elastic scattering, the target nucleus remains in its ground state, but in inelastic scattering, it can absorb energy from the incident particle (the absorbed energy usually is re-emitted as gamma rays). Both of these events are "two-body" collisions, much like billiard-ball collisions, and the products fly off at different angles. Mathematical analysis reveals that the energies of the scattered particle and the recoil nucleus are completely determined by the angle of emission of the scattered particle, and many of these angular distributions have been measured or calculated over the years. An example is shown in the following figure:


At the highest energies, the scattering is basically the diffraction of a wave around a hard sphere, and the results are similar to diffraction patterns for light. The forward peak (at Cosine=1.0) is like the bright central spot in a diffraction pattern, and the oscillations at larger angles (smaller cosines) are analogous to the fringes seen for light.

It is also possible for the incident particle to merge right into the target nucleus, thus adding its mass and kinetic energy into an excited "compound nucleus." If enough time elapses before re-emission, the compound nucleus is said to come into equilibrium. You can visualize the incident particle bouncing around inside the nucleus until all its energy has been shared out with the other nucleons in the compound system. However, this compound system is "hot," almost like the tea kettle on your stove, and it can "evaporate" off particles just like the tea pot emits steam. The evaporated particles can be the same as the incident one, or different. For example, you might get an (n,2n) reaction, or an (n,p) reaction.

If equilibrium has been reached, the particles in the compound nucleus will have bounced around enough to "forget" what direction the incident particle was going originally. The secondary particles will come off in all directions with uniform probability; this is call isotropic emission. The energy spectrum of the emitted particles will show a distribution similar in shape to emission of evaporated atoms from a liquid. Such shapes are characterized by the temperature of the medium, and they are called "Maxwellians" or "Maxwell-Boltzmann distributions" after the scientists who originally described them.

At higher energies, particles do not always come into equilibrium before escaping from the nucleus. You could envision one just bouncing a few times and then coming out with much of its energy intact. This is called "preequilibrium emission." It is also possible for an incident particle of one type to transfer its energy to one of another type, and you could have preequilibrium proton emission from an (n,p) reaction. Preequilibrium particles "remember" more about their original direction, and they tend to come out in the forward direction. They also tend to come out with more energy than equilibrium emissions. An example of some of these effects is shown in the next figure:

proton emission

The peaks at lower secondary energies are the "evaporation" protons, and the long shoulders at higher secondary energies result from preequilibrium emission of protons. This figure is an average over all emission directions, but a more careful look would show that the particles in the shoulders are emitted in the forward direction. This plot was made from the ENDF/B section section of our Data Area.

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5 May 1998 (updated May 2012)