Nuclear Reactions And Scattering

Type of physical science: Nuclear physics

Field of study: Nuclei

The collision of an atomic nucleus with another nucleus or other subatomic particle can result in a nuclear reaction, in which the interacting particles change their identities, or a scattering event, in which the particles simply rebound. These processes are important in a stellar energy production, production of radioisotopes for medical uses, trace element analysis, and nuclear power generation.

Overview

A variety of processes can occur when two or more atomic nuclei or other subatomic particles approach each other to within about one nuclear diameter. In elastic scattering, the particles retain their identity and essentially bounce off each other with a total kinetic energy before the collision that is equal to that afterward. In inelastic scattering, the particles rebound with less final total kinetic energy: The difference is retained as excitation energy in one or more of the recoiling nuclei. In a nuclear reaction, the particles after the collision are different from those before. There may be one, two, or many final particles, depending on the process and the amount of energy available.

Reactions are described in terms of reactants and reaction products, but they are also often characterized by the mechanism that describes the reaction process. For example, deuterium and tritium nuclei, two isotopes of hydrogen, can be forced into close proximity by heating or by other means. Deuterium contains one neutron and one proton in its nucleus; tritium contains two neutrons and one proton. These particles can combine to form an α particle (a helium nucleus that contains two neutrons and two protons) and a free neutron. In addition, energy is released, which is shared as energy of motion of the reaction products. The reaction is a "fusion" reaction because two light nuclei fuse to produce a heavier one. It is also called a "thermonuclear" reaction when thermal (heat) energy has initiated it. Reactions of this type are the primary energy source in thermonuclear weapons.

All nuclei are electrically charged in proportion to the number of protons they contain.

An electric repulsion, called the Coulomb barrier, therefore exists between them. This barrier must be overcome before the nuclei can react. This can be accomplished by projecting one of the particles toward the other, known as the target, with enough kinetic energy to surmount the barrier or to bring the particles sufficiently close together that they can quantum-mechanically tunnel through the barrier. If the particles have insufficient energy to overcome the barrier, elastic scattering is usually the only possible interaction.

Projectiles come in many forms. Cosmic rays, which consist of high-energy protons and other particles, and which constantly bombard the earth, can produce nuclear reactions.

Alpha particles from naturally radioactive elements were used as projectiles for early scattering and reaction studies. Charged projectiles such as protons, helium nuclei, and heavier ions are now usually obtained from atoms that are ionized and then accelerated by machines (accelerators) to energies sufficient to induce reactions. Fewer than 1 million electronvolts of kinetic energy may be sufficient to produce reactions with very light nuclei, but because barrier height increases as the product of the electrical charges of the projectile and the target nucleus, several hundred million electronvolts may be necessary with very heavy ions. Neutrons, which are uncharged, do not encounter a Coulomb barrier, but they must be ejected from nuclei by means of nuclear reactions before they are used as projectiles. Although neutrons are stable in many nuclei, they live only for minutes as free particles.

Target nuclei are usually contained in samples of ordinary material, preferably in solid or liquid form to maximize the density of nuclei. They are usually considered to be at rest, since velocities of thermal motion are small compared to projectile velocity. Projectiles are usually incident on the material from a well-defined direction. The reaction products can be observed directly if the target is thin enough to allow them to emerge without loss of energy or identity.

This may limit target thickness to several micrometers for low-energy charged reaction products.

In some cases, the distinction between projectile and target is not clear. To obtain very high energies for elementary particles studies, for example, colliding beams of particles approach each other with equal speeds near the speed of light. In thermonuclear reactions, both reactants move randomly, but sometimes they collide with relative thermal velocities sufficient to overcome the Coulomb barrier. The distinction is even more blurred in stars that have high central densities, in which more than two particles can combine to form a heavier nucleus.

Nuclear interactions take place over very short time intervals during which the interacting particles are essentially isolated from their environment. Certain quantities, such as total energy, momentum, angular momentum, and electric charge, must therefore have precisely the same values immediately before and after the collision. Such quantities are said to be conserved.

Total energy consists of the sum of the kinetic and the rest mass energies of the particles. (Nuclear excitation energy, if any, is added to the rest mass energy). The value of a nuclear reaction is defined as the total mass energy of the reactants minus the mass energy of the reaction products. If the Q value is positive, the total kinetic energy of the particles after the reaction must be greater than that of the particles before the reaction in order to keep the total energy constant. Such reactions, in which mass energy is converted to kinetic energy, are called exoergic or exothermic. If the Q value is negative, kinetic energy must be supplied by the reactants before the reaction can occur. Those reactions are termed "endoergic" or "endothermic."

For projectile kinetic energies lower than about 1 billion electronvolts, the number of nucleons before the reaction is observed to be the same as that afterward. At higher energies, which make possible the creation of nucleons, antinucleons, and other nucleonlike particles, this conservation law must be revised. The number of nucleonlike particles, or baryons, is conserved, but particle-antiparticle pairs are excluded from the count. Electric charge is conserved regardless of the number of particles created.

Reactions can also be characterized by the time scale over which they occur. Direct reactions occur in a time that is comparable to the time that it takes for the projectile to traverse a target nucleus. A "knockout" reaction is one example in which the incident particle knocks an individual nucleon out of the target nucleus. The original particle may also promptly emerge, but with reduced energy. "Stripping" reactions can occur when a composite projectile such as deuterium passes close to a nucleus. One of the nucleons can be stripped from the projectile and incorporated directly into a nuclear excited state. The remaining nucleons continue with sufficient energy to keep total energy constant.

Compound nuclear reactions occur over time scales one thousand to one million times longer than those required for direct reactions. The projectile is absorbed by the target, and its energy is distributed over the nucleons of the composite system. Eventually, the energy may be concentrated again in one, two, or more nucleons or particles, which then emerge. The process takes so long on a nuclear time scale that the mode of formation of the compound nucleus is independent of its mode of decay. Fission reactions are an example. They may be induced when a heavy nucleus such as uranium absorbs a neutron. The compound system has excessive energy and begins to undergo shape oscillations and distortions, and may eventually split into two (or more) fragments, usually with the release of additional neutrons. The fragments can gain substantial energy because of the electric repulsion between them. In an appropriate environment, the neutrons that are released can produce additional fission reactions and more neutrons. The continuation of this process is called a chain reaction.

Nuclei are quantum-mechanical systems, and one cannot predict with certainty what will happen when a target is bombarded. One can only specify the probability that a particular reaction will occur. Probabilities are expressed in terms of an effective cross-sectional area that the target nucleus presents to a projectile. In a thin slab of target material in which all nuclei are exposed to projectiles, the probability per incident particle for a specific reaction is the ratio of the total effective cross-sectional area of the nuclei to the front surface area of the target slab.

One might expect the cross section for a nuclear process to equal the geometrical cross section of the nucleus. This is not the case. Effective cross sections range from zero (when the process does not occur) to thousands of times larger than the geometrical area. This reflects the wave nature of the particles and the fact that nuclei can exist only in certain limited quantum states. Reaction and scattering cross sections are not easily predictable and can be determined only by means of theoretical calculations, which are often inaccurate, or measurements.

Applications

Measurements of nuclear reactions and scattering are important sources of knowledge about nuclei. In a typical set of measurements, selected projectiles bombard specific nuclei in a thin target. Reaction products that leave the target are detected, and data, such as the numbers, types, and energies of particles, are recorded. Cross sections for each reaction are calculated.

These quantities are often determined for a number of different projectile energies and at a number of different angles with respect to the projectile direction.

The data are used to characterize quantum states of nuclei in terms of parameters such as excitation energy, angular momentum, lifetime, decay modes, and decay probabilities.

Recurrent patterns in the behavior of these parameters from nucleus to nucleus, and in the cross-section data themselves, are often the inspiration for theoretical models of reaction mechanisms and types of excitations. Recognized excitation models now range from those involving a single nucleon to collective vibrational and rotational excitations of the nucleus as a whole.

As a result of analyzing nuclear reaction data and models of stars it is now known that nuclear reactions in stars are primarily responsible for the existence and abundance of the chemical elements and isotopes. Fusion reactions of primordial hydrogen and helium head a series of fusion reactions that lead to elements as heavy as iron. Neutron-capture reactions involving these light elements, followed by radioactive decays, contribute to the abundance of heavier elements. Most of the naturally occurring radioactive isotopes on Earth most likely originated in the evolution and explosion of ancient stars.

Nuclear reactions play an important role in various methods of age dating diverse specimens. For example, radioactive carbon is continuously produced in the atmosphere by cosmic-ray bombardment and incorporated into living organisms in small amounts. After an organism dies, it can no longer assimilate carbon, but the radiocarbon already there continues to decay. The amount of radioactive carbon, as opposed to ordinary carbon, therefore decreases with the time elapsed since death and can be used to determine that time. This particular technique is well suited for dating archaeological specimens, since about five thousand years is required for half the radiocarbon in a static sample to decay.

Short-lived radioactive isotopes of elements such as carbon, oxygen, and phosphorus, which are important in biological materials, can be produced by means of accelerator-induced reactions. They can be chemically separated from the target and incorporated into various organic compounds. When such labeled compounds are involved in chemical reactions or biological processes, the fate of the element can be traced by means of its radioactive emissions.

Labeled compounds are also used in medicine for therapeutic and diagnostic purposes.

Some pharmaceutical compounds tend to concentrate in specific organs. Iodine, for example, concentrates in the thyroid gland. If a compound labeled with radioactive iodine is ingested, an image of the gland can be formed from the γ rays emitted by the iodine concentrated there.

There are now many related imaging techniques that can be used to assess organ function, identify tumors, and trace metabolic activity.

Neutron activation analysis is a useful technique for determining the trace-element content of a wide variety of materials. The specimen, a mineral sample, for example, is exposed to an intense neutron flux from a nuclear reactor or other source. Neutrons are captured by nuclei in the specimen, inducing reactions that may result in radioactive isotopes. The isotopes can be identified by their characteristic decay modes, energies, and lifetimes. The rate of radioactive decay is proportional to the number of radioactive atoms and can be related through cross-section data to the number of target nuclei in the original specimen.

There are other techniques that use nuclear reactions and scattering directly for trace-element surface analysis. One example is Rutherford backscattering analysis. Charged particles, usually protons or α particles with energies below the barrier, bombard the target.

The energy and number of particles elastically scattered back toward the source are detected.

Particles backscattered from light elements at the surface will have less energy than those scattered from heavy elements because light target nuclei will have more recoil energy. The energy distribution of scatter particles therefore reflects elemental surface composition.

The importance of fission reactions in nuclear power generation is well known, but nuclear reactions are also important in the production of transuranic elements that can be used as fuel, and as a source of neutrons for applied and basic research in solid-state and nuclear physics.

Because the fuel supply for fission reactions is limited, controlled fusion reactions are being explored as an alternative source of power.

Context

The study of nuclear reactions and nuclei has its roots in the discovery of natural radioactivity by Antoine-Henri Becquerel in 1896. Within the following fifteen years, α, β, and γ decay were discovered, and the α particle was identified as a helium nucleus, the β particle as an electron, and the γ ray as electromagnetic energy. The transmutation of one chemical element into another as a result of α and β decay was also established.

Ernest Rutherford used α particles as projectiles with which to bombard a variety of materials. In particular, he found that when metallic foils were bombarded, some of the α particles were elastically scattered back toward the source. In 1911, he concluded from this observation that most of the mass and all of the positive charge of the atom were concentrated in a tiny nucleus at the center of the atom. Subsequent measurements of the dependence of scattering cross section on scattering angle verified this hypothesis and indicated that the nucleus is about 100,000 times smaller in diameter than the atom itself.

Rutherford also observed the first artificially induced nuclear reaction in 1919, when he bombarded nitrogen with α particles and produced protons and oxygen nuclei as reaction products. In 1932, James Chadwick proposed that electrically neutral particles, now known as neutrons, were produced when beryllium nuclei were bombarded by α particles.

From 1932 on, it was clear that nuclei contained both protons and neutrons, and understanding of nuclei rapidly increased. John Douglas Crockcroft and Ernest Thomas Sinton Walton observed the first nuclear reaction to be induced by machine accelerated protons in 1932.

Irene Joliot-Curie and Frederic Joliot were the first to produce artificial radioactivity by means of a nuclear reaction. Otto Hahn and Fritz Strassman discovered nuclear fission in 1939. In 1942, Enrico Fermi produced the first self-sustaining chain reaction.

After World War II, more powerful accelerators were developed, and knowledge of nuclei and nuclear forces extended to higher energies and shorter distances. Whereas reactions induced at random by cosmic rays were once the only way to produce exotic short-lived particles, such particles began to be produced in quantity in the laboratory. From studies of these particles, physicists are beginning to understand the nature of the forces that hold nuclei together despite the electric repulsion that tends to tear them apart. It is now generally accepted that the electromagnetic interaction between charged particles is closely related to the weak interaction that governs the β decay of nuclei.

In the future, more powerful accelerators will be built to extend the knowledge of the strong nuclear force and to seek a relationship between it and the electroweak interaction. The Superconducting Supercollider, a machine designed to produce high-energy counter-rotating beams of protons for ultrahigh energy collisions, is one such machine. It is also likely that a relativistic heavy ion collider will be constructed to study new states of matter that might be produced when nuclei are compressed to high density.

Principal terms

ALPHA PARTICLE: a particle containing two protons and two neutrons (a helium nucleus) that is emitted in radioactive decay

BETA DECAY: a form of radioactive decay in which a neutron, for example, is transformed into a proton, an electron, and an antineutrino

ELECTRONVOLT: a unit of energy equivalent to the energy gained by an electron that is accelerated through an electrical potential difference of 1 volt

GAMMA RAY: electromagnetic radiation emitted when a nuclear excited state decays to a lower energy state

ION: an atom that has had one or more electrons added or removed in order to produce an electrically charged particle

ISOTOPE: nuclei that have the same number of protons, and therefore belong to the same chemical element, but have different numbers of neutrons

KINETIC ENERGY: energy of motion, which, at low speeds, is proportional to mass times speed squared

MASS ENERGY: the energy equivalent of mass is the amount of mass times the speed of light squared

NUCLEONS: a generic term for neutrons and protons, the particles that compose the atomic nucleus

RADIOACTIVITY: the spontaneous decay of a nucleus, usually by the emission of α, β, or γ rays

Bibliography

Asimov, Isaac. INSIDE THE ATOM. New York: Abelard-Schuman, 1956. A short, nonmathematical book written at an elementary level by a popular science-fiction author. Early chapters describe atoms and their constituents, isotopes, and radioactivity. Later chapters deal with nuclear reactions and some applications of nuclear physics.

Cohen, Bernard L. THE HEART OF THE ATOM. Garden City, N.Y.: Doubleday, 1967. This brief monograph is primarily intended for high school students. It starts by explaining the structure of nuclei and the behavior of nucleons in nuclei. It continues with radioactive decay, and discusses nuclear reactions in chapter 7. Applications such as age dating, fission and fusion power, and energy generation in stars are also included.

Fowler, William A. "The Origin of the Elements." SCIENTIFIC AMERICAN 195 (September, 1956): 82-91. This article summarizes some of the reactions through which stars produce the elements. It mentions two reaction chains that convert hydrogen to helium and continues to describe the production of elements from carbon to iron. Includes a brief discussion of heavy element production by means of neutron capture reactions.

Hewitt, Paul G. CONCEPTUAL PHYSICS. 5th ed. Boston: Little, Brown, 1985. A popular introductory physics textbook for college students who are not mathematically inclined. The discussion in chapter 31, "The Atomic Nucleus and Radioactivity" and chapter 32, "Nuclear Fission and Fusion" is clear and brief, and does not rely on the preceding material in the book to any substantial degree.

Krane, Kenneth S. MODERN PHYSICS. New York: John Wiley & Sons, 1983. A clearly written textbook at the college sophomore-junior level. Nuclear structure and radioactivity are treated in chapter 9, and nuclear reactions with applications are covered in chapter 10. The treatment of radioactivity uses some calculus, but the discussion of applications is nonmathematical.

Leachman, R. B. "Nuclear Fission." SCIENTIFIC AMERICAN 213 (August, 1965): 49-56. This article is devoted to the fission reaction mechanism. The liquid-drop model of the nucleus is described: There are interesting photographs of a water drop splitting into two droplets to illustrate the analogy. Results of theoretical calculations are described and compared to observations.

McHarris, William C., and John O. Rasmussen. "High Energy Collisions Between Atomic Nuclei." SCIENTIFIC AMERICAN 250 (January, 1984): 56-58. Presents a brief history of heavy ion accelerators and collisions. It describes several types of collision processes and speculates about the properties of nuclear matter at the high temperatures and pressures that may be achieved by these reactions.

Trefil, James S. FROM ATOMS TO QUARKS. New York: Charles Scribner's Sons, 1980. This popular book is basically a history of elementary particle physics. It does not emphasize nuclear reactions and scattering as such, but dwells more on the types of particles produced in high-energy collisions and how they can be classified and interpreted. Concludes with discussions of the quark model and the nature of the strong and weak interactions.

Atomic nuclei must overcome Coloumb barrier before interacting

Fission and Thermonuclear Weapons

Materials Analysis with Nuclear Reactions and Scattering

Nuclear Synthesis in Stars

Radioactive Nuclear Decay and Nuclear Excited States

Thermonuclear Reactions in Stars