Science
CROSS SECTION
Science > Nuclear Physics
Physicists use the concept of "cross section" to describe the likelihood that a certain particle interaction will occur. The cross section is expressed in terms of area, and it tells physicists the probability that two particles will interact if particles cross into the area of space described. The most common unit for cross section is "barns" (10-24 square cm). Particles can interact in a number of ways, and there are different cross sections to describe these different kinds of interactions. During the Manhattan Project, physicists needed to predict the probability of a free neutron striking the nucleus of a fissionable substance, forcing the nucleus to undergo fission. The area within which fission would be expected to occur, is defined to be the "fission cross-section." Fission is not the only potential interaction between neutrons and nuclei. Another possibility is that the free neutron will interact by "bouncing" off or "scattering" from the atom. In this case the free neutron has come close enough to the nucleus to feel its presence, but no fission event will occur because the neutron did not hit the nucleus. The area within which the neutron would be expected to interact with the nuclei by scattering is called the "scattering cross-section." Another possibility, however, is that the neutron will neither hit the nucleus causing it to undergo fission, nor scatter off of it, but will be "absorbed" by the nucleus. In this process, termed neutron capture, the atom gobbles up the neutron without undergoing fission, to form a heavier atom. Neutron capture is very important for plutonium production, but undesirable for initiating a nuclear chain-reaction. The distinct cross-sectional area of space within which the neutron would be expected to interact with the nuclei by capture is called the "capture cross-section." 
The cross section for these different nuclear interactions is not constant. They are related to both the energy with which the neutrons move and the type of material with which they are trying to interact. The fission cross section for uranium-235, for example, is larger for slow neutrons than it is for fast neutron. A larger cross section for slow neutrons means that it is easier to get nuclei to fission with slow neutrons than it is with fast neutrons. Because of such differences, physicists needed to know the fission cross section of uranium-235 for neutrons over a wide range of neutron speeds before a successful bomb could be designed. During the Manhattan Project neutron data for such experiments could be generated to some extent within experimental reactors. Nuclear physicists and condensed matter physicists often employ neutron scattering to probe the characteristics of matter and are thus often interested in the scattering cross-section, bomb designers would be most interested in the cross section for fission by fast neutrons, reactor scientists might want to know the cross-section at which capture occurs. 
During the Manhattan Project, Robert Bacher's (above left) Experimental Physics Division at Los Alamos, employed particle accelerators to conduct cross section measurements for different reactions given a range of neutron and nuclei conditions. Click the "Los Alamos Primer" at right to read Robert Serber's lecture on factors affecting cross section determinations (pages 2-4).
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The text for this page is original to the Department of Energy's Office of History and Heritage Resources. Major sources consulted include the following. For an introduction to the scientific and technical issues at stake in determination of particle cross sections, see the section entitled "Designing the Bomb" in Los Alamos Scientific Laboratory, Los Alamos: Beginning of an Era, 1943-1945 (Los Alamos: Public Relations Office, Los Alamos Scientific Laboratory, ca. 1967-1971), 19-20. More information on the definition of a "barn" appears in John F. Hogerton, ed., "Cross Section," The Atomic Energy Deskbook (New York: Reinhold Publishing Corporation, 1963; prepared under the auspices of the Division of Technical Information, U.S. Atomic Energy Commission), 114-115. To see current data on cross sections for particle interactions see, http://www.physics.nist.gov/cuu/Constants/index.html. For more information on important wartime cross section calculations, see Lillian Hoddeson, et. al., Critical Assembly: a Technical History of Los Alamos During the Oppenheimer Years, 1943-1945 (Cambridge: Cambridge University Press, 1993); and Richard G. Hewlett and Oscar E. Anderson, Jr., The New World, 1939-1946: Volume I, A History of the United States Atomic Energy Commission (Washington: U.S. Atomic Energy Commission, 1972). The photograph of the neutron cross section experiment is courtesy LANL; it is reprinted in Rachel Fermi and Esther Samra, Picturing the Bomb: Photographs from the Secret World of the Manhattan Project (New York: Harry N. Abrams, Inc., Publishers, 1995), 99 and 109. The lecture on factors effecting cross section determinations comes from Serber, Robert, The Los Alamos Primer, Los Alamos, NM: April 1943.