MadSci Network: Physics |
I will break my answer into two parts--the formation of the unstable nucleus that will undergo fission, and then why it fissions. Thermal (slow) neutrons are required for fission because the neutron must be captured to form the unstable nucleus (U-235 + n --> U-236* or Th-228 + n --> Th-229* are examples of neutron capture leaving the product nucleus in a high energy state). Fast neutrons will cause nuclear reactions such as (n,p) where a fast neutron collides with a nucleus and then a proton is emitted. You can also have an (n, 2n) reaction where a fast neutron collides with a nucleus and 2 neutrons are emitted. It is also possible to cause fission in some nuclides with fast neutrons (Ra-226, Th-232, Pa-231, U-238, and Pu-242 are examples) where the neutron energy is in the range 0.2 to 1.7 MeV. The reference by Friedlander, et.al. gives graphs of the probability of fission as a function of neutron energy. The probability of fission for a thermal neutron hitting a nucleus that will fission with capture of a thermal neutron is hundreds of times greater than that for fission induced by a fast neutron. The neutron to be captured must be of low enough energy that it can "fall" into the potential energy well of the target nucleus and form a compound nucleus in an excited state. In Friedlander et.al. there is a discussion of the formation of the excited compound nucleus (in the above examples U-236* and Th-229*). This is part of the general theory of Formation and Decay of the Compound Nucleus as a part of the theory of particle-induced nuclear reactions. The decay of the compound nucleus usually has many possible pathways, in the case of U-236*, it can decay by the emission of gamma rays, beta particles, alpha particles, and nuclear fission. In this case, fission is the most probable method of decay because of the greater stability of the product nuclei. The Binding Energy of a nucleus (the difference between the mass of A hydrogen atoms and N neutrons and the mass of the nuclide peaks at iron (Fe-56 is the nuclide with the highest binding energy--equivalently, the greatest difference in mass between 28 Hydrogen Atoms plus 28 Neutrons minus the mass of Fe-56. This resultant difference is converted to energy (about 941 MeV per atomic mass unit). There are two other major effects that enter into why fission occurs: the first is the nuclear shell theory which shows that certain nuclei with "magic numbers" of protons or neutrons are especially stable (nuclear equivalents of inert gases; Z=50 and N=82 are important in fission). The second is the liquid-drop model of fission. Large nuclei are not spherical, but usually oblate spheriods. The addition of a neutron sets up oscillations that can lead to fission. The large amount of energy emitted from fission (appx 200 MeV per fission) yielding more stable products than alpha or beta decay also drives the reaction. The fission products are also excited, but they do not have the energy for fission, so they decay by beta and gamma emission. Ref: Nuclear and Radiochemistry, 3rd Edition by Friedlander, Kennedy, Macias, and Miller (Wiley Interscience 1981 ISBN 0-471-86255-X pbk) The Atomic Nucleus, R.D. Evans, McGraw Hill 1955, 14th printing May 26, 1972 Library of Congress Catalog Card Number 55-7275. This is considered to be the bible of low energy nuclear physics. This is a long answer, possibly quite complicated, but using the references, or other books on Nuclear Chemistry will make it clearer.
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