Excerpted from Section 2 of Nuclear Weapons Frequently Asked Qustions by Carey Sublette.
Nuclear fission occurs when the nuclei of certain isotopes of very heavy elements, isotopes of uranium and plutonium for example, capture neutrons. The nuclei of these isotopes are just barely stable and the addition of a small amount of energy to one by an outside neutron will cause it to promptly split into two roughly equal pieces, with the release of a great deal of energy (180 MeV of immediately available energy) and several new neutrons (an average of 2.52 for U-235, and 2.95 for Pu-239). If on average one neutron from each fission is captured and successfully produces fission then a self-sustaining chain reaction is produced. If on average *more* than one neutron from each fission triggers another fission, then the number of neutrons and the rate of energy production will increase exponentially with time.
Two conditions must be met before fission can be used to create powerful explosions: 1) the number of neutrons lost to fission (from non-fission producing neutron captures, or escape from the fissionable mass) must be kept low, and 2) the speed with which the chain reaction proceeds must be very fast. A fission bomb is in a race with itself: to successfully fission most of the material in the bomb before it blows itself apart. The degree to which a bomb design succeeds in this race determines its efficiency. A poorly designed or malfunctioning bomb may "fizzle" and release only a tiny fraction of its potential energy.
The nucleus of an atom can interact with a neutron that travels nearby in two basic ways. It can scatter the neutron - deflecting the neutron in a different direction while robbing it of some of its kinetic energy. Or it can capture the neutron, which in turn can affect the nucleus in several ways - absorption and fission being most important here. The probability that a particular nucleus will scatter or capture a neutron is measured by its scattering cross-section and capture cross-section respectively. The overall capture cross-section can be subdivided into other cross-sections - the absorption cross- section and the fission cross-section.
The stability of an atomic nucleus is determined by its binding energy - the amount of energy required to disrupt it. Any time a neutron or proton is captured by an atomic nucleus, the nucleus rearranges its structure. If energy is released by the rearrangement, the binding energy decreases. If energy is absorbed, the binding energy increases.
The isotopes important for the large scale release of energy through fission are uranium-235 (U-235), plutonium-239 (Pu-239), and uranium- 233 (U-233). The binding energy of these three isotopes is so low that when a neutron is captured, the energy released by rearrangement exceeds it. The nucleus is then no longer stable and must either shed the excess energy, or split into two pieces. Since fission occurs regardless of the neutron's kinetic energy (i.e. no extra energy from its motion is needed to disrupt the nucleus), this is called "slow fission".
By contrast, when the abundant isotope uranium-238 captures a neutron it still has a binding energy deficit of 1 MeV after internal rearrangement. If it captures a neutron with a kinetic energy exceeding 1 MeV, then this energy plus the energy released by rearrangement can over come the binding energy and cause fission. Since a fast neutron with a large kinetic energy is required, this is called "fast fission".
The slow fissionable isotopes have high neutron fission cross-sections for neutrons of all energies, while having low cross-sections for absorption. Fast fissionable isotopes have zero fission cross-sections below a certain threshold (1 MeV for U-238), but the cross-sections climb quickly above the threshold. Generally though, slow-fissionable isotopes are more fissionable than fast-fissionable isotopes for neutrons of all energies.
A general trend among the elements is that the ratio of neutrons to protons in an atomic nucleus increases with the element's atomic number (the number of protons the nucleus contains, which determines which element it is). Heavier elements require relatively more neutrons to stabilize the nucleus. When the nucleus of a heavy element like uranium (atomic number 92) is split the fragments, having lower atomic numbers, will tend to have excess neutrons. These neutrons are shed very rapidly by the excited fragments. More neutrons are produced on average than are consumed in fission.
Fission is a statistical process. The nucleus rarely splits into pieces with nearly the same mass and atomic number. Instead both the size and atomic numbers of the fragments have a Gaussian distributions around two means (one for the lighter fragment around 95, one for the heavier around 135). Similarly, the number of neutrons produced varies from zero to six or more, and their kinetic energy varies from 0.5 MeV to more than 4 MeV, the most probable energy is 0.75 MeV, the average (and median) is 2 MeV.
A breakdown of the energy released by fission is given below:
MeV Kinetic energy of fission fragments 165 +/- 5 Instantaneous gamma rays 7 +/- 1 Kinetic energy of neutrons 5 +/- 0.5 Beta particles from product decay 7 +/- 1 Gamma rays from product decay 6 +/- 1 Neutrinos from product decay 10 TOTAL 200 +/- 6
All of the kinetic energy is released to the environment instantly, as are most of the instantaneous gamma rays. The unstable fission products release their decay energies at varying rates, some almost immediately. The net result is that about 180 MeV is actually available to generate nuclear explosions, the remainder of the decay energy shows up over time as fallout (or is carried away by the virtually undetectable neutrinos).
A neutron entering a pure chunk of one of the slow-fissionable isotopes would have a high probability of causing fission compared with the chance of unproductive absorption. If the chunk is large and compact enough, then the rate of neutron escape from its surface will be so low that it becomes a "critical mass", a mass in which a self- sustaining chain reaction occurs. Non-fissionable materials mixed with these isotopes tend to absorb some of the neutrons uselessly, and increase the required size of the critical mass or may even make it impossible to achieve altogether.
Typical figures for critical masses for bare (unreflected) spheres of fissionable materials are:
U-233 16 kg U-235 52 kg Pu-239 (alpha phase) 10 kg