U-238 Neutron Capture Cross Section
Andree Vandestreek
When a neutron passes near to a heavy nucleus, for example uranium-235 (U-235), the neutron may be captured by the nucleus and this may or may not be followed by fission. Capture involves the addition of the neutron to the uranium nucleus to form a new compound nucleus. A simple example is U-238 + n ==> U-239, which represents formation of the nucleus U-239. The new nucleus may decay into a different nuclide. In this example, U-239 becomes Np-239 after emission of a beta particle (electron). But in certain cases the initial capture is rapidly followed by the fission of the new nucleus. Whether fission takes place, and indeed whether capture occurs at all, depends on the velocity of the passing neutron and on the particular heavy nucleus involved.
Fission may take place in any of the heavy nuclei after capture of a neutron. However, low-energy (slow, or thermal) neutrons are able to cause fission only in those isotopes of uranium and plutonium whose nuclei contain odd numbers of neutrons (e.g. U-233, U-235, and Pu-239). Thermal fission may also occur in some other transuranic elements whose nuclei contain odd numbers of neutrons. For nuclei containing an even number of neutrons, fission can only occur if the incident neutrons have energy above about one million electron volts (MeV). (Newly-created fission neutrons are in this category and move at about 7% of the speed of light, while moderated neutrons move a lot slower, at about eight times the speed of sound).
A neutron is said to have thermal energy when it has slowed down to be in thermal equilibrium with the surroundings (when the kinetic energy of the neutrons is similar to that possessed by the surrounding atoms due to their random thermal motion). Hence the main application of uranium fission today is in thermal reactors fuelled by U-235 and incorporating a moderator such as water to slow the neutrons down. The most common examples of this are light water reactors*.
The probability that fission or any another neutron-induced reaction will occur is described by the neutron cross-section for that reaction. This may be imagined as an area surrounding the target nucleus and within which the incoming neutron must pass if the reaction is to take place. The fission and other cross-sections increase greatly as the neutron velocity reduces from around 20,000 km/s to 2 km/s, making the likelihood of some interaction greater. In nuclei with an odd number of neutrons, such as U-235, the fission cross-section becomes very large at the thermal energies of slow neutrons.
As implied previously, high-energy (> 0.1 MeV) neutrons are travelling too quickly to have much interaction with the nuclei in the fuel. We therefore say that the fission cross-section of those nuclei is much reduced at high neutron energies relative to its value at thermal energies (for slow neutrons). It is nonetheless possible to use this so-called fast fission in a fast neutron reactor whose design minimises the moderation of the high-energy neutrons produced in the fission process. See below.
Using U-235 in a thermal reactor as an example, when a neutron* is captured the total energy is distributed amongst the 236 nucleons (protons & neutrons) now present in the compound nucleus. This nucleus is relatively unstable, and it is likely to break into two fragments of around half the mass. These fragments are nuclei found around the middle of the Periodic Table and the probabilistic nature of the break-up leads to several hundred possible combinations. Creation of the fission fragments is followed almost instantaneously by emission of a number of neutrons (typically 2 or 3, average 2.45), which enable the chain reaction to be sustained.
* The chain reaction is started by inserting some beryllium mixed with polonium, radium or other alpha-emitter. Alpha particles from the decay cause a release of neutrons from the beryllium as it turns to carbon-12.
About 85% of the energy released is initially the kinetic energy of the fission fragments. However, in solid fuel they can only travel a microscopic distance, so their energy becomes converted into heat. The balance of the energy comes from gamma rays emitted during or immediately following the fission process and from the kinetic energy of the neutrons. Some of the latter are immediate (so-called prompt neutrons), but a small proportion (0.66% for U-235, 0.27% for U-233, 0.23% for Pu-239) is delayed, as these are associated with the radioactive decay of certain fission products. The longest delayed neutron group has a half-life of about 56 seconds.
The delayed neutron release is the crucial factor enabling a chain reacting system (or reactor) to be controllable and to be able to be held precisely critical. At criticality the chain reacting system is exactly in balance, such that the number of neutrons produced in fissions remains constant. This number of neutrons may be completely accounted for by the sum of those causing further fissions, those otherwise absorbed, and those leaking out of the system. Under these circumstances the power generated by the system remains constant. To raise or lower the power, the balance must be changed (using the control system) so that the number of neutrons present (and hence the rate of power generation) is either reduced or increased. The control system is used to restore the balance when the desired new power level is attained.
The number of neutrons and the specific fission products from any fission event are governed by statistical probability, in that the precise break up of a single nucleus cannot be predicted. However, conservation laws require the total number of nucleons and the total energy to be conserved. The fission reaction in U-235 produces fission products such as Ba, Kr, Sr, Cs, I and Xe with atomic masses distributed around 95 and 135. Examples may be given of typical reaction products, such as:
In such an equation, the number of nucleons (protons + neutrons) is conserved, e.g. 235 + 1 = 141 + 92 + 3, but a small loss in atomic mass may be shown to be equivalent to the energy released. Both the barium and krypton isotopes subsequently decay and form more stable isotopes of neodymium and yttrium, with the emission of several electrons from the nucleus (beta decays). It is the beta decays, with some associated gamma rays, which make the fission products highly radioactive. This radioactivity (by definition!) decreases with time.
About 6% of the heat generated in the reactor core originates from radioactive decay of fission products and transuranic elements formed by neutron capture, mostly the former. This must be allowed for when the reactor is shut down, since heat generation continues after fission stops. It is this decay which makes used fuel initially generate heat and hence need cooling, as very publicly demonstrated in the Fukushima accident when cooling was lost an hour after shutdown and the fuel was still producing about 1.5% of its full-power heat. Even after one year, typical used fuel generates about 10 kW of decay heat per tonne, decreasing to about 1 kW/t after ten years.
Neutrons may be captured by non-fissile nuclei, and some energy is produced by this mechanism in the form of gamma rays as the compound nucleus de-excites. The resultant new nucleus may become more stable by emitting alpha or beta particles. Neutron capture by one of the uranium isotopes will form what are called transuranic elements, actinides beyond uranium in the periodic table.
As already noted, Pu-239 is fissile in the same way as U-235, i.e. with thermal neutrons. It is the other main source of energy in any nuclear reactor. If fuel is left in the reactor for a typical three years, about two-thirds of the Pu-239 is fissioned with the U-235, and it typically contributes about one-third of the energy output. The masses of its fission products are distributed around 100 and 135 atomic mass units. One difference is that Pu-239 fission in a thermal reactor results in 2.9 neutrons on average, instead of almost 2.5 for U-235, and its fission cross-section is three times its capture cross-section so that about one-quarter of reactions result in the formation of Pu-240 which is not fissile. In a fast reactor, Pu-239 produces more neutrons per fission (e.g. at 2 MeV: four), so is better suited to the fast neutron spectrum (see below).
The main transuranic constituents of used fuel are isotopes of plutonium, curium, neptunium and americium, the last three being 'minor actinides'. These are alpha-emitters and have long half-lives, decaying on a similar time scale to the uranium isotopes. They are the reason that used fuel needs secure disposal beyond the few thousand years or so which might be necessary for the decay of fission products alone.
Apart from transuranic elements in the reactor fuel, activation products are formed wherever neutrons impact on any other material surrounding the fuel. Activation products in a reactor (and particularly its steel components exposed to neutrons) range from tritium (H-3) and carbon-14, to cobalt-60, iron-55 and nickel-63. The latter four radioisotopes create difficulties during eventual demolition of the reactor, and affect the extent to which materials can be recycled.
In a fast neutron reactor the fuel in the core is Pu-239 and the abundant neutrons which leak from the core breed more Pu-239 in a fertile blanket of U-238 around the core. A minor fraction of U-238 might be subject to fission, but most of the neutrons reaching the U-238 blanket will have lost some of their original energy and are therefore subject only to capture and thus breeding of Pu-239. Cooling of the fast reactor core requires a heat transfer medium which has minimal moderation of the neutrons, and hence liquid metals are used, typically sodium.
Such reactors can be up to 100 times more efficient at converting fertile material than ordinary thermal reactors because of the arrangement of fissile and fertile materials, and there is some advantage from the fact that Pu-239 yields more neutrons per fission than U-235. Although both yield more neutrons per fission when split by fast rather than slow neutrons, this is incidental since the fission cross sections are much smaller at high neutron energies. While the conversion ratio (the ratio of new fissile nuclei to fissioned nuclei) in a normal reactor is around 0.6, that in a fast reactor may exceed 1.0. Fast neutron reactors may be designed as breeders to yield more fissile material than they consume, or to be plutonium burners to dispose of excess plutonium. A plutonium burner would be designed without a breeding blanket, simply with a core optimised for plutonium fuel, and this is the likely shape of future fast neutron reactors, even if they have some breeding function.
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