# Nuclear fission

File:Nuclear fission.gif
Sketch of induced nuclear fission, a neutron (n) strikes a uranium nucleus which splits into similar products (F. P.), and releases more neutrons to continue the process, and energy in the form of gamma and other radiation.

Nuclear fission (in nuclear physics, simply fission) is a process in which the nucleus of an atom splits into two or more smaller nuclei (fission products) and usually some by-product particles. Hence, fission is a form of elemental transmutation. The by-products include free neutrons, photons (usually gamma rays), and other nuclear fragments such as beta particles and alpha particles. Fission of heavy elements can release substantial amounts of useful energy both as gamma rays and as kinetic energy of the fragments.

Nuclear fission is used to produce energy for nuclear power and to drive explosion of nuclear weapons such as the atomic bomb. Fission is useful as a power source because some materials, called nuclear fuels, both generate neutrons as part of the fission process and also undergo triggered fission when impacted by a free neutron. Nuclear fuels can be part of a self-sustaining chain reaction that releases energy at an controlled rate (in a nuclear reactor) or a very rapid uncontrolled rate (in a nuclear bomb).

The amount of free energy contained in nuclear fuel is millions of times the amount of energy contained in a similar mass of chemical fuel such as gasoline, making nuclear fission a very tempting source of energy; however, the waste products of nuclear fission are highly radioactive and remain so for millennia, giving rise to a nuclear waste problem. Concerns over nuclear waste accumulation and over the immense destructive potential of nuclear weapons balance the desirable qualities of fission as an energy source, and give rise to intense ongoing political debate over nuclear power.

# Physical overview

Nuclear fission differs from other forms of radioactive decay in that it can be harnessed and controlled via a chain reaction. Chemical isotopes that can sustain a fission chain reaction are called nuclear fuels, and are said to be fissile. The most common nuclear fuels are 235U (the isotope of uranium with an atomic mass of 235) and 239Pu (the isotope of plutonium with an atomic mass of 239). These fuels break apart into a range of chemical elements with atomic masses near 100 (fission products). Most nuclear fuels undergo spontaneous fission very slowly, gradually disintegrating over periods of eons. In a nuclear reactor or nuclear weapon, most fission events are induced by bombardment with another particle such as a neutron.

Typical fission events release several hundred MeV of energy for each fuel atom that undergoes fission, which is why nuclear fission is used as an energy source. By contrast, most chemical oxidation reactions (such as burning coal) release at most a few tens of eV per event, so nuclear fuel contains between one and ten million times more usable energy than does chemical fuel. The energy of nuclear fission is released as kinetic energy of the fission products and fragments, and as electromagnetic radiation (gamma rays); in a nuclear reactor, the energy is converted to heat as the particles and gamma rays collide with the atoms that make up the reactor and its working fluid (usually water).

Nuclear fission produces energy because the binding energy of intermediate-mass nuclei (with atomic numbers and atomic masses close to 56Fe) is greater than the binding energy of very heavy nuclei, so that energy is released when heavy nuclei are broken apart. The total mass of the fission products from a single reaction is less than the mass of the original fuel nucleus, and the excess is released as energy via Einstein's relation E=mc2.

The variation in binding energy is due to the interplay of the two fundamental forces acting on the component nucleons (protons and neutrons) that make up the nucleus. Nuclei are bound by an attractive strong nuclear force between nucleons, which overcomes the intense electrostatic repulsion between protons. However, the strong nuclear force acts only over extremely short ranges (it follows a yukawa potential), so that large nuclei are less tightly bound than small nuclei, and breaking a large nucleus into two or more intermediate-sized nuclei releases energy.

File:Neutron proton ratio.gif
Neutron and proton counts for all stable atomic nuclei. The slight upward bend to the curve ensures that fission products are too heavy to be stable, giving rise to the nuclear waste problem

Because of the short range of the strong binding force, large nuclei contain proportionally more neutrons than do light elements, which are most stable with a 1-1 ratio of protons and neutrons. Fission products have, on average, the same ratio of neutrons and protons as their parent nucleus, and are therefore usually very unstable because they have too many neutrons compared to stable isotopes of similar mass. This is the fundamental cause of the problem of radioactive high level waste from nuclear reactors. Fission products tend to be beta emitters, emitting fast-moving electrons to conserve electric charge as neutrons convert to protons inside the nucleus.

The most common nuclear fuels, 235U and 239Pu, are not major radiologic hazards by themselves: 235U has a half-life measured in billions of years, and although 239Pu has a half-life of only about 25,000 years it is a pure alpha particle emitter and hence not particularly dangerous unless ingested. Once a fuel element has been used, the remaining fuel material is intimately mixed with highly radioactive fission products that emit energetic beta particles and gamma rays. Some fission products have half-lives as short as seconds; others have half-lives of tens of thousands of years, requiring long-term storage in facilities such as Yucca mountain until the fission products decay into non-radioactive stable isotopes.

# Physics of fission reactors

Nuclear reactors use a chain reaction to induce a controlled rate of fission in nuclear fuel. A reactor consists of an assembly of nuclear fuel (a reactor core), usually surrounded by a neutron moderator such as water, graphite, or zirconium hydride, and fitted with mechanisms such as control rods that control the rate of the reaction.

Reactors are built for three primary purposes, which typicallly involve different engineering trade-offs:

• research reactors are intended to produce neutrons and/or activate radioactive sources for scientific, medical, engineering, or other research purposes.
• breeder reactors are intended to produce 239Pu (a nuclear fuel) from the naturally very abundant 238U (not a nuclear fuel).

While, in principle, all reactors can act in all three capacities, in practice the tasks lead to conflicting engineering goals and most reactors have been built with only one of the above tasks in mind. (There are several early counter-examples, such as the Hanford N reactor, now decommissioned). Power reactors generally convert the kinetic energy of fission products into heat, which is used to heat a working fluid and drive a heat engine that generates mechanical or or electrical power. The working fluid is usually water with a steam turbine, but some designs use other materials such as gaseous helium. Research reactors produce neutrons that are used in various ways, with the heat of fission being treated as an unavoidable waste product. Breeder reactors are a specialized form of research reactor, with the caveat that the sample being irradiated is usually the fuel itself, a mixture of 238U and 235U.

All nuclear fuels undergo a small amount of spontaneous fission, which releases a few free neutrons into any sample of fuel. The neutrons typically escape rapidly from the fuel and either decay into protons (with a half-life of about 15 minutes) or impact and are absorbed by other nuclei in the vicinity. However, nuclear fuels can also undergo induced fission when impacted by a free neutron. If enough fuel is assembled into one place, and/or if the escaping neutrons are sufficiently contained, then these induced fissions can replace or more than replace the neutrons lost to escape or absorption, and the spontaneous fission has become a full chain reaction. Such an assembly is called a critical assembly, or (colloquially) a critical mass; the word critical refers to a cusp in the behavior of the differential equation that governs the neutron flux in the reactor. The actual mass of a critical mass of nuclear fuel depends strongly on the geometry and surrounding materials.

## Criticality

In a nuclear reactor, most fission events are caused by neutrons impacting nuclear fuel. Hence, the power output (and neutron production) of a nuclear reactor at present depends on the number of neutrons that are already in the core from previous fissions, and on the expected value of how many fissions will occur as a result of each neutron before the neutron is absorbed or lost.

If the rate of production of new neutrons from fission in an assembly of nuclear fuel (a "core") is less than the rate of loss from absorption or escape, then the core is subcritical and will not support a self-sustaining chain reaction. If the rate of production exceeds the rate of loss, then the core is supercritical and the amount of neutrons produced will grow exponentially. The rate of growth depends on the ratio of neutron production to loss, and on the average lifetime of a neutron in the reactor core.

If we write 'N' for the number of free neutrons in a reactor core and '$\displaystyle \tau$ ' for the average lifetime of each neutron (before it either escapes from the core or is absorbed by a nucleus), then the reactor will follow this differential equation (the evolution equation)

$\displaystyle dN/dt = \alpha N/\tau$

where $\displaystyle \alpha$ is a constant of proportionality, and $\displaystyle dN/dt$ is the rate of change of the neutron count in the core. This type of differential equation describes exponential growth or exponential decay, depending on the sign of the constant $\displaystyle \alpha$ , which is just the expected number of neutrons after one average neutron lifetime has elapsed:

$\displaystyle \alpha = P_{impact}P_{fission} n_{avg} - P_{absorb} - P_{escape}$

Here, $\displaystyle P_{impact}$ is the probability that a particular neutron will strike a fuel nucleus, $\displaystyle P_{fission}$ is the probability that the neutron, having struck the fuel, will cause that nucleus to undergo fission, $\displaystyle P_{absorb}$ is the probability that it will be absorbed by something other than fuel, and $\displaystyle P_{escape}$ is the probability that it will "escape" by leaving the core altogether. $\displaystyle n_{avg}$ is the number of neutrons produced, on average, by a fission event -- it is between 2 and 3 for both 235U and 239Pu.

If $\displaystyle \alpha$ is positive, then the core is supercritical and the rate of neutron production will grow exponentially until some other effect stops the growth. If $\displaystyle \alpha$ is negative, then the core is "subcritical" and the number of free neutrons in the core will shrink exponentially until it reaches an equilibrium at zero (or the background level from spontaneous fission). If $\displaystyle \alpha$ is exactly zero, then the reactor is critical and its output does not vary in time ($\displaystyle dN/dt = 0$ , from above).

Nuclear reactors are engineered to reduce $\displaystyle P_{escape}$ and $\displaystyle P_{absorb}$ . Small, compact structures reduce the probability of direct escape by minimizing the surface area of the core, and some materials (such as graphite) can reflect some neutrons back into the core, further reducing $\displaystyle P_{escape}$ . Light metals such as aluminum that are not strong neutron absorbers are used to build the structure of reactor cores.

The probability of fission, $\displaystyle P_{fission}$ , depends on the nuclear physics of the fuel, and is often expressed as a cross section. Reactors are usually controlled by adjusting $\displaystyle P_{absorb}$ . control rods made of a strongly neutron-absorbent material such as cadmium or boron can be inserted into the core: any neutron that happens to impact the control rod is lost from the chain reaction, reducing $\displaystyle \alpha$ . $\displaystyle P_{absorb}$ is also controlled by the recent history of the reactor core itself (see below).

The mere fact that an assembly is supercritical does not guarantee that it contains any free neutrons at all. At least one neutron is required to "strike" a chain reaction, and if the spontaneous fission rate is sufficiently low it may take a long time (in 235U reactors, as long as many minutes) before a chance neutron encounter starts a chain reaction even if the reactor is supercritical. Most nuclear reactors include a "starter" neutron source that ensures there are always a few free neutrons in the reactor core, so that a chain reaction will begin immediately when the core is made critical.

## Subcritical multiplication

Even in a subcritical assembly such as a shut-down reactor core, any stray neutron that happens to be present in the core (for example from spontaneous fission of the fuel, from radioactive decay of fission products, or from a neutron source) will trigger an exponentially decaying chain reaction. Although the chain reaction is not self-sustaining, it acts as a multiplier that increases the equilibrium number of neutrons in the core. This subcritical multiplication effect can be used in two ways: as a probe of how close a core is to criticality, and as a way to generate fission power without the risks associated with a critical mass.

As a measurement technique, subcritical multiplication was used during the Manhattan Project in early experiments to determine the minimum critical masses of 235U and of 239Pu. It is still used today to calibrate the controls for nuclear reactors during startup, as many effects (discussed in the following sections) can change the required control settings to achieve criticality in a reactor. As a power-generating technique, subcritical multiplication allows generation of nuclear power for fission where a critical assembly is undesirable for safety or other reasons. A subcritical assembly together with a neutron source can serve as a steady source of heat to generate power from fission.

Including the effect of an external neutron source ("external" to the fission process, not physically external to the core), one can write a modified evolution equation:

$\displaystyle dN/dt = \alpha N/\tau + R_{ext}$

where $\displaystyle R_{ext}$ is the rate at which the external source injects neutrons into the core. In equilibrium, the core is not changing and dN/dt is zero, so the equilibrium number of neutrons is given by:

$\displaystyle N = \tau R_{ext} / (-\alpha)$

If the core is subcritical, then $\displaystyle \alpha$ is negative so there is an equilibrium with a positive number of neutrons. If the core is close to criticality, then $\displaystyle \alpha$ is very small and thus the final number of neutrons can be made arbitrarily large.

## Neutron moderators

To improve $\displaystyle P_{fission}$ and enable a chain reaction, uranium-fueled reactors must include a neutron moderator that interacts with newly produced fast neutrons from fission events to reduce their kinetic energy from several MeV to several eV, making them more likely to induce fission. This is because 235U is much more likely to undergo fission when struck by one of these thermal neutrons than by a freshly-produced neutron from fission.

Neutron moderators are materials that interact weakly with the neutrons but absorb kinetic energy from them. Most moderators rely on either weakly bound hydrogen or a loose crystal structure of another light element such as carbon to transfer kinetic energy from the fast-moving neutrons.

Hydrogen moderators include water (H2O), heavy water(D2O), and zirconium hydride (ZnH2), all of which work because a hydrogen nucleus has nearly the same mass as a free neutron: neutron-H2O or neutron-ZnH2 impacts excite rotational modes of the molecules (spinning them around). Deuterium nuclei (in heavy water) absorb kinetic energy less well than do light hydrogen nuclei, but they are much less likely to absorb the impacting neutron. Water or heavy water have the advantage of being transparent liquids, so that, in addition to shielding and moderating a reactor core, they permit direct viewing of the core in operation and can also serve as a working fluid for heat transfer.

Crystal structure moderators rely on a floppy crystal matrix to absorb phonons from neutron-crystal impacts. Graphite is the most common example of such a moderator. It was used in Chicago Pile-1, the world's first man-made critical assembly, and was commonplace in early reactor designs including the Soviet RBMK nuclear power plants, of which the Chernobyl plant was one.

### Moderators and reactor design

The amount and nature of neutron moderation affects reactor controllability and hence safety. Because moderators both slow and absorb neutrons, there is an optimum amount of moderator to include in a given geometry of reactor core. Less moderation reduces the effectiveness by reducing the $\displaystyle P_{fission}$ term in the evolution equation, and more moderation reduces the effectiveness by increasing the $\displaystyle P_{escape}$ term.

Most moderators become less effective with increasing temperature, so under-moderated reactors are stable against changes in temperature in the reactor core: if the core overheats, then the quality of the moderator is reduced and the reaction tends to slow down (there is a "negative temperature coefficient" in the reactivity of the core). Water is an extreme case: in extreme heat, it can boil, producing effective voids in the reactor core without destroying the physical structure of the core; this tends to shut down the reaction and reduce the possibility of a fuel meltdown. Over-moderated reactors are unstable against changes in temperature (there is a "positive temperature coefficient" in the reactivity of the core), and so are less inherently safe than under-moderated cores.

Most reactors in use today use a combination of moderator materials. For example, TRIGA type research reactors use ZnH2 moderator mixed with the 235U fuel, an H2O-filled core, and C (graphite) moderator and reflector blocks around the periphery of the core.

## Delayed neutrons and controllability

Fission reactions and subsequent neutron escape happen very quickly; this is important for nuclear weapons, where the object is to make a nuclear core release as much energy as possible before it physically explodes. Most neutrons emitted by fission events are prompt: they are emitted essentially instantaneously. Once emitted, the average neutron lifetime ($\displaystyle \tau$ ) in a typical core is on the order of a millisecond, so if the exponential factor $\displaystyle \alpha$ is as small as 0.01, then in one second the reactor power will vary by a factor of (1+0.01)1000, or more than ten thousand. Nuclear weapons are engineered to maximize the power growth rate, with lifetimes well under a millisecond and exponential factors close to 2; but such rapid variation would render it practically impossible to control the reaction rates in a nuclear reactor.

Fortunately, the effective neutron lifetime is much longer than the average lifetime of a single neutron in the core. About 0.65% of the neutrons produced by 235U fission, and about 0.75% of the neutrons produced by 239Pu fission, are not produced immediately, but rather are emitted by radioactive decay of fission products, with an average lifetime of about 15 seconds. These delayed neutrons increase the effective average lifetime of neutrons in the core, to nearly 0.1 seconds, so that a core with $\displaystyle \alpha$ of 0.01 would increase in one second by only a factor of (1+0.01)10, or about 1.1 -- a 10% increase. This is a controllable rate of change.

Most nuclear reactors are hence operated in a prompt subcritical, delayed critical condition: the prompt neutrons alone are not sufficient to sustain a chain reaction, but the delayed neutrons make up the small difference required to keep the reaction going. This has effects on how reactors are controlled: when a small amount of control rod is slid into or out of the reactor core, the power level changes at first very rapidly due to prompt subcritical multiplication and then more gradually, following the exponential growth or decay curve of the delayed critical reaction. Further, increases in reactor power can be performed at any desired rate simply by pulling out a sufficient length of control rod -- but decreases are limited in speed, because even if the reactor is taken deeply subcritical, the delayed neutrons are produced by ordinary radioactive decay of fission products and that decay cannot be hastened.

## Reactor poisons

Any element that strongly absorbs neutrons is called a reactor poison, because it tends to shut down (poison) an ongoing fission chain reaction. Some reactor poisons are deliberately inserted into fission reactor cores to control the reaction; boron or cadmium control rods are the best example. Many reactor poisons are produced by the fission process itself, and buildup of neutron-absorbing fission products affects both the fuel economics and the controllability of nuclear reactors.

### Long-lived poisons and fuel reprocessing

In practice, buildup of reactor poisons in nuclear fuel is what determines the lifetime of nuclear fuel in a reactor: long before all possible fissions have taken place, buildup of long-lived neutron absorbing fission products damps out the chain reaction. This is the reason that nuclear reprocessing is a useful activity: spent nuclear fuel contains about 99% of the original fissionable material present in newly manufactured nuclear fuel. Chemical separation of the fission products restores the nuclear fuel so that it can be used again.

Nuclear reprocessing is useful economically because chemical separation is much simpler to accomplish than the difficult isotope separation required to prepare nuclear fuel from natural uranium ore, so that in principle chemical separation yields more generated energy for less effort than mining, purifying, and isotopically separating new uranium ore. In practice, both the difficulty of handling the highly radioactive fission products and other political concerns make fuel reprocessing a contentious subject. One such concern is the fact that spent uranium nuclear fuel contains significant quantities of 239Pu, a prime ingredient in nuclear weapons (see breeder reactor).

### Short-lived poisons and controllability

Short-lived reactor poisons in fission products strongly affect how nuclear reactors can operate. Unstable fission product nuclei transmute into many different elements (secondary fission products) as they undergo a decay chain to a stable isotope. The most important such element is Xenon, because the isotope 135Xe, a secondary fission product with a half-life of about 9 hours, is an extremely strong neutron absorber. In an operating reactor, each nucleus of 135Xe is destroyed by neutron capture almost as soon as it is created, so that there is no buildup in the core. However, when a reactor shuts down, the level of 135Xe builds up in the core for about 9 hours before beginning to decay. The result is that, about 6-8 hours after a reactor is shut down, it can become physically impossible to restart the chain reaction until the 135Xe has had a chance to decay over the next several hours; this is one reason why nuclear power reactors are best operated at an even power level around the clock.

135Xe buildup in a reactor core makes it extremely dangerous to operate the reactor a few hours after it has been shut down. Because the 135Xe absorbs neutrons strongly, starting a reactor in a high-Xe condition requires pulling the control rods out of the core much farther than normal. But if the reactor does achieve criticality, then the neutron flux in the core will become quite high and the 135Xe will be destroyed rapidly -- this has the same effect as very rapidly removing a great length of control rod from the core, and can cause the reaction to grow too rapidly or even become prompt critical.

135Xe played a large part in the Chernobyl accident: about eight hours after a scheduled maintenance shutdown, workers tried to bring the the reactor to a zero power critical condition to test a control circuit, but because the core was loaded with 135Xe from the previous day's power generation, the reaction rapidly grew uncontrollably, leading to steam explosion in the core, fire, and violent destruction of the facility.

# History

The results of the bombardment of uranium by neutrons had proved interesting and puzzling. First studied by Enrico Fermi and his colleagues in 1934, they were not properly interpreted until several years later.

On January 16 1939, Niels Bohr of Copenhagen, Denmark, arrived in the United States to spend several months in Princeton, N. J., and was particularly anxious to discuss some abstract problems with Albert Einstein. (Four years later Bohr was to escape to Sweden from Nazi-occupied Denmark in a small boat, along with thousands of other Danish Jews, in large scale operation.) Just before Bohr left Denmark, two of his colleagues, Otto Robert Frisch and Lise Meitner (both refugees from Germany), had told him their guess that the absorption of a neutron by a uranium nucleus sometimes caused that nucleus to split into approximately equal parts with the release of enormous quantities of energy, a process that they dubbed nuclear "fission."

The occasion for this hypothesis was the important discovery of Otto Hahn and Fritz Strassmann in Germany (published in Naturwissenschaften in early January 1939) which proved that an isotope of barium was produced by neutron bombardment of uranium. Bohr had promised to keep the Meitner/Frisch interpretation secret until their paper was published to preserve priority, but on the boat he discussed it with Léon Rosenfeld, but forgot to tell him to keep it secret. Rosenfeld immediately upon arrival told everyone at Princeton University, and from them the news spread by word of mouth to neighboring physicists including Enrico Fermi at Columbia University. As a result of conversations among Fermi, John R. Dunning, and G. B. Pegram, a search was undertaken at Columbia for the heavy pulses of ionization that would be expected from the flying fragments of the uranium nucleus. On January 26, 1939, there was a conference on theoretical physics at Washington, D. C., sponsored jointly by the George Washington University and the Carnegie Institution of Washington.

Fermi left New York to attend this meeting before the Columbia fission experiments had been tried. At the meeting Bohr and Fermi discussed the problem of fission, and in particular Fermi mentioned the possibility that neutrons might be emitted during the process. Although this was only a guess, its implication of the possibility of a chain reaction was obvious. A number of sensational articles were published in the press on this subject. Before the meeting in Washington was over, several other experiments to confirm fission had been initiated, and positive experimental confirmation was reported from four laboratories (Columbia University, Carnegie Institution of Washington, Johns Hopkins University, University of California) in the February 15 1939, issue of the Physical Review. By this time Bohr had heard that similar experiments had been made in his laboratory in Copenhagen about January 15. (Letter by Frisch to Nature dated January 16 1939, and appearing in the February 18 issue.) Frédéric Joliot in Paris had also published his first results in the Comptes Rendus of January 30 1939. From this time on there was a steady flow of papers on the subject of fission, so that by the time (December 6 1939) L. A. Turner of Princeton wrote a review article on the subject in the Reviews of Modern Physics nearly one hundred papers had appeared. Complete analysis and discussion of these papers have appeared in Turner's article and elsewhere.

## Inducing fission

• Though fission is most often and most easily initiated by the absorption of a free neutron, it can also be induced by striking a fissionable nucleus with other particles. These other particles can include protons, other nuclei, or even high intensity high-energy photons (gamma rays).
• Very infrequently, a fissionable nucleus will undergo spontaneous nuclear fission without an incoming neutron.
• Inducing fission is easiest in heavy elements and generally, the more massive the nucleus the more likely it is able to be fissioned. Fission in any element heavier than iron produces energy, and fission in any element lighter than iron requires energy. The opposite is true of nuclear fusion reactions - fusion in elements lighter than iron produces energy, and fusion in elements heavier than iron requires energy. (see: the curve of binding energy)
• The most frequently used elements to produce nuclear fission are uranium and plutonium. Uranium is the heaviest naturally occurring element in any appreciable abundance; plutonium undergoes spontaneous fission reactions and has a relatively short half-life. So, although other elements can be used, these have the best combination of abundance and ease of fission. For further detail, see fissile.

## Effects of isotopes

Natural uranium contains three isotopes: U-234 (0.006%), U-235 (0.7%), and U-238 (99.3%). The speed required for a fission event vs. a non-fission capture event is different for different isotopes.

U-238 will fission with neutrons at energies >1 MeV such as those produced in a nuclear fusion explosion, but uranium fission does not produce such extremely energetic neutrons. U-238 merely captures less energetic neutrons without fissioning, so it cannot support a chain reaction as can U-235; U-238 has no critical mass. However, when U-238 absorbs slow neutrons, the resulting U-239 is not stable. It decays first to Np-239, which in turn decays to Pu-239, which will fission with slow neutrons just as U-235 does. Therefore, some of the output of a reactor fueled only with uranium comes from plutonium fission.

U-235 fissions over a much wider range of neutron energies than U-238. U-235 has the greatest cross section (i.e., is most likely to fission) when hit with very low speed ("thermal") neutrons much less energetic than those produced when U-235 fissions. A moderator, usually water or graphite, is often used to slow down fission-generated neutrons so they can fission more U-235. Since U-238 just gets in the way of the chain reaction, most reactors use uranium enriched in U-235. If the U-235 fraction is high enough, a chain reaction can be sustained even without a moderator.

U-235 is present in natural uranium only to the extent of about one part in 140. Also, the relatively small difference in mass between the two isotopes makes isotope separation difficult. Nevertheless, the possibility of separating U-235 was recognized early on in the Manhattan Project as being of the greatest importance to their success.

## Reduction of non-fission capture by isotope separation

An additional complication is that natural uranium contains three isotopes: U-234, U-235, and U-238, present to the extent of approximately 0.006, 0.7, and 99.3 per cent, respectively. We have already seen that the probabilities of processes (2) and (4) are different for different isotopes. We have also seen that the probabilities are different for neutrons of different energies.

For neutrons of certain intermediate speeds (corresponding to energies of a few electron volts) U-238 has a large capture cross section for the production of U-239 but not for fission. There is also a considerable probability of inelastic (i.e., non-capture-producing) collisions between high speed neutrons and U-238 nuclei. Thus the presence of the U-238 tends both to reduce the speed of the fast neutrons and to effect the capture of those of moderate speed. Although there may be some non-fission capture by U-235, it is evident that if we can separate the U-235 from the U-238 and discard the U-238, we can reduce non-fission capture and can thus promote the chain reaction. In fact, the probability of fission of U-235 by high speed neutrons may be great enough to make the use of a moderator unnecessary once the U-238 has been removed. Unfortunately, U-235 is present in natural uranium only to the extent of about one part in 140. Also, the relatively small difference in mass between the two isotopes makes separation difficult. Nevertheless, the possibility of separating U-235 was recognized early on in the Manhattan Project as being of the greatest importance.

## Production and purification of materials

It has been stated above that the cross section for capture of neutrons varies greatly among different materials. In some it is very high compared to the maximum fission cross section of uranium. If, then, we are to hope to achieve a chain reaction, we must reduce effect (3) - non-fission capture by impurities -to the point where it is not serious. This means very careful purification of the uranium metal and very careful purification of the moderator. Calculations show that the maximum permissible concentrations of many impurity elements are a few parts per million- in either the uranium or the moderator. When it is mentioned that up to 1940 the total amount of uranium metal produced in the USA was not more than a few grams and even this was of doubtful purity, that the total amount of metallic beryllium produced in the USA was not more than a few kilograms, that the total amount of concentrated deuterium produced was not more than a few kilograms, and that carbon had never been produced in quantity with anything like the purity required of a moderator, it is clear that the problem of producing and purifying materials was a major one.

The problem of producing large amounts of high purity uranium was solved by Frank Spedding using the thermite process. Ames Laboratory was established in 1942 to produce the large amounts of uranium that would be necessary for the research to come.

## Control - weapons or power?

The problems that have been discussed so far have to do merely with the realization of the chain reaction. If such a reaction is going to be of use, we must be able to control it. The problem of control is different depending on whether we are interested in steady production of power or in an explosion. In general, the steady production of atomic power requires a slow-neutron-induced fission chain reaction occurring in a mixture or lattice of uranium and moderator, while an atomic bomb requires a fast-neutron-induced fission chain reaction in U-235 or Pu-239, although both slow- and fast-neutron fission may contribute in each case. It seemed likely even in 1940, that by using neutron absorbers a power chain reaction could be controlled. It was also considered likely, though not certain, that such a chain reaction would be self-limiting by virtue of the lower probability of fission-producing capture when a higher temperature was reached. Nevertheless, there was a possibility that a chain-reacting system might get out of control, and it therefore seemed necessary to perform the chain-reaction experiment in an uninhabited location.

Up to this point we have been discussing how to produce and control a nuclear chain reaction but not how to make use of it. The technological gap between producing a controlled chain reaction and using it as a large-scale power source or an explosive is comparable to the gap between the discovery of fire and the manufacture of a steam locomotive.

Although production of power has never been the principal object of this project, enough attention has been given to the matter to reveal the major difficulty: the attainment of high-temperature operation. An effective heat engine must not only develop heat but must develop heat at a high temperature. To run a chain-reacting system at a high temperature and to convert the heat generated to useful work is very much more difficult than to run a chain-reacting system at a low temperature.

Of course, the proof that a chain reaction is possible does not itself ensure that nuclear energy can be effective in a bomb. To have an effective explosion it is necessary that the chain reaction build up extremely rapidly; otherwise only a small amount of the nuclear energy will be utilized before the bomb flies apart and the reaction stops. It is also necessary that no premature explosion occur. This entire "detonation" problem was and still remains one of the most difficult problems in designing a high-efficiency atomic bomb.

Three ways of increasing the likelihood of a chain reaction have been mentioned: use of a moderator; attainment of high purity of materials; and use of special material, either U-235 or Pu-239. The three procedures are not mutually exclusive, and many schemes have been proposed for using small amounts of separated U-235 or Pu-239 in a lattice composed primarily of ordinary uranium or uranium oxide and of a moderator or two different moderators. Such proposed arrangements are usually called "enriched piles".