13.1 Nuclear Reactions
13.2 Reaction Kinematics
13.3 Reaction Mechanisms
13.4 Fission
13.5 Fission Reactors
13.6 Fusion
13.7 Special Applications
CHAPTER 13
Nuclear Interactions and Applications Nuclear Interactions and Applications
Ernest Lawrence, upon hearing the first self-sustaining chain reaction would be developed at the University of Chicago in 1942 rather than at his University of California, Berkeley lab said, “You’ll never get the chain reaction going here. The whole tempo of the University of Chicago is too slow.”
- Quoted by Arthur Compton in Atomic Quest
13.1: Nuclear Reactions
First nuclear reaction was a nitrogen target bombarded with alpha particles, which emitted protons. The reaction is written as:
The first particle is the projectile and the second is the nitrogen target. These two nuclei react to form proton projectiles and the residual oxygen target.
The reaction can be rewritten in shorthand as:
14N(α, p)
17O.
In general a reaction x + X → y + Y can be rewritten as
X(x, y)Y
3 Important Technological Advances
The high-voltage multiplier circuit was developed in 1932 by J.D. Cockcroft and E.T.S. Walton. This compact circuit
produces high-voltage, low-current pulses.
High voltage is required to accelerate charged particles.
The Van de Graaff electrostatic accelerator was developed in 1931. It produces a high voltage from the friction between two
different materials.
3) The first cyclotron (at
left) was built in 1932. It
accelerated charged
particles using large
circular magnets.
Types of Reactions
Nuclear photodisintegration is the initiation of a nuclear reaction by a photon.
Neutron or proton radioactive capture occurs when the nucleon is absorbed by the target nucleus, with energy and momentum conserved by gamma ray emission.
The projectile and the target are said to be in the entrance channel of a nuclear reaction. The reaction products are in the exit channel.
In elastic scattering, the entrance and exit channels are identical and the particles in the exit channels are not in excited states.
In inelastic scattering, the entrance and exit channels are also identical but one or more of the reaction products is left in an excited state.
The reaction product need not always be in the exit channel.
Cross Sections
The probability of a particular nuclear reaction occurring is determined by measuring the cross section σ. It is determined by measuring the number of particles produced in a given nuclear reaction.
The number of target nuclei is
The probability of the particle being scattered is
The cross section is the number of detected particles as a function of the incoming particles. At different scattering angles, they are differential cross sections.
Integrating over the whole range of scattering angles yields the total cross sections:
13.2: Reaction Kinematics
Consider the reaction: x + X → y + Y. For a target X at rest, conservation of energy is
Rearranging this by separating mass from energy yields a quantity similar to the disintegration energy:
The difference between the final and initial kinetic energies is the difference between the initial and final mass energies. This is called the Q value.
The energy released when Q > 0 is from an exoergic (or exothermic) reaction. When Q < 0, kinetic energy is converted to mass energy in an endoergic (or endothermic) reaction.
Collisions in this reaction are inelastic.
Elastic collisions have Q = 0.
Threshold energy for an endoergic reaction:
13.3: Reaction Mechanisms
The Compound Nucleus
For low energies of E < 10 MeV, the Coulomb force dominates the reaction. This is described by the compound nucleus.
The compound nucleus is a composite of the projectile and target nuclei, usually in a high state of excitation.
The kinetic energy available in the center of mass frame
can excite the compound nucleus to even higher excitation energies than that from just the masses.
Once formed, the compound nucleus may exist for a relatively long time
compared to the time taken by the bombarding particle to cross the nucleus. This latter time is sometimes referred to as the nuclear time scale tN.
When the compound nucleus finally does decay from its highly excited state, it decays into all the possible exit channels according to statistical rules consistent with the conservation laws.
Resonances
Nuclear physicists study nuclear excited states by varying the projectile bombarding energy Kx and measuring the cross section at each energy, generally at fixed angles for the outgoing particles. This is called an excitation function.
Sharp peaks in the excitation function of the reacting particles are called resonances, and they represent a quantum state of the
compound nucleus being formed.
The uncertainty principle may be used to
Resonances
Because neutrons have zero net
charge, they interact more easily with nuclei at low energies than do
charged particles, because of the Coulomb barrier. This process is called neutron activation and the
reaction is called neutron radioactive transfer.
The average neutron capture cross section (at energies up to about 100 keV) varies empirically as 1/v, where v is the neutron’s velocity. The 1/v dependence can be explained in
terms of the time the neutron spends
near the nucleus.
For large bombarding energies, the bombarding particle spends less time within the range of the nuclear force. Stripping one or more nucleons off the projectile or picking up one or more
nucleons from the target becomes more probable.
The projectile could also knock out energetic nucleons from the target nucleus.
These are called direct reactions.
The chief advantage of direct reactions is that the final residual nucleus may be left in any one of many low-lying excited states.
By using different direct reactions, the nuclear excited states can be studied in a variety of ways to learn more about nuclear
structure.
Direct Reactions
13.4: Fission
In fission a nucleus separates into two fission fragments. As we will show, one fragment is typically somewhat larger than the other.
Fission occurs for heavy nuclei because of the increased Coulomb forces between the protons.
We can understand fission by using the semi-empirical mass formula based on the liquid drop model. For a spherical nucleus of with mass number A ~ 240, the attractive short-range nuclear forces offset the
Coulomb repulsive term. As a nucleus
becomes nonspherical, the surface energy is increased, and the effect of the short-range nuclear interactions is reduced.
Nucleons on the surface are not surrounded by other nucleons, and the unsaturated
nuclear force reduces the overall nuclear
attraction. For a certain deformation, a critical energy is reached, and the fission barrier is overcome.
Spontaneous fission can
occur for nuclei with
Induced Fission
Fission may also be induced by a nuclear reaction. A neutron absorbed by a heavy nucleus forms a highly excited compound nucleus that may
quickly fission.
An induced fission example is
The fission products have a ratio of N/Z much too high to be stable for their A value.
There are many possibilities for the Z and A of the fission products.
Symmetric fission (products with equal Z) is possible, but the most
probable fission is asymmetric (one mass larger than the other).
Thermal Neutron Fission
Fission fragments are highly unstable because they are so neutron rich.
Prompt neutrons are emitted simultaneously with the fissioning process. Even after prompt neutrons are released, the fission fragments undergo beta decay, releasing more energy.
Most of the ~200 MeV released in fission goes to the kinetic energy of the fission products, but the neutrons, beta particles, neutrinos, and
gamma rays typically carry away 30–40 MeV of
the kinetic energy.
Because several neutrons are produced in fission, these neutrons may subsequently
produce other fissions. This is the basis of the
self-sustaining chain reaction.
If slightly more than one neutron, on the
average, results in another fission, the chain reaction becomes critical.
A sufficient amount of mass is required for a neutron to be absorbed, called the critical mass.
If less than one neutron, on the average, produces another fission, the reaction is
subcritical.
If more than one neutron, on the average, produces another fission, the reaction is
supercritical.Chain Reactions
Chain Reactions
A critical-mass fission reaction can be controlled by absorbing neutrons. A self-sustaining controlled fission process requires that not all the neutrons are prompt. Some of the neutrons are delayed by several seconds and are emitted by daughter
nuclides. These delayed neutrons allow the control of the nuclear reactor.
Control rods regulate the absorption of neutrons to sustain a
controlled reaction.
13.5: Fission Reactors
Several components are important for a controlled nuclear reactor:
1) Fissionable fuel
2) Moderator to slow down neutrons
3) Control rods for safety and to control criticality of reactor
4) Reflector to surround moderator and fuel in order to contain neutrons and thereby improve efficiency
5) Reactor vessel and radiation shield
6) Energy transfer systems if commercial power is desired
Two main effects can “poison”
reactors: (1) neutrons may be
absorbed without producing fission [for example, by neutron radiative
Core Components
Fission neutrons typically have 1–2 MeV of kinetic energy, and because the fission cross section increases as 1/v at low energies, slowing down the neutrons helps to increase the chance of producing another fission.
A moderator is used to elastically scatter the high-energy neutrons and thus reduce their energies. A neutron loses the most energy in a single collision with a light stationary particle. Hydrogen (in water), carbon (graphite), and beryllium are all good moderators.
The simplest method to reduce the loss of neutrons escaping from the
fissionable fuel is to make the fuel zone larger. The fuel elements are
normally placed in regular arrays within the moderator.
Core Components
The delayed neutrons produced in fission allow the mechanical movement of the rods to control the fission reaction. A “fail-safe”
system automatically drops the control rods into the reactor in an emergency shutdown.
If the fuel and moderator are surrounded by a material with a very low neutron capture cross section, there is a reasonable chance that after one or even many scatterings, the neutron will be backscattered or
“reflected” back into the fuel area. Water is often used both as moderator and reflector.
The most common method is to pass hot water heated by the reactor through some form of heat exchanger.
In boiling water reactors (BWRs) the
moderating water turns into steam, which drives a turbine producing electricity.
In pressurized water reactors (PWRs) the moderating water is under high pressure and circulates from the reactor to an external
heat exchanger where it produces steam, which drives a turbine.
Boiling water reactors are inherently simpler than pressurized water reactors. However, the possibility that the steam driving the turbine may become radioactive is greater with the BWR. The two-step process of the PWR helps to isolate the power generation system from possible radioactive
contamination.
Energy Transfer
Power reactors produce commercial electricity.
Research reactors are operated to produce high neutron fluxes for neutron-scattering experiments.
Heat production reactors supply heat in some cold countries.
Some reactors are designed to produce radioisotopes.
Several training reactors are located on college campuses.
Types of Reactors
Nuclear Reactor Problems
The danger of a serious accident in which radioactive elements are released into the atmosphere or groundwater is of great concern to the general public.
Thermal pollution both in the atmosphere and in lakes and rivers used for cooling may be a significant ecological problem.
A more serious problem is the safe disposal of the radioactive wastes produced in the fissioning process, because some fission fragments have a half-life of thousands of years.
Two widely publicized accidents at nuclear reactor facilities—one at Three Mile Island in Pennsylvania in 1979, the other at Chernobyl in Ukraine in 1986—have significantly dampened the general public’s support for nuclear reactors.
Large expansion of nuclear power can succeed only if four critical
problems are overcome: lower costs, improved safety, better nuclear
waste management, and lower proliferation risk.
Breeder Reactors
A more advanced kind of reactor is the breeder reactor, which produces more fissionable fuel than it consumes.
The chain reaction is:
The plutonium is easily separated from uranium by chemical means.
Fast breeder reactors have been built that convert
238U to
239Pu. The reactors are designed to use fast neutrons.
Breeder reactors hold the promise of providing an almost unlimited supply of fissionable material.
One of the downsides of such reactors is that plutonium is highly
13.6: Fusion
If two light nuclei fuse together, they also form a nucleus with a larger binding energy per nucleon and energy is released. This reaction is called nuclear fusion.
The most energy is released if two isotopes of hydrogen
fuse together in the reaction.
Formation of Elements
The proton-proton chain includes a series of reactions that eventually converts four protons into an alpha particle.
As stars form due to gravitational attraction of interstellar
matter, the heat produced by the attraction is enough to cause protons to overcome their Coulomb repulsion and fuse by the following reaction:
The deuterons are then able to combine with
1H to produce
3
He:
The He atoms can then combine to produce He:
As the reaction proceeds, however, the temperature increases, and eventually
12C nuclei are formed by a process that converts three
4He into
12C.
Another cycle due to carbon is also able to produce
4He. The series of reactions responsible for the carbon or CNO cycle are
Proton-proton and CNO cycles are the only nuclear reactions that can supply the energy in stars.
Formation of Elements
Hydrostatic Equilibrium
A hydrostatic equilibrium exists in the sun between the gravitational attraction tending to contract a star and a gas pressure pushing out due to all the particles.
As the lighter nuclides are “burned up” to produce the heavier nuclides, the gravitational attraction succeeds in contracting the
star’s mass into a smaller volume and the temperature increases. A higher temperature allows the nuclides with higher Z to fuse.
This process continues in a star until a large part of the star’s mass is converted to iron. The star then collapses under its own
gravitational attraction to become, depending on its mass, a white dwarf star, neutron star, or black hole. It may even undergo a
supernova explosion.
Nuclear Fusion on Earth
Among the several possible fusion reactions, three of the simplest involve the three isotopes of hydrogen.
Three main conditions are necessary for controlled nuclear fusion:
1)
The temperature must be hot enough to allow the ions, for example, deuterium and tritium, to overcome the Coulomb barrier and fuse their nuclei together. This requires a temperature of 100–200 million K.
2)
The ions have to be confined together in close proximity to allow the ions to fuse. A suitable ion density is 2–3 × 10
20ions/m
3.
3)
The ions must be held together in close proximity at high temperature
long enough to avoid plasma cooling. A suitable time is 1–2 s.
Fusion Product
The product of the plasma density n and the containment time τ must have a minimum value at a sufficiently high temperature in order to initiate fusion and produce as much energy as it consumes. The minimum value is
This relation is called the Lawson criterion after the British physicist J. D. Lawson who first derived it in 1957. A triple product of nτT
called the fusion product is sometimes used (where T is the ion temperature).
The factor Q is used to represent the ratio of the power produced in the fusion reaction to the power required to produce the fusion
(heat). This Q factor is not to be confused with the Q value.
The breakeven point is Q = 1, and ignition occurs for Q >> 1. For
controlled fusion produced in the laboratory, temperatures on the
order of 20 keV are satisfactory.
Controlled Thermonuclear Reactions
Because of the large amount of energy produced and the relatively small Coulomb barrier, the first fusion reaction will most likely be the D + T reaction. The tritium will be derived from two possible reactions:
The problem of controlled fusion involves significant scientific and engineering difficulties. The two major schemes to control thermonuclear reactions are magnetic confinement fusion (MCF) and inertial confinement fusion (ICF).
Magnetic confinement of plasma is done in a tokomak, which has many confinement boundaries.
Heating of the plasma to sufficiently high temperatures begins with the resistive heating from the electric current flowing in the plasma. There are two other schemes to add additional heat: (1) injection of high-energy (40–120 keV) neutral (so they pass through the magnetic field) fuel
atoms that interact with the plasma, and (2) radio-frequency (RF) induction heating of the plasma
Inertial Confinement
The concept of inertial confinement fusion is to use an intense high-
powered beam of heavy ions or light (laser) called a driver to implode a pea-sized target (a few mm in diameter) composed of D + T to a density and temperature high enough to cause fusion ignition.
The National Ignition Facility at Livermore will use 192 lasers to create a thermonuclear burn for research purposes.
Sandia National Laboratories has
used a device called a Z-pinch
that uses a huge jolt of current to
create a powerful magnetic field
that squeezes ions into implosion
and heats the plasma. Sandia
has proposed an upgrade that
13.7: Special Applications
A specific isotope of a radioactive element is called a radioisotope.
Radioisotopes are produced for useful purposes by different methods:
1) By particle accelerators as reaction products
2) In nuclear reactors as fission fragments or decay products
3) In nuclear reactors using neutron activation
An important area of applications is the search for a very small concentration of a particular element, called a trace element.
Trace elements are used in detecting minute quantities of trace
elements for forensic science and environmental purposes.
Medicine
Over 1100 radioisotopes are available for clinical use.
Radioisotopes are used in tomography, a technique for displaying images of practically any part of the body to look for abnormal physical shapes or for testing functional
characteristics of organs. By using detectors (either
surrounding the body or rotating around the body)
together with computers, three- dimensional images of the body can be obtained.
They use single-photon emission computed
Archaeology
Investigators can now measure a large number of trace elements in many ancient specimens and then compare the results with the
concentrations of components having the same origin.
Radioactive dating indicates that humans had a settlement near
Clovis, New Mexico 12,000 years ago. Several claims have surfaced in the past few years, especially from South America, that dispute this earliest finding, but no conclusive proof has been confirmed.
The Chauvet Cave, discovered in France in 1995, is one of the most important archaeological finds in decades. More than 300 paintings and engravings and many traces of human activity, including
hearths, fiintstones, and footprints, were found. These works are
believed, from
14C radioactive dating, to be from the Paleolithic era,
some 32,000 years ago.
Art
Neutron activation is a nondestructive technique that is becoming more widely used to examine oil paintings. A thermal neutron beam from a nuclear reactor is spread broadly and evenly over the painting. Several elements within the painting become radioactive. X-ray films
sensitive to beta emissions from the radioactive nuclei are subsequently placed next to the painting for varying lengths of time. This method is called an autoradiograph.
It was used to examine Van Dyck’s Saint Rosalie
Interceding for the Plague-Stricken of Palermo, from the New York Metropolitan Museum of Art collection and
revealed an over-painted self-portrait of Van Dyck
himself.
Crime Detection
The examination of gunshots by measuring trace
amounts of barium and antimony from the gunpowder has proven to be 100 to 1000 times more sensitive than looking for the residue itself.
Scientists are also able to detect toxic elements in hair by
neutron activation analysis.
Mining and Oil
Geologists and petroleum engineers use radioactive sources routinely to search for oil and gas. A source and detector are inserted down an
exploratory drill hole to examine the material at different depths. Neutron sources called PuBe (plutonium and beryllium) or AmBe (americium and beryllium) are particularly useful.
The neutrons activate nuclei in the
material surrounding the borehole, and
Materials
Natural silicon consists of 3.1% of the isotope
30Si, which undergoes the reaction
Phosphorus-doped silicon can be produced with fast-neutron
irradiation. Apparently the neutrons reduce the intrinsic resistivity in the silicon substrate so that the extraneous ionization caused later is much less likely to reset a bit.
Neutrons are particularly useful because they have no charge and do not ionize the material, as do charged particles and photons.
They penetrate matter easily and introduce uniform lattice
distortions or impurities. Because they have a magnetic dipole moment, neutrons can probe bulk magnetization and spin
phenomena.
Small Power Systems
Alpha-emitting radioactive sources have been used as power sources in heart pacemakers.
Smoke detectors use
241Am sources of alpha
particles as current generators. The scattering of the alpha particles by the smoke particles reduces the current flowing to a sensitive solid-state device, which results in an alarm.
Spacecraft have been powered by radioisotope
generators (RTGs) since the early 1960s.
New Elements
No transuranic elements—those with atomic number greater than Z = 92 (uranium)—are found in nature because of their short half-lives.
Reactors and especially accelerators have been able to produce 22 of these new elements up to Z = 116.
Over 150 new isotopes heavier than uranium have been discovered.
