13.1Nuclear Reactions

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CHAPTER 13Nuclear Interactions and Applications

• 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

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, Youll 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
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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(a, p)17O.
• In general a reaction x X ? y Y can be
  rewritten as
• X(x, y)Y

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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.
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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.

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Cross Sections

• The probability of a particular nuclear reaction
  occurring is determined by measuring the cross
  section s. 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

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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 gt 0 is from an
  exoergic (or exothermic) reaction. When Q lt 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

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13.3 Reaction Mechanisms

• The Compound Nucleus
• For low energies of E lt 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.

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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 relate
  the energy width of a particular nuclear state
  (called G) to its lifetime (called t)

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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 neutrons velocity. The
  1/v dependence can be explained in terms of the
  time the neutron spends near the nucleus.

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Direct Reactions

• 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.

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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

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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).

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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 3040 MeV of the
  kinetic energy.

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Chain Reactions

• 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.
• An atomic bomb is an extreme example of a
  supercritical fission chain reaction.

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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.

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13.5 Fission Reactors

• Several components are important for a controlled
  nuclear reactor
• Fissionable fuel
• Moderator to slow down neutrons
• Control rods for safety and to control
  criticality of reactor
• Reflector to surround moderator and fuel in order
  to contain neutrons and thereby improve
  efficiency
• Reactor vessel and radiation shield
• 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
  capture, and (2) neutrons may escape from the
  fuel zone.

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Core Components

• Fission neutrons typically have 12 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.

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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.

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Energy Transfer

• 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.

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Types of Reactors

• 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.

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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 facilitiesone at Three Mile Island in
  Pennsylvania in 1979, the other at Chernobyl in
  Ukraine in 1986have significantly dampened the
  general publics 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.

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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 toxic, and there is concern
  about its use in unauthorized weapons production.

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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.

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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 3He
• The 3He atoms can then combine to produce 4He

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Formation of Elements

• 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.

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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 stars
  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 stars 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.

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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
• 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
  100200 million K.
• The ions have to be confined together in close
  proximity to allow the ions to fuse. A suitable
  ion density is 23 1020 ions/m3.
• The ions must be held together in close proximity
  at high temperature long enough to avoid plasma
  cooling. A suitable time is 12 s.

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Fusion Product

• The product of the plasma density n and the
  containment time t 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 ntT
  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 gtgt 1. For controlled fusion produced in the
  laboratory, temperatures on the order of 20 keV
  are satisfactory.

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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 (40120 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 (similar to a microwave oven).

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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 may be a serious
  contender in the fusion race.

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13.7 Special Applications

• A specific isotope of a radioactive element is
  called a radioisotope.
• Radioisotopes are produced for useful purposes by
  different methods
• By particle accelerators as reaction products
• In nuclear reactors as fission fragments or decay
  products
• 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.

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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
  tomography, positron emission tomography, and
  magnetic resonance imaging.

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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.

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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 Dycks 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.

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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.

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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 these nuclei
  produce gamma decays characteristic of the
  particular element.

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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.

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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.

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New Elements

• No transuranic elementsthose 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.
• Physicists have reasons to suspect from shell
  model calculations that superheavy elements with
  atomic numbers of 110120 and 184 neutrons may be
  particularly long-lived.