1. Nuclear Energy and Elementary Particles
Chapter 30
Nuclear Energy
and
Elementary Particles

2. Processes of Nuclear Energy
Fission
A nucleus of large mass number splits into two smaller nuclei
Fusion
Two light nuclei fuse to form a heavier nucleus
Large amounts of energy are released in either case

3. Nuclear Fission A heavy nucleus splits into two smaller nuclei
The total mass of the products is less than the original mass of the heavy nucleus
First observed in 1939 by Otto Hahn and Fritz Strassman following basic studies by Fermi
Lisa Meitner and Otto Frisch soon explained what had happened

4. Fission Equation Fission of 235U by a slow (low energy) neutron
236U* is an intermediate, short-lived state
X and Y are called fission fragments
Many combinations of X and Y satisfy the requirements of conservation of energy and charge

5. Sequence of Events in Fission
The 235U nucleus captures a thermal (slow-moving) neutron
This capture results in the formation of 236U*, and the excess energy of this nucleus causes it to undergo violent oscillations
The 236U* nucleus becomes highly elongated, and the force of repulsion between the protons tends to increase the distortion
The nucleus splits into two fragments, emitting several neutrons in the process

6. Sequence of Events in Fission – Diagram

7. Energy in a Fission Process
Binding energy for heavy nuclei is about 7.2 MeV per nucleon
Binding energy for intermediate nuclei is about 8.2 MeV per nucleon
Therefore, the fission fragments have less mass than the nucleons in the original nuclei
This decrease in mass per nucleon appears as released energy in the fission event

8. Energy, cont An estimate of the energy released
Assume a total of 240 nucleons
Releases about 1 MeV per nucleon
8.2 MeV – 7.2 MeV
Total energy released is about 240 Mev
This is very large compared to the amount of energy released in chemical processes

9. QUICK QUIZ 30.1
In the first atomic bomb, the energy released was equivalent to about 30 kilotons of TNT, where a ton of TNT releases an energy of 4.0 × 109 J. The amount of mass converted into energy in this event is nearest to: (a) 1 g, (b) 1 mg, (c) 1 g, (d) 1 kg, (e) 20 kilotons

10. QUICK QUIZ 30.1 ANSWER
(c). The total energy released was E = (30 ×103 ton)(4.0 × 109 J/ton) = 1.2 × 1014 J. The mass equivalent of this quantity of energy is:

11. Chain Reaction Neutrons are emitted when 235U undergoes fission
These neutrons are then available to trigger fission in other nuclei
This process is called a chain reaction
If uncontrolled, a violent explosion can occur
The principle behind the nuclear bomb, where 1 g of U can release energy equal to about tons of TNT

12. Chain Reaction – Diagram

13. Nuclear Reactor
A nuclear reactor is a system designed to maintain a self-sustained chain reaction
The reproduction constant, K, is defined as the average number of neutrons from each fission event that will cause another fission event
The maximum value of K from uranium fission is 2.5
In practice, K is less than this
A self-sustained reaction has K = 1

14. K Values When K = 1, the reactor is said to be critical
The chain reaction is self-sustaining
When K < 1, the reactor is said to be subcritical
The reaction dies out
When K > 1, the reactor is said to be supercritical
A run-away chain reaction occurs

15. Basic Reactor Design Fuel elements consist of enriched uranium
The moderator material helps to slow down the neutrons
The control rods absorb neutrons

16. Reactor Design Considerations – Neutron Leakage
Loss (or “leakage”) of neutrons from the core
These are not available to cause fission events
The fraction lost is a function of the ratio of surface area to volume
Small reactors have larger percentages lost
If too many neutrons are lost, the reactor will not be able to operate

17. Reactor Design Considerations – Neutron Energies
Slow neutrons are more likely to cause fission events
Most neutrons released in the fission process have energies of about 2 MeV
In order to sustain the chain reaction, the neutrons must be slowed down
A moderator surrounds the fuel
Collisions with the atoms of the moderator slow the neutrons down as some kinetic energy is transferred
Most modern reactors use heavy water as the moderator

18. Reactor Design Considerations – Neutron Capture
Neutrons may be captured by nuclei that do not undergo fission
Most commonly, neutrons are captured by 238U
The possibility of 238U capture is lower with slow neutrons
The moderator helps minimize the capture of neutrons by 238U

19. Reactor Design Considerations – Power Level Control
A method of control is needed to adjust the value of K to near 1
If K >1, the heat produced in the runaway reaction can melt the reactor
Control rods are inserted into the core to control the power level
Control rods are made of materials that are very efficient at absorbing neutrons
Cadmium is an example
By adjusting the number and position of the control rods, various power levels can be maintained

20. Pressurized Water Reactor – Diagram

21. Pressurized Water Reactor – Notes
This type of reactor is commonly used in electric power plants in the US
Fission events in the reactor core supply heat to the water contained in the primary system
The primary system is a closed system
This water is maintained at a high pressure to keep it from boiling
The hot water is pumped through a heat exchanger

22. Pressurized Water Reactor – Notes, cont
The heat is transferred to the water contained in a secondary system
This water is converted into steam
The steam is used to drive a turbine-generator to create electric power
The water in the secondary system is isolated from the water in the primary system
This prevents contamination of the secondary water and steam by the radioactive nuclei in the core

23. Reactor Safety – Containment
Radiation exposure, and its potential health risks, are controlled by three levels of containment
Reactor vessel
Contains the fuel and radioactive fission products
Reactor building
Acts as a second containment structure should the reactor vessel rupture
Location
Reactor facilities are in remote locations

24. Reactor Safety – Loss of Water
If the water flow was interrupted, the nuclear reaction could stop immediately
However, there could be enough residual heat to build up and melt the fuel elements
The molten core could also melt through the containment vessel and into the ground
Called the China Syndrome
If the molten core struck ground water, a steam explosion could spread the radioactive material to areas surrounding the power plant
Reactors are built with emergency cooling systems that automatically flood the core if coolant is lost

25. Reactor Safety – Radioactive Materials
Disposal of waste material
Waste material contains long-lived, highly radioactive isotopes
Must be stored over long periods in ways that protect the environment
Present solution is sealing the waste in waterproof containers and burying them in deep salt mines
Transportation of fuel and wastes
Accidents during transportation could expose the public to harmful levels of radiation
Department of Energy requires crash tests and manufacturers must demonstrate that their containers will not rupture during high speed collisions

26. Nuclear Fusion
Nuclear fusion occurs when two light nuclei combine to form a heavier nucleus
The mass of the final nucleus is less than the masses of the original nuclei
This loss of mass is accompanied by a release of energy

27. Fusion in the Sun All stars generate energy through fusion
The Sun, along with about 90% of other stars, fuses hydrogen
Some stars fuse heavier elements
Two conditions must be met before fusion can occur in a star
The temperature must be high enough
The density of the nuclei must be high enough to ensure a high rate of collisions

28. Proton-Proton Cycle
The proton-proton cycle is a series of three nuclear reactions believed to operate in the Sun
Energy liberated is primarily in the form of gamma rays, positrons and neutrinos

29. Fusion Reactors
Energy releasing fusion reactions are called thermonuclear fusion reactions
A great deal of effort is being directed at developing a sustained and controllable thermonuclear reaction
A thermonuclear reactor that can deliver a net power output over a reasonable time interval is not yet a reality

30. Advantages of a Fusion Reactor
Inexpensive fuel source
Water is the ultimate fuel source
If deuterium is used as fuel, 0.06 g of it can be extracted from 1 gal of water for about 4 cents
Comparitively few radioactive by-products are formed

31. Considerations for a Fusion Reactor
The proton-proton cycle is not feasible for a fusion reactor
The high temperature and density required are not suitable for a fusion reactor
The most promising reactions involve deutrium and tritium

32. Considerations for a Fusion Reactor, cont
Tritium is radioactive and must be produced artifically
The Coulomb repulsion between two charged nuclei must be overcome before they can fuse

33. Requirements for Successful Thermonuclear Reactor
High temperature ~ 108 K
Needed to give nuclei enough energy to overcome Coulomb forces
At these temperatures, the atoms are ionized, forming a plasma
Plasma ion density, n
The number of ions present
Plasma confinement time, 
The time the interacting ions are maintained at a temperature equal to or greater than that required for the reaction to proceed successfully

34. Lawson’s Criteria
Lawson’s criteria states that a net power output in a fusion reactor is possible under the following conditions
n  1014 s/cm3 for deuterium-tritium
n  1016 s/cm3 for deuterium-deuterium
The plasma confinement time is still a problem

35. Magnetic Confinement
One magnetic confinement device is called a tokamak
Two magnetic fields confine the plasma inside the doughnut
A strong magnetic field is produced in the windings
A weak magnetic field is produced in the toroid
The field lines are helical, spiral around the plasma, and prevent it from touching the wall of the vacuum chamber

36. Current Research in Fusion Reactors
NSTX – National Spherical Torus Experiment
Produces a spherical plasma with a hole in the center
Is able to confine the plasma with a high pressure
ITER – International Thermonuclear Experimental Reactor
An international collaboration involving four major fusion programs is working on building this reactor
It will address remaining technological and scientific issues concerning the feasibility of fusion power

37. Elementary Particles Atoms Atom constituents
From the Greek for “indivisible”
Were once thought to the elementary particles
Atom constituents
Proton, neutron, and electron
Were viewed as elementary because they are very stable

38. Discovery of New Particles
Beginning in 1937, many new particles were discovered in experiments involving high-energy collisions
Characteristically unstable with short lifetimes
Over 300 have been cataloged
A pattern was needed to understand all these new particles

39. Quarks Physicists recognize that most particles are made up of quarks
Exceptions include photons, electrons and a few others
The quark model has reduced the array of particles to a manageable few
The quark model has successfully predicted new quark combinations that were subsequently found in many experiments

40. Fundamental Forces
All particles in nature are subject to four fundamental forces
Strong force
Electromagnetic force
Weak force
Gravitational force

41. Strong Force
Is responsible for the tight binding of the quarks to form neutrons and protons
Also responsible for the nuclear force binding the neutrons and the protons together in the nucleus
Strongest of all the fundamental forces
Very short-ranged
Less than m

42. Electromagnetic Force
Is responsible for the binding of atoms and molecules
About 10-2 times the strength of the strong force
A long-range force that decreases in strength as the inverse square of the separation between interacting particles

43. Weak Force Is responsible for instability in certain nuclei
Is responsible for beta decay
A short-ranged force
Its strength is about 10-6 times that of the strong force
Scientists now believe the weak and electromagnetic forces are two manifestions of a single force, the electroweak force

44. Gravitational Force
A familiar force that holds the planets, stars and galaxies together
Its effect on elementary particles is negligible
A long-range force
It is about times the strength of the strong force
Weakest of the four fundamental forces

45. Explanation of Forces
Forces between particles are often described in terms of the actions of field particles or quanta
For electromagnetic force, the photon is the field particle
The electromagnetic force is mediated, or carried, by photons

46. Forces and Mediating Particles (also see table 30.1)
Interaction (force)
Mediating Field Particle
Strong
Gluon
Electromagnetic
Photon
Weak
W and Z0
Gravitational
Gravitons

47. Antiparticles For every particle, there is an antiparticle
From Dirac’s version of quantum mechanics that incorporated special relativity
An antiparticle has the same mass as the particle, but the opposite charge
The positron (electron’s antiparticle) was discovered by Anderson in 1932
Since then, it has been observed in numerous experiments
Practically every known elementary particle has a distinct antiparticle
Exceptions – the photon and the neutral pi particles are their own antiparticles

48. Mesons Developed from a theory to explain the strong nuclear force
Background notes
Two atoms can form a covalent bond by the exchange of electrons
In electromagnetic interactions, charged particles interact by exchanging a photon
A new particle was proposed to explain the strong nuclear force
It was called a meson

49. Mesons, cont
The proposed particle would have a mass about 200 times that of the electron
Efforts to establish the existance of the particle were done by studying cosmic rays in the 1930’s
Actually discovered multiple particles
Pi meson (pion)
Muon
Not a meson

50. Pion There are three varieties of pions Pions are very unstable
+ and -
Mass of MeV/c2 0
Mass of MeV/c2
Pions are very unstable
- decays into a muon and an antineutrino with a lifetime of about 2.6 x10-8 s

51. Feynman Diagrams
A graphical representation of the interaction between two particles
Feynman diagrams are named for Richard Feynman who developed them

52. Feynman Diagram – Two Electrons
The photon is the field particle that mediates the interaction
The photon transfers energy and momentum from one electron to the other
The photon is called a virtual photon
It can never be detected directly because it is absorbed by the second electron very shortly after being emitted by the first electron

53. The Virtual Photon
The existance of the virtual photon would violate the law of conservation of energy
But, due to the uncertainty principle and its very short lifetime, the photon’s excess energy is less than the uncertainty in its energy
The virtual photon can exist for short time intervals, such that ΔE~  / Δt

54. Feynman Diagram – Proton and Neutron
The exchange is via the nuclear force
The existance of the pion is allowed in spite of conservation of energy if this energy is surrendered in a short enough time
Analysis predicts the rest energy of the pion to be 130 MeV / c2
This is in close agreement with experimental results

55. Classification of Particles
Two board categories
Classified by interactions
Hadrons – interact through strong force
Leptons – interact through weak force

56. Hadrons Interact through the strong force Two subclasses
Mesons
Decay finally into electrons, positrons, neutrinos and photons
Integer spins
Baryons
Masses equal to or greater than a proton
Noninteger spin values
Decay into end products that include a proton (except for the proton)
Composed of quarks

57. Leptons Interact through weak force All have spin of ½
Leptons appear truly elementary
No substructure
Point-like particles
Scientists currently believe only six leptons exist, along with their antiparticles
Electron and electron neutrino
Muon and its neutrino
Tau and its neutrino

58. Conservation Laws
A number of conservation laws are important in the study of elementary particles
Two new ones are
Conservation of Baryon Number
Conservation of Lepton Number

59. Conservation of Baryon Number
Whenever a baryon is created in a reaction or a decay, an antibaryon is also created
B is the Baryon Number
B = +1 for baryons
B = -1 for antibaryons
B = 0 for all other particles
The sum of the baryon numbers before a reaction or a decay must equal the sum of baryon numbers after the process

60. Conservation of Lepton Number
There are three conservation laws, one for each variety of lepton
Law of Conservation of Electron-Lepton Number states that the sum of electron-lepton numbers before a reaction or a decay must equal the sum of the electron-lepton number after the process

61. Conservation of Lepton Number, cont
Assigning electron-lepton numbers
Le = 1 for the electron and the electron neutrino
Le = -1 for the positron and the electron antineutrino
Le = 0 for all other particles
Similarly, when a process involves muons, muon-lepton number must be conserved and when a process involves tau particles, tau-lepton numbers must be conserved
Muon- and tau-lepton numbers are assigned similarly to electron-lepton numbers

62. Which of the following reactions cannot occur?
QUICK QUIZ 30.2
Which of the following reactions cannot occur?

63. (a). This reaction fails to conserve charge and cannot occur.
QUICK QUIZ 30.2 ANSWER

64. Which of the following reactions cannot occur?
QUICK QUIZ 30.3
Which of the following reactions cannot occur?

65. (b). This reaction fails to conserve charge and cannot occur.
QUICK QUIZ 30.3 ANSWER

66. QUICK QUIZ 30.4
Suppose a claim is made that the decay of a neutron is given by n  p+ + e_. Which of the following conservation laws are violated by this proposed decay scheme? (a) energy, (b) linear momentum, (c) spin angular momentum, (d) electric charge, (e) lepton number, (f) baryon number.

67. QUICK QUIZ 30.4 ANSWER
(c), (e). The proton and the electron each have spin s = ½ . The two possible resultant spins after decay are 1 (spins aligned) or 0 (spins anti-aligned). Neither equal the spin of a neutron, s = ½ , so spin angular momentum is not conserved. The are no leptons present before the proposed decay and one lepton (the electron) present after decay. Thus, the decay also fails to conserve lepton number.

68. Strange Particles
Some particles discovered in the 1950’s were found to exhibit unusual properties in their production and decay and were given the name strange particles
Peculiar features include
Always produced in pairs
Although produced by the strong interaction, they do not decay into particles that interact via the strong interaction, but instead into particles that interact via weak interactions
They decay much more slowly than particles decaying via strong interactions

69. Strangeness
To explain these unusual properties, a new law, the conservation of strangeness was introduced
Also needed a new quantum number, S
The Law of Conservation of Strangeness states that the sum of strangeness numbers before a reaction or a decay must equal the sum of the strangeness numbers after the process
Strong and electromagnetic interactions obey the law of conservation of strangeness, but the weak interaction does not

70. Bubble Chamber Example
The dashed lines represent neutral particles
At the bottom,
- + p  Λ0 + K0
Then Λ0  - + p and
K0   + µ- + µ

71. The Eightfold Way
Many classification schemes have been proposed to group particles into families
These schemes are based on spin, baryon number, strangeness, etc.
The eightfold way is a symmetic pattern proposed by Gell-Mann and Ne’eman
There are many symmetrical patterns that can be developed
The patterns of the eightfold way have much in common with the periodic table
Including predicting missing particles

72. An Eightfold Way for Baryons
A hexagonal pattern for the eight spin ½ baryons
Stangeness vs. charge is plotted on a sloping coordinate system
Six of the baryons form a hexagon with the other two particles at its center

73. An Eightfold Way for Mesons
The mesons with spins of 0 can be plotted
Strangeness vs. charge on a sloping coordinate system is plotted
A hexagonal pattern emerges
The particles and their antiparticles are on opposite sides on the perimeter of the hexagon
The remaining three mesons are at the center

74. Quarks Hadrons are complex particles with size and structure
Hadrons decay into other hadrons
There are many different hadrons
Quarks are proposed as the elementary particles that constitute the hadrons
Originally proposed independently by Gell-Mann and Zweig

75. Original Quark Model Three types
u – up
d – down
s – originally sideways, now strange
Associated with each quark is an antiquark
The antiquark has opposite charge, baryon number and strangeness
Quarks have fractional electrical charges
+1/3 e and –2/3 e
All ordinary matter consists of just u and d quarks

76. Original Quark Model – Rules
All the hadrons at the time of the original proposal were explained by three rules
Mesons consist of one quark and one antiquark
This gives them a baryon number of 0
Baryons consist of three quarks
Antibaryons consist of three antiquarks

77. Additions to the Original Quark Model – Charm
Another quark was needed to account for some discrepencies between predictions of the model and experimental results
Charm would be conserved in strong and electromagnetic interactions, but not in weak interactions
In 1974, a new meson, the J/Ψ was discovered that was shown to be a charm quark and charm antiquark pair

78. More Additions – Top and Bottom
Discovery led to the need for a more elaborate quark model
This need led to the proposal of two new quarks
t – top (or truth)
b – bottom (or beauty)
Added quantum numbers of topness and bottomness
Verification
b quark was found in a Y meson in 1977
t quark was found in 1995 at Fermilab

79. Numbers of Particles
At the present, physicists believe the “building blocks” of matter are complete
Six quarks with their antiparticles
Six leptons with their antiparticles

80. Color
Isolated quarks
Physicist now believe that quarks are permanently confined inside ordinary particles
No isolated quarks have been observed experimentally
The explanation is a force called the color force
Color force increases with increasing distance
This prevents the quarks from becoming isolated particles

81. Colored Quarks Color “charge” occurs in red, blue, or green
Antiquarks have colors of antired, antiblue, or antigreen
Color obeys the Exclusion Principle
A combination of quarks of each color produces white (or colorless)
Baryons and mesons are always colorless

82. Quark Structure of a Meson
A red quark is attracted to an antired quark
The quark – antiquark pair forms a meson
The resulting meson is colorless

83. Quark Structure of a Baryon
Quarks of different colors attract each other
The quark triplet forms a baryon
The baryon is colorless

84. Quantum Chromodynamics (QCD)
QCD gave a new theory of how quarks interact with each other by means of color charge
The strong force between quarks is often called the color force
The strong force between quarks is carried by gluons
Gluons are massless particles
There are 8 gluons, all with color charge
When a quark emits or absorbs a gluon, its color changes

85. More About Color Charge
Like colors repel and unlike colors attract
Different colors attract, but not as strongly as a color and its anticolor
The color force between color-neutral hadrons is negligible at large separations
The strong color force between the constituent quarks does not exactly cancel at small separations
This residual strong force is the nuclear force that binds the protons and neutrons to form nuclei

86. QCD Explanation of a Neutron-Proton Interaction
Each quark within the proton and neutron is continually emitting and absorbing virtual gluons
Also creating and annihilating virtual quark-antiquark pairs
When close enough, these virtual gluons and quarks can be exchanged, producing the strong force

87. Weak Interaction
The weak interaction is an extremely short-ranged force
This short range implies the mediating particles are very massive
The weak interaction is responsible for the decay of c, s, b, and t quarks into u and d quarks
Also responsible for the decay of  and  leptons into electrons

88. Weak Interaction, cont
The weak interaction is very important because it governs the stability of the basic matter particles
The weak interaction is not symmetrical
Not symmetrical under mirror reflection
Not symmetrical under charge exchange

89. Electroweak Theory
The electroweak theory unifies electromagnetic and weak interactions
The theory postulates that the weak and electromagnetic interactions have the strength at very high particle energies
Viewed as two different manifestions of a single interaction

90. The Standard Model
A combination of the electroweak theory and QCD form the standard model
Essential ingredients of the standard model
The strong force, mediated by gluons, holds the quarks together to form composite particles
Leptons participate only in electromagnetic and weak interactions
The electromagnetic force is mediated by photons
The weak force is mediated by W and Z bosons

91. The Standard Model – Chart

92. Mediator Masses
Why does the photon have no mass while the W and Z bosons do have mass?
Not answered by the Standard Model
The difference in behavior between low and high energies is called symmetry breaking
The Higgs boson has been proposed to account for the masses
Large colliders are necessary to achieve the energy needed to find the Higgs boson

93. Grand Unification Theory (GUT)
Builds on the success of the electroweak theory
Attempted to combine electroweak and strong interactions
One version considers leptons and quarks as members of the same family
They are able to change into each other by exchanging an appropriate particle

94. The Big Bang
This theory of cosmology states that during the first few minutes after the creation of the universe all four interactions were unified
All matter was contained in a quark soup
As time increased and temperature decreased, the forces broke apart
Starting as a radiation dominated universe, as the universe cooled it changed to a matter dominated universe

95. A Brief History of the Universe

96. Cosmic Background Radiation (CBR)
CBR is represents the cosmic “glow” left over from the Big Bang
The radiation had equal strengths in all directions
The curve fits a blackbody at ~3K
There are small irregularities that allowed for the formation of galaxies and other objects

97. Connection Between Particle Physics and Cosmology
Observations of events that occur when two particles collide in an accelerator are essential to understanding the early moments of cosmic history
There are many common goals between the two fields

98. Some Questions Why so little antimatter in the Universe?
Do neutrinos have mass?
Is it possible to unify electroweak and strong forces?
Why do quark and leptons form similar but distinct families?
Why do quarks carry fractional charge?
What determines the masses of fundamental particles?
Do leptons and quarks have a substructure?