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The international sign of radioactivity
Chapter 9 Nuclear Physics
Understanding the atoms was exclusively a pursuit
of scientists for a long time. Over sixty years ago,
scientists irrefutably demonstrated the power of
these tiny particles (the atoms) to the world. The
USA military dropped atomic bombs in Japan:
Hiroshima (over 100,000 people were killed) and
Nagasaki. Nuclear weapons have killed hundreds of
thousands of people, and have the potential of
destroying most life on earth. The threat of nuclear
warfare is a serious problem.
On the other side, more and more countries are
obtaining and developing nuclear weapons, these
include of USA, Russia, France, UK, China (first
atomic bomb in 1964, first Hydrogen bomb in 1967)
India, Pakistan and Israel;
the suspected countries: North Korea, South Africa,
Iran, Syria, Libya, Algeria.
Applications
 The nuclear energy:
advantage: it is potential of becoming the safest,
cleanest, cheapest and most efficient type of
energy;
disadvantage: it carries the risk of a reactor
meltdown and lots of harmful released radiation.
 Medical imaging, such as CT scans and MRI, is
used to determine the amount of radiation a
person being exposed to. There have been quite a
few different techniques and more are still being
developed and improved presently.
Radioactive dating uses radioactive
properties of certain elements to determine the
age of something such as an ancient person.
Radiation detection involves different
instruments used in order to detect radiation
present somewhere.
The short history of the nuclear physics
1896, A. H. Becquerel discovered the radioactivity of 92U;
1897, Mrs and Mr. P. & M. Curie discovered that the
elements of 84Po and 88Ra have radioactive behaviors;
1899,  and  rays, 1900,  rays;
1903, Rutherford found that  ray is 2He++ and  ray is
electron;
1911, Planet model of atoms;
1919, man-made nuclear reactions;
1932, J. Chadwick discovered neutron, Heisenberg:
nucleus consists of protons and neutrons;
1934, Mrs. and Mr. F. & I. Joliot Curie discovered manmade radioactivity;
1939, O. Hahn, F. Strassmann, L. Meitner and O.
Frisch, Fission of heavy elements;
1942, E. Feimi, hot neutron proliferation reactor;
1945, J. Oppenheimer at Los Alamos: atomic bomb
1952, E. Teller, Hydrogen bomb;
1954, Soviet set up a nuclear power plant;
1964, China, atomic bomb; 1967, hydrogen bomb.
§9.1 the basic properties of the nuclei
The atom and nucleus are two different
levels of the matter:
 The main contribution of nucleus is the mass
and charge;
 The chemical and physical properties, and the
properties of optical spectra are due to electron
structure;
 The radioactivity is due to the characteristic
of some isotopes.
§9.1 the basic properties of the nuclei
The components of atom: nuclei + electrons
Nuclei: neutrons + protons
nucleons
1 u = 1.66 x 10- 27 kg = 939 MeV/c 2
Mp = 1.008665 u, mn = 1.007277 u
The electrons, protons and neutrons which make
up an atom have definite charges and masses
Element: atoms with the same atomic
number Z
Isotope: the same elements with different
neutron number;
Nuclide: a type of atoms specified by its
atomic number, atomic mass, and energy
state.
At present it knows 112 elements. All of the elements heavier
than 92U are man-made; approximately 270 stable isotopes and
more than 2000 unstable isotopes.
Chart of Nuclide
Nuclide byland
Isotopic Abundances by Mass Spectrometry
The relative abundances of the isotopes
of an element may be obtained with a mass
spectrometer.
For example, the relative abundances of
krypton are shown below on an
experimental spectrum adapted from Krane,
Introductory Nuclear Physics.
78Kr
0.356%
80Kr
2.27%
82Kr
11.6%
83Kr
11.5%
84Kr
57.0%
86Kr
17.3%
A weighted average of the isotopes above gives 83.8 u, the
accepted atomic mass of krypton which appears in the periodic
table. Other isotopes of krypton are known, but they do not
appear in natural samples because they are unstable
(radioactive).
§9.2 radioactivity
Radioactivity means atoms decay, which emit some
kind of radiation. The reason for these decays is that
they are instable.
The discovered 2000 nuclides, most of
them are unstable, and can decay to another
nuclide. An atomic nucleus is instable
when it is too heavy or when a balance is
missing between the protons and neutrons.
Every atoms which has higher number of
nucleons than 210 is instable.
The nucleus decays are quantum statistical behaviors.
It is impossible to predict which nucleus will be the
next one who decays. It is possible to predict how
many nuclei will decay in a certain time.
 dN  N 0 dt
N  N 0e
 t
N: the number of nuclei;
-dN: the number of nuclei decayed;
: decay constant, the probability of nuclei decay in a unit time
Radioactive Half-Life
The radioactive half-life for a given
radioisotope is the time for half the
radioactive nuclei in any sample to undergo
radioactive decay. After two half-lives, there
will be one fourth the original sample, after
three half-lives one eight the original sample,
and so forth.
1
 T1 / 2
N 0  N 0e
2
T1 / 2 
1

ln 2
Examples of half life time
239Pu:
24,000 years,
238Ra:
6.7 years,
232Th:
14,000,000 years,
212Po:
0.0000003 s,
235U:
0.70 ×109 years,
238U:
4.5 × 109 years;
Proton: 1030 years.
Empirical results:
decay constant  and half-life time T1/2 are
characteristic of radioactivity, and they almost
have no correlation with its circumstances:
temperature: 24k ~ 1500k,
pressure: 0 ~ 2000 atm,
magnetic field: 0 ~ 8.3T,
For 7Be: 70 days in sun, and 53 days in earth,
30% in change
Activity:
the intensity of radioactive source
dN
 t
A
 N 0 e  N
dt
1 Ci (Curie) = 3.7 × 1010 s-1, the activity of 1 g 216Ra
In china: 1 Bq = 1 s-1,
1 Ci = 3.7 × 1010 Bq
The determination of the nuclides with long half
life by measuring the activity.
The most common types of radiation are
called ,  and  radiations, and several
other varieties of radiation decays
Historically, the products of radioactivity were called alpha, beta,
and gamma when it was found that they could be analyzed into
three distinct species by either a magnetic field or an electric field.
Penetration of matter
Through the most massive and most energetic of radioactive
emissions, the alpha particle is the shortest in range because of
its strong interaction with matter. The electromagnetic gamma
ray is extremely penetrating, even penetrating considerable
thicknesses of concrete. The electron of beta radioactivity
strongly interacts with matter and has a short range.
 radioactivity
 particle composes of two protons
and two neutrons, the alpha particle
is a nucleus of the element of helium.
 decay:
A
Z
X
A 4
Z 2
Y 
For instance:
210
84
206
Po 82
Pb  
U
238
92
234
90
Th  
Alpha Barrier Penetration
The energy of emitted alpha particles was a mystery
to early investigators because it was evident that
they did not have enough energy, according to
classical physics, to escape the nucleus. Once an
approximate size of the nucleus was obtained by
Rutherford scattering, one could calculate the height
of the Coulomb barrier at the radius of the nucleus.
It was evident that this energy was several times
higher than the observed alpha particle energies.
There was also an incredible range of half lives for
the alpha particle which could not be explained by
anything in classical physics.
Alpha Tunneling Model
Quantum mechanical tunneling gives a small
probability that the alpha can penetrate the barrier.
To evaluate this probability, the alpha particle inside
the nucleus is represented by a free-particle
wavefunction subject to the nuclear potential. Inside
the barrier, the solution to the Schrodinger equation
becomes a decaying exponential.
Calculating the ratio of the wavefunction outside the
barrier and inside and squaring that ratio gives the
probability of alpha emission.
The illustration represents the barrier faced by an alpha
particle in polonium-212, which emits an 8.78 MeV
alpha particle with a half-life of 0.3 microseconds. The
following characteristics of the nuclear environment
can be calculated from a basic model of the nucleus:
Separation of centers of alpha and nucleus at
edge of barrier
9.1 fm
Height of barrier
26.4
MeV
Radius at which barrier drops to alpha
energy
26.9 fm
Width of barrier seen by alpha
17.9 fm
Alpha's frequency of hitting the barrier
1.1 x
10^21/s
Alpha Binding Energy
The mass of a nucleus is always less than the sum
of the individual masses of the protons and neutrons
which constitute it. The difference is a measure of
the nuclear binding energy which holds the nucleus
together. This binding energy can be calculated
from the Einstein relationship:
Nuclear binding energy = Δmc2
The nuclear binding energy of the alpha particle
is extremely high, 28.3 MeV. It is an
exceptionally stable collection of nucleons. This
contrasts with a binding energy of only 8 MeV
for helium-3, which forms an intermediate step
in the proton-proton fusion cycle.
Warning
Because of its very large mass (more than 7000
times the mass of the beta particle) and its charge, it
has a very short range. The alpha particle is not
suitable for radiation therapy since its range is less
than a tenth of a millimeter inside the body. Its main
radiation hazard comes when it is ingested into the
body; it has great destructive power within its short
range. In contact with fast-growing membranes and
living cells, it is positioned for maximum damage.
Beta Radioactivity
Beta particles are just electrons from the
nucleus, the term "beta particle" being an
historical term used in the early
description of radioactivity.
Beta emission is accompanied by the
emission of an electron antineutrino which
shares the momentum and energy of the
decay.
The emission of the electron's antiparticle,
the positron, is also called beta decay.
The radiation hazard from betas is greatest
if they are ingested.
Beta decay can be seen as the decay of one of the neutrons to a
proton via the weak interaction. The use of a weak interaction
Feynman diagram can clarify the process.
n  p  e  e

The beta decay:
A
Z
X  Y  e  e
32
15
3
1

A
Z 1
P S  e  e
32
16

H  He  e   e
3
2

The energy released in decay, Q:
M X c  M Y c  me c  Q
2
2
2
Q = 1.71 Mev for 32P  32S
Positron and Neutrino
The emission of a positron or an electron is referred
to as beta decay. The positron is accompanied by a
neutrino, a massless(?) and chargeless particle.
Positrons are emitted with the same kind of energy
spectrum as electrons in negative beta decay because
of the emission of the neutrino.
Beta Energy Spectrum
In the process of beta decay, either an electron or a positron is
emitted. There is a spectrum of energies for the electron or
positron, depending upon what fraction of the reaction energy Q
is carried by the massive particle. The shape of this energy curve
can be predicted from the Fermi theory of beta decay.
From the Fermi theory of beta decay, the shape of
the energy distribution for this "allowed" transition is
given approximately by the expression:
N KEe  


C KE  2 KEe me c Q  KEe  KEe  me c 2 F Z ' , KEe 
2
e
2
2
where F(Z',KEe) is called the Fermi function. It accounts for the
nuclear coulomb interaction which shifts this distribution toward
lower energies because of the coulomb attraction between the
daughter nucleus and the emitted electron. (It shifts the distribution
upward for positrons.) Q represnts the energy yield of the transition
and as such is the upper bound on the kinetic energy of the electron,
KEe. The apparent complexity of the expression is partly because it
is necessary to use relativistic momentum for the electron.
Gamma Radioactivity
Gamma radioactivity is composed
of electromagnetic rays.
Z
A
X * (excited state) AZ X (lower energy )  
Gama radioactivity is distinguished from x-rays only
by the fact that it comes from the nucleus. Most
gamma rays are somewhat higher in energy than xrays and therefore are very penetrating.
It is the most useful type of radiation for medical
purposes, but at the same time it is the most
dangerous because of its ability to penetrate large
thickness of material.
Gamma Radioactivity
Binding energies
for 203Tl
K
85.529 keV
LI
15.347 keV
LII 14.698 keV
LIII 12.657 keV
M
Electron emissions from the Hg-203 to
Tl-203 decay, measured by A. H. Wapstra,
et al., Physica 20, 169 (1954).
3.704 keV
Other Radioactive Processes
Electron capture: A parent nucleus may capture one
of its own electrons and emit a neutrino. Most
commonly, it is a K-shell electron which is captured,
and this is referred to as K-capture. A typical
example is
Internal conversion is the use of electromagnetic
energy from the nucleus to expel an orbital electron
from the atom. It is another electromagnetic process
which can occur in the nucleus and which competes
with gamma emission.
This process is not the same as emitting a gamma ray
which knocks an electron out of the atom. It is also
not the same as beta decay, since the emitted electron
was previously one of the orbital electrons, whereas
the electron in beta decay is produced by the decay
of a neutron.
Radioactive Decay Paths
Radioactivity involves the emission of particles
from the nuclei. In the case of gamma emission, the
nucleus remaining will be of the same chemical
element, but for alpha, beta, and other radioactive
processes, the nucleus will be transmuted into the
nucleus of another chemical element. Each decay
path will have a characteristic half-life, but some
radioisotopes have more than one competing decay
path.
Radioactive Decay Paths
§9.3 Nuclear reactions
Many kinds of nuclear reactions occur in response to the
absorption of particles such as neutrons or protons. Other types
of reactions may involve the absorption of gamma rays or the
scattering of gamma rays.
Specific nuclear reactions can be written down in a manner
similar to chemical reaction equations. If a target nucleus X is
bombarded by a particle a and results in a nucleus Y with emitted
particle b, this is commonly written in one of two ways.
Reaction energy
We can characterize the energy of the reaction with a reaction
energy Q, defined as the energy released in the reaction. The Q is
positive if the total mass of the products is less than that of the
projectile and target, indicating that the total nuclear binding
energy has increased. The probability of a given type of nuclear
reaction taking place is often stated as a "cross section".
A commonly used unit is the barn:
1 barn = 10-28 m2
Some Nuclear Reactions
Nuclear Binding Energy curve
Iron limit
Nuclear binding energy = Δmc2
Nuclear Fission
If a massive nucleus like uranium-235 breaks apart (fissions), then
there will be a net yield of energy because the sum of the masses of
the fragments will be less than the mass of the uranium nucleus.
In one of the most remarkable
phenomena in nature, a slow
neutron can be captured by a
uranium-235 nucleus, rendering it
unstable toward nuclear fission. A
fast neutron will not be captured,
so neutrons must be slowed down
by moderation to increase their
capture probability in fission
reactors.
Uranium Fuel
Natural uranium is composed of 0.72% U-235 (the
fissionable isotope), 99.27% U-238, and a trace quantity
0.0055% U-234 . The 0.72% U-235 is not sufficient to
produce a self-sustaining critical chain reaction in U.S. style
light-water reactors, although it is used in Canadian
CANDU reactors. For light-water reactors, the fuel must be
enriched to 2.5-3.5% U-235.
Uranium is found as uranium oxide which when purified has
a rich yellow color and is called "yellowcake". After
reduction, the uranium must go through an isotope
enrichment process. Even with the necessity of enrichment,
it still takes only about 3 kg of natural uranium to supply the
energy needs of one American for a year.
Light Water Reactors
The nuclear fission reactors used in the United States for
electric power production are classified as "light water
reactors" in contrast to the "heavy water reactors" used in
Canada. Light water (ordinary water) is used as the moderator
in U.S. reactors as well as the cooling agent and the means by
which heat is removed to produce steam for turning the
turbines of the electric generators. The use of ordinary water
makes it necessary to do a certain amount of enrichment of the
uranium fuel before the necessary criticality of the reactor can
be maintained.
The two varieties of the light water reactor are the pressurized
water reactor (PWR) and boiling water reactor (BWR).
Heavy Water Reactors
Nuclear fission reactors used in Canada use
heavy water as the moderator in their reactors.
Since the deuterium in heavy water is slightly
more effective in slowing down the neutrons
from the fission reactions, the uranium fuel
needs no enrichment and can be used as mined.
The Canadian style reactors are commonly
called CANDU reactors.
Fissionable Isotopes
While uranium-235 is the naturally occuring fissionable isotope,
there are other isotopes which can be induced to fission by
neutron bombardment. Plutonium-239 is also fissionable by
bombardment with slow neutrons, and both it and uranium-235
have been used to make nuclear fission bombs. Plutonium-239
can be produced by "breeding" it from uranium-238. Uranium238, which makes up 99.3% of natural uranium, is not
fissionable by slow neutrons. U-238 has a small probability for
spontaneous fission and also a small probability of fission when
bombarded with fast neutrons, but it is not useful as a nuclear
fuel source. Some of the nuclear reactors at Hanford, Washington
and the Savannah-River Plant (SC) are designed for the
production of bomb-grade plutonium-239. Thorium-232 is
fissionable, so could conceivably be used as a nuclear fuel. The
only other isotope which is known to undergo fission upon slowneutron bombardment is uranium-233.
History of U-235 Fission
In the 1930s, German physicists/chemists Otto Hahn
and Fritz Strassman attempted to create transuranic
elements by bombarding uranium with neutrons.
Rather than the heavy elements they expected, they
got several unidentified products. When they finally
identified one of the products as Barium-141, they
were reluctant to publish the finding because it was
so unexpected. When they finally published the
results in 1939, they came to the attention of Lise
Meitner, an Austrian-born physicist who had worked
with Hahn on his nuclear experiments.
Upon Hitler's invasion of Austria, she had been
forced to flee to Sweden where she and Otto Frisch,
her nephew, continued to work on the neutron
bombardment problem. She was the first to realize
that Hahn's barium and other lighter products from
the neutron bombardment experiments were coming
from the fission of U-235. Frisch and Meitner
carried out further experiments which showed that
the U-235 fission yielded an enormous amount of
energy, and that the fission yielded at least two
neutrons per neutron absorbed in the interaction.
They realized that this made possible a chain
reaction with an unprecedented energy yield.
§9.4 Radioactive dating in Archeology
湖南马王堆汉墓
辛追
Dating in Geography
Radioactive dating
Because the radioactive half-life of a given radioisotope
is not affected by temperature, physical or chemical state,
or any other influence of the environment outside the
nucleus, then radioactive samples continue to decay at a
predictable rate. If determinations or reasonable
estimates of the original composition of a radioactive
sample can be made, then the amounts of the
radioisotopes present can provide a measurement of the
time elapsed.
carbon dating (in Archeology) is limited
to the dating of organic (once living)
materials. It is a variety of radioactive
dating which is applicable only to matter
which was once living and presumed to be
in equilibrium with the atmosphere, taking
in carbon dioxide from the air for
photosynthesis.
The longer-lived radioisotopes in minerals
provide evidence of long time scales in
geological processes. While original
compositions cannot be determined with
certainty, various combination measurements
provide self-consistent values for the the
times of formations of certain geologic
deposits. These clocks-in-the-rocks methods
(in Geography) provide data for modeling the
formation of the Earth and solar system.
Carbon Dating
Cosmic ray protons blast nuclei in
the upper atmosphere, producing
neutrons which in turn bombard
nitrogen, the major constituent of the
atmosphere.
This
neutron
bombardment
produces
the
radioactive isotope carbon-14. The
radioactive carbon-14 combines with
oxygen to form carbon dioxide and
is incorporated into the cycle of
living things.
The carbon-14 forms at a rate which appears to
be constant, so that by measuring the
radioactive emissions from once-living matter
and comparing its activity with the equilibrium
level of living things, a measurement of the time
elapsed can be made.
Carbon dating
Carbon-14 decays with a halflife of about
5730 years by the emission of an electron of
energy 0.016 MeV. This changes the atomic
number of the nucleus to 7, producing a
nucleus of nitrogen-14. At equilibrium with
the atmosphere, a gram of carbon shows an
activity of about 15 decays per minute.
The low activity of the carbon-14 limits age
determinations to the order of 50,000 years
by counting techniques. That can be
extended to perhaps 100,000 years by
accelerator techniques for counting the
carbon-14 concentration.
Clocks in the rocks
The clocks-in-the-rocks methods provide data
for modeling the formation of the Earth and
solar system.
The following radioactive decay processes have
proven particularly useful in radioactive dating for
geologic processes:
Parent half-life(billion yrs.) daughter materials
Zircon, uraninite, pitchblende, Muscovite, biotite,
hornblende, volcanic rock, glauconite, K-feldspar
Zircon, uraninite, pitchblende K-micas, Kfeldspars, biotite, metamorphic rock, glauconite
Potassium-Argon Method
40
19
K  e  Ar  
11.2%
40
19
K  Ca  e  
88.8%

40
18

40
20
It is hard to determine how much Calcium was initially present.


40

Ar
t  ln 1 
  0.112  40 K
1

,

 
T1/2 = 1.26 billion
Potassium-Argon dating has the advantage that the
argon does not react chemically, so any found
inside a rock is very likely the result of radioactive
decay of potassium. Since the argon will escape if
the rock is melted, the dates obtained are to the last
molten time for the rock. The radioactive transition
which produces the argon is electron capture.
Disadvantage: very tiny air bubbles is usually
trapped in the rock.
Rubidium-Strontium
87
37
Rb  Sr  e  e ,
87
38

T1/2 = 48.8 billion yrs
The rubidium-strontium pair is often used for dating and has a
non-radiogenic isotope, strontium-86, which can be used as a
check on original concentrations of the isotopes.
This process is often used along with potassium-argon dating on
the same rocks. The ratios of rubidium-87 and strontium-87 to the
strontium-86 found in different parts of a rock sample can be
plotted against each other in a graph called an isochron which
should be a straight line. The slope of the line gives the measured
age. The oldest ages obtained from the Rb/Sr method can be
taken as one indicator of the age of the earth.
From an example by Jelley, the following five
chondritic meteorites are reported to have the
following proportions of the rubidium and
strontium isotopes:
87Rb/86Sr
87Sr/86Sr
Modoc
0.86Sr
0.757
Homestead
0.8Sr
0.751
Bruderheim
0.72Sr
0.747
Kyushu
0.6Sr
0.739
Buth Furnace
0.09Sr
0.706
Meteorites
Uranium-Lead Dating
The Uranium-Lead method is the oldest-used
dating method (since 1907) and more complicated.
Common lead contains a mixture of four isotopes.
None of the lead isotopes is produced directly
from U and Th with a series of intermediate
products.
U  Pb ,
235
92
207
82
Th Pb ,
232
90
208
82
U  Pb
238
92
204
82
206
82
Pb : not  radiogenic
204Pb,
which is not produced by radioactive decay
provides a measure of what was "original" lead. It is
observed that for most minerals, the proportions of
the lead isotopes is very nearly constant, so the 204Pb
can be used to project the original quantities of 206Pb
and 207Pb.
This method has proved to be less reliable. Yet, three
dating systems all in one, which it is easily to
determine whether the system has been disturbed or
not.
Age of the Earth
"The oldest rocks on earth that have been dated thus far include 3.4
billion year old granites from the Barberton Mountain Land of
South Africa, 3.7 billion year old granites of southwestern
Greenland, ..." Levin, 1983
But later in 1983: "Geologists working in the mountains of western
Australia have discovered grains of rock that are 4.1 to 4.2 billion
years old, by far the oldest ever found on the Earth" This dating
was done on grains of zircon, a mineral so stable that it can retain
its identity through volcanic activity, weathering, and
sedimentation. It is a compound of zirconium, silicon and oxygen
which in its colorless form is used to make brilliant gems.
Samples more than 3.5 billion years old have been found in eight
or more locations, including Wisconsin, Minnesota, South Africa,
Greenland, and Labrador.
Meteorite Dating
Meteorites, which many consider to be remnants of
a disrupted planet that originally formed at about
the same time as the earth, have provided uraniumlead and rubidium-strontium ages of about 4.6
billion years. From such data, and from estimates
of how long it would take to produce the quantities
of various lead isotopes now found on the earth,
geochronologists feel that the 4.6-billion-year age
for the earth can be accepted with confidence."
Levin
Moon Rock Dating
The ages of rocks returned to Earth from the
Apollo missions range from 3.3 to about 4.6
billion years. The older age determinations are
derived from rocks collected on the lunar
highland, which may represent the original
lunar crust.
§9.5 Radioactive Detection
Nuclear radiation and x-rays are ionizing radiation and they can be
detected from the ionizing events they produced.
Ionization Counters
Radiation detection can be accomplished by
stretching a wire inside a gas-filled cylinder
and raising the wire to a high positive voltage.
The total charge produced by the passage of an
ionizing particle through the active volume
can be collected and measured.
Different names are used for the devices based on the amount
of voltage applied to the center electrode and the consequent
nature of the ionizing events.
 ionization chamber: The voltage is high enough for the
primary electron-ion pair to reach the electrodes but not high
enough for secondary ionization. The collected charge is
proportional to the number of ionizing events, and such devices
are typically used as radiation dosimeters.
 proportional counter: At a higher voltage, the number of
ionizations associated with a particle detection rises steeply
because of secondary ionizations. A single event can cause a
voltage pulse proportional to the energy loss of the primary
particle.
 Geiger counters: At a still higher voltage, an avalanche pulse
is produced by a single event in the devices.
Scintillation Counters
Radiation detection can be accomplished by the use of a
scintillator: a substance which emits light when struck
by an ionizing particle.
 phosphor screens (in the Geiger-Marsden
experiment): which emitted a flash of light when struck
by an alpha particle.
 single crystals of NaI doped with thallium (for
modern scintillation counters): use electrons from the
ionizing event are trapped into an excited state of the
thallium activation center and emit a photon when they
decay to the ground state.
Photomultiplier tubes are used to intensify
the signal from the scintillations. The decay
times are on the order of 200 ns and the
magnitude of the output pulse from the
photomultiplier is proportional to the energy
loss of the primary particle.
 Organic scintillators such as a mixture of
polystyrene and tetraphenyl butadine. They
have the advantage of faster decay time
(about 1 ns) and can be molded into
experimentally useful configurations.
Particle Track Devices
Radiation detection can take the form of devices
which visualize the track of the ionizing particle.
Cloud chambers can show the track of a passing particle
which can be photographed.
D. A. Glaser's invention of the bubble chamber in 1952
largely replaced the cloud chamber. Placed in an intense
magnetic field, the curvature of the tracks of the primary
particles and their products give information about their charge
and momentum.
Spark chambers can also visualize the tracks of particles and
has the advantage that the paths can be recorded electronically.
§9.6 Fundamental forces
The Electromagnetic Force
The electric force between charges may be calculated using
Coulomb's law.
The electric force is straightforward, being in the direction of
the electric field if the charge q is positive:
The Electromagnetic Force
the magnetic force on a moving charge, the direction of the
magnetic part of the force is given by the right hand rule:
The Electromagnetic Force
The electromagnetic force are summarized in
the Lorentz force law.
The electromagnetic force is a force of infinite range which
obeys the inverse square law:
Fundamentally, both magnetic and electric forces are
manifestations of an exchange force involving the
exchange of photons . The quantum approach to the
electromagnetic force is called quantum
electrodynamics or QED.
The electromagnetic force holds atoms and molecules
together. In fact, the forces of electric attraction and
repulsion of electric charges are so dominant over the
other three fundamental forces that they can be
considered to be negligible as determiners of atomic
and molecular structure. Even magnetic effects are
usually apparent only at high resolutions, and as
small corrections.
Gravity force
Gravity is the weakest of the four fundamental
forces, yet it is the dominant force in the
universe for shaping the large scale structure
of galaxies, stars, etc.
The gravitational force between two masses m1
and m2 is given by the relationship:
This is often called the "universal law of gravitation" and G the
universal gravitation constant. It is an example of an inverse
square law force. The force is always attractive and acts along
the line joining the centers of mass of the two masses. The
forces on the two masses are equal in size but opposite in
direction, obeying Newton's third law. Viewed as an exchange
force, the massless exchange particle is called the graviton (not
yet observed).
Tides
The Earth experiences two high tides per day because
of the difference in the Moon's gravitational field at
the Earth's surface and at its center:
Moon as Dominant Tidal Source
The tidal effect of the sun
is smaller than that of the
Moon because tides are
caused by the difference
in gravity field across the
Earth.
The
Earth's
diameter is such a small
fraction of the Sun-Earth
distance
The Strong Force
The strong force is the strongest of the four fundamental forces,
which can hold a nucleus together against the enormous forces of
repulsion of the protons is strong indeed. However, it is not an
inverse square force like the electromagnetic force and it has a
very short range. The range of a particle exchange force is
limited by the uncertainty principle.
At the most fundamental level the strong force is an exchange
force between quarks mediated by gluons, as modeled by
Yukawa. As an exchange force in which the exchange particles
are pions and other heavier particles.
Feynman diagram to visualize the strong interactions involves
with quarks and gluons.
The characteristics of the strong force
A short range force;
~1fm, much stronger than Coulomb force;
at the distance of atom size (~0.1nm) essentially zero,
so that each nucleon just interacts with its nearest
neighbors, and the total binding energy is proportional
to the number of nucleus.
An attractive force with a repulsive core;
nuclei are held together but they do not collapse; the
density of all nuclei is about the same, the nucleons
bound in the nucleus are tend to maintain the same
average separation
Not all particles experiences the nuclear forces;
the division of the matter into two classes of
fundamental particles, quarks and leptons.
a) the quarks are bound together by the strong
forces into hadrons, like the protons, pion, etc.
b) the leptons do not participate in the strong
interactions.
The nucleon-nucleon force is the same and
irresponsive to whether the nucleons are protons
or neutrons;
The exchange force
All four of the fundamental forces involve the exchange of one
or more particles. In 1935, Hideki Yukawa reasoned that the
electromagnetic force was infinite in range because the
exchange particle was massless. He proposed that the short
range strong force came about from the exchange of a massive
particle which he called a meson.
Such exchange forces may be either attractive or repulsive, but
are limited in range by the nature of the exchange force. The
maximum range of an exchange force is dictated by the
uncertainty principle since the particles involved are created
and exist only in the exchange process - they are called
"virtual" particles.
Range of Forces
If a force involves the exchange of a particle, in the sense that it
must fit within the constraints of the uncertainty principle. A
particle of mass m and rest energy E = mc2 can be exchanged if
it does not go outside the bounds of the uncertainty principle in
the form:

Et  mc t 
2
2
A particle which can exist only within the constraints of the
uncertainty principle is called a "virtual particle", and the time in
the expression above represents the maximum lifetime of the
virtual exchange particle. The maximum range of the force
would then be on the order of

Range  ct 
2mc
Pion Range of Strong Force
An estimate of the range of the strong force can be made
by assuming that it is an exchange force involving neutral
pions. When the range expression is used as followings:

Range  ct 
2mc
With a pion mass of
 0 mass  264me  135.0MeV / c 2
Range  0.73 10
15
m  0.61 Classical proton radius
quarks
Since the protons and neutrons which make up the nucleus are
themselves considered to be made up of quarks, and the quarks
are considered to be held together by the color force, the strong
force between nucleons may be considered to be a residual color
force. In the standard model, therefore, the basic exchange
particle is the gluon which mediates the forces between quarks.
Quark
Up
Down
Charm
Strange
Top
Bottom
Symbol Spin Charge
Baryon
S
Number
C
B
T
D
C
S
T
1/2
1/2
1/2
1/2
1/2
+2/3
-1/3
+2/3
-1/3
+2/3
1/3
1/3
1/3
1/3
1/3
0 0
0 0
0 +1
-1 0
0 0
B
1/2
-1/3
1/3
0 0 +1 0
U
0 0
0 0
0 0
0 0
0 +1
Mass*
360 MeV
360 MeV
1500 MeV
540 MeV
174 GeV
5 GeV
Elementary particles
Leptons and quarks are the basic building blocks of matter, i.e.,
they are seen as the "elementary particles". There are six
leptons in the present structure, the electron, muon, and tau
particles and their associated neutrinos. The different varieties
of the elementary particles are commonly called "flavors", and
the neutrinos here are considered to have distinctly different
flavor.
Feynman Diagrams
Feynman diagrams are graphical ways to represent exchange
forces. Developed by Feynman to describe the interactions in
quantum electrodynamics (QED), the diagrams have found
use in describing a variety of particle interactions.
They are space-time diagrams, ct vs x. The time axis points
upward and the space axis to the right. (Particle physicists often
reverse that orientation.) Each point at which lines come
together is called a vertex, and at each vertex one may examine
the conservation laws which govern particle interactions. Each
vertex must conserve charge, baryon number and lepton number.
Particles are represented by
lines with arrows to denote
the direction of their travel,
with antiparticles having
their arrows reversed. Virtual
particles are represented by
wavy or broken lines and
have no arrows.
Electromagnetic interactions
All electromagnetic interactions can be
described with combinations of primitive
diagrams like this one.
Other electromagnetic process can be represented, as in the
examples below. A backward arrow represents the
antiparticle, in these cases a positron.
Feynman diagram for strong interaction
Gluon-mediated interaction
between two quarks
The Weak Force
the weak interaction involves the exchange of the intermediate
vector bosons, the W and the Z. Since the mass of these particles
is on the order of 80 GeV, the uncertainty principle dictates a
range of about 10-18 meters which is about 0.1% of the diameter
of a proton.
It was in radioactive decay such as beta decay that the existence
of the weak interaction was first revealed. The weak interaction is
the only process in which a quark can change to another quark, or
a lepton to another lepton - the so-called "flavor changes".
The weak force
The weak interaction acts between both quarks and leptons,
whereas the strong force does not act between leptons.
"Leptons have no color, so they do not participate in the strong
interactions; neutrinos have no charge, so they experience no
electromagnetic forces; but all of them join in the weak
interactions."(Griffiths)
It is crucial to the structure of the universe in that
1. The sun would not burn without it since the weak
interaction causes the transmutation p -> n so that deuterium
can form and deuterium fusion can take place.
2. It is necessary for the buildup of heavy nuclei.
the decay of the muon
  e    e


Feynman diagram for weak force
A free neutron will decay
by emitting a W-, which
produces an electron and
an antineutrino.
A neutron or proton can
interact with a neutrino or
antineutrino by the exchange
of a Z0.
Feynman diagram for weak force
When a neutrino interacts
with a neutron, a W- can be
exchanged, transforming the
neutron into a proton and the
neutrino into an electron.
This interaction is the same as
the one at left since a W+
going right to left is
equivalent to a W- going left
to right.
the weak interaction with quarks
Feynman diagram for the four
fundamental forces
Fundamental forces