The international sign of radioactivity

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The international sign of radioactivity
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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.
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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.
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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.

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• 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.

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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
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1934, Mrs. and Mr. F. I. Joliot Curie
discovered man-made 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.
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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.

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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
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The electrons, protons and neutrons which make up
an atom have definite charges and masses
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Element atoms with the same atomic number
ZIsotope the same elements with different
neutron numberNuclide 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.
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Chart of Nuclide
Nuclide byland
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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.
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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).
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9.2 radioactivity
Radioactivity means atoms decay, which emit some
kind of radiation. The reason for these decays is
that they are instable.
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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.
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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.
N the number of nuclei -dN the number of
nuclei decayed ? decay constant, the
probability of nuclei decay in a unit time
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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.
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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.
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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
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Activity the intensity of radioactive source
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.
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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.
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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.
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? radioactivity

• particle composes of two protons and two
  neutrons, the alpha particle is a nucleus of the
  element of helium.
• decay

For instance
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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.
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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.
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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
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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 Nuclea
r binding energy ?mc2
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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.
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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.
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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.
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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.
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The beta decay
The energy released in decay, Q
Q 1.71 Mev for 32P ? 32S
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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.
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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.
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From the Fermi theory of beta decay, the shape of
the energy distribution for this "allowed"
transition is given approximately by the
expression
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.
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Gamma Radioactivity
Gamma radioactivity is composed of
electromagnetic rays.
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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 x-rays 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.
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Gamma Radioactivity
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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
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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.
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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.
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Radioactive Decay Paths
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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.
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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
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Some Nuclear Reactions
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Nuclear Binding Energy curve
Iron limit
Nuclear binding energy ?mc2
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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.
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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.
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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).
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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.
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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. Uranium-238,
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 slow-neutron
bombardment is uranium-233.
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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.
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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.
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9.4 Radioactive dating in Archeology
??????? ??
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Dating in Geography
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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.
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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.
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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.
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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.
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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.
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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.
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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
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Zircon, uraninite, pitchblende, Muscovite,
biotite, hornblende, volcanic rock, glauconite,
K-feldspar Zircon, uraninite, pitchblende
K-micas, K-feldspars, biotite, metamorphic rock,
glauconite
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Potassium-Argon Method
11.2 88.8
It is hard to determine how much Calcium was
initially present.
T1/2 1.26 billion
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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.
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Rubidium-Strontium
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.
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From an example by Jelley, the following five
chondritic meteorites are reported to have the
following proportions of the rubidium and
strontium isotopes
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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.
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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.
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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.
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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
uranium-lead 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
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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.
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9.5 Radioactive Detection
Nuclear radiation and x-rays are ionizing
radiation and they can be detected from the
ionizing events they produced.
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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.
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• 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.

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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.

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• 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.

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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.

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9.6 Fundamental forces
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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
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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
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The Electromagnetic Force
The electromagnetic force are summarized in the
Lorentz force law.
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The electromagnetic force is a force of infinite
range which obeys the inverse square law
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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.
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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.
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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).
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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
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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
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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.
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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

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• 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

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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.
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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
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
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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
With a pion mass of
98
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.
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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.
100
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.
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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.
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Electromagnetic interactions
All electromagnetic interactions can be described
with combinations of primitive diagrams like this
one.
103
Other electromagnetic process can be represented,
as in the examples below. A backward arrow
represents the antiparticle, in these cases a
positron.
104
Feynman diagram for strong interaction
Gluon-mediated interaction between two quarks
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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".
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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 -gt n so
that deuterium can form and deuterium fusion can
take place. 2. It is necessary for the buildup of
heavy nuclei.
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the decay of the muon
108
Feynman diagram for weak force
A neutron or proton can interact with a neutrino
or antineutrino by the exchange of a Z0.
A free neutron will decay by emitting a W-, which
produces an electron and an antineutrino.
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Feynman diagram for weak force
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.
When a neutrino interacts with a neutron, a W-
can be exchanged, transforming the neutron into a
proton and the neutrino into an electron.
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the weak interaction with quarks
111
Feynman diagram for the four fundamental forces
112
Fundamental forces