CHAPTER 13
Nuclear Interactions and Applications
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13.1
13.2
13.3
13.4
13.5
13.6
13.7
Nuclear Reactions
Reaction Kinematics
Reaction Mechanisms
Fission
Fission Reactors
Fusion
Special Applications
Ernest Lawrence, upon hearing the first self-sustaining chain reaction would be
developed at the University of Chicago in 1942 rather than at his University of
California, Berkeley lab said, “You’ll never get the chain reaction going here. The
whole tempo of the University of Chicago is too slow.”
- Quoted by Arthur Compton in Atomic Quest
1
13.1: Nuclear Reactions
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First nuclear reaction was a nitrogen target bombarded with
alpha particles, which emitted protons. The reaction is written
as:
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The first particle is the projectile and the second is the
nitrogen target. These two nuclei react to form proton
projectiles and the residual oxygen target.
The reaction can be rewritten in shorthand as: 14N(α, p)17O.
In general a reaction x + X → y + Y can be rewritten as
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X(x, y)Y
2
3 Important Technological Advances
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The high-voltage multiplier circuit was
developed in 1932 by J.D. Cockcroft and
E.T.S. Walton. This compact circuit
produces high-voltage, low-current pulses.
High voltage is required to accelerate
charged particles.
The Van de Graaff electrostatic accelerator
was developed in 1931. It produces a high
voltage from the friction between two
different materials.
3) The first cyclotron (at
left) was built in 1932. It
accelerated charged
particles using large
circular magnets.
3
Types of Reactions
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Nuclear photodisintegration is the initiation of a nuclear reaction by a
photon.
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Neutron or proton radioactive capture occurs when the nucleon is
absorbed by the target nucleus, with energy and momentum
conserved by gamma ray emission.
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The projectile and the target are said to be in the entrance channel of a
nuclear reaction. The reaction products are in the exit channel.
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In elastic scattering, the entrance and exit channels are identical and
the particles in the exit channels are not in excited states.
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In inelastic scattering, the entrance and exit channels are also identical
but one or more of the reaction products is left in an excited state.
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The reaction product need not always be in the exit channel.
4
Cross Sections
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The probability of a particular nuclear reaction occurring is determined by
measuring the cross section σ. It is determined by measuring the number of
particles produced in a given nuclear reaction.
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The number of target nuclei is
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The probability of the particle
being scattered is
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The cross section is the number of detected particles as a function of the
incoming particles. At different scattering angles, they are differential cross
sections.
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Integrating over the whole range of
scattering angles yields the total
cross sections:
5
13.2: Reaction Kinematics
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Consider the reaction: x + X → y + Y. For a target X at rest, conservation of
energy is
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Rearranging this by separating mass from energy yields a quantity similar to the
disintegration energy:
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The difference between the final and initial kinetic energies is the difference
between the initial and final mass energies. This is called the Q value.
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The energy released when Q > 0 is
from an exoergic (or exothermic)
reaction. When Q < 0, kinetic energy is
converted to mass energy in an
endoergic (or endothermic) reaction.
Collisions in this reaction are inelastic.
Elastic collisions have Q = 0.
Threshold energy for an endoergic
reaction:
6
13.3: Reaction Mechanisms
The Compound Nucleus
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For low energies of E < 10 MeV, the Coulomb force dominates the reaction. This
is described by the compound nucleus.
The compound nucleus is a composite of the projectile and target nuclei, usually
in a high state of excitation.
The kinetic energy available in the center of mass frame
can excite the compound nucleus to even higher excitation energies than that
from just the masses.
Once formed, the compound nucleus may exist for a relatively long time
compared to the time taken by the bombarding particle to cross the nucleus. This
latter time is sometimes referred to as the nuclear time scale tN.
When the compound nucleus finally does decay from its highly excited state, it
decays into all the possible exit channels according to statistical rules consistent
with the conservation laws.
7
Resonances
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Nuclear physicists study nuclear excited
states by varying the projectile bombarding
energy Kx and measuring the cross section at
each energy, generally at fixed angles for the
outgoing particles. This is called an excitation
function.
Sharp peaks in the excitation function of the
reacting particles are called resonances, and
they represent a quantum state of the
compound nucleus being formed.
The uncertainty principle may be used to
relate the energy width of a particular nuclear
state (called Γ) to its lifetime (called τ):
8
Resonances
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Because neutrons have zero net
charge, they interact more easily with
nuclei at low energies than do
charged particles, because of the
Coulomb barrier. This process is
called neutron activation and the
reaction is called neutron radioactive
transfer.
The average neutron capture cross
section (at energies up to about 100
keV) varies empirically as 1/v, where
v is the neutron’s velocity. The 1/v
dependence can be explained in
terms of the time the neutron spends
near the nucleus.
9
Direct Reactions
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For large bombarding energies, the bombarding particle spends
less time within the range of the nuclear force. Stripping one or
more nucleons off the projectile or picking up one or more
nucleons from the target becomes more probable.
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The projectile could also knock out energetic nucleons from the
target nucleus.
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These are called direct reactions.
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The chief advantage of direct reactions is that the final residual
nucleus may be left in any one of many low-lying excited states.
By using different direct reactions, the nuclear excited states can
be studied in a variety of ways to learn more about nuclear
structure.
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13.4: Fission
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In fission a nucleus separates into two fission
fragments. As we will show, one fragment is
typically somewhat larger than the other.
Fission occurs for heavy nuclei because of
the increased Coulomb forces between the
protons.
We can understand fission by using the
semi-empirical mass formula based on the
liquid drop model. For a spherical nucleus of
with mass number A ~ 240, the attractive
short-range nuclear forces offset the
Coulomb repulsive term. As a nucleus
becomes nonspherical, the surface energy is
increased, and the effect of the short-range
nuclear interactions is reduced.
Nucleons on the surface are not surrounded
by other nucleons, and the unsaturated
nuclear force reduces the overall nuclear
attraction. For a certain deformation, a
critical energy is reached, and the fission
barrier is overcome.
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Spontaneous fission can
occur for nuclei with
11
Induced Fission
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Fission may also be induced by a nuclear reaction. A neutron absorbed by
a heavy nucleus forms a highly excited compound nucleus that may
quickly fission.
An induced fission example is
The fission products have a ratio of N/Z much too high to be stable for
their A value.
There are many possibilities for the Z and A of the fission products.
Symmetric fission (products with equal Z) is possible, but the most
probable fission is asymmetric (one mass larger than the other).
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Thermal Neutron Fission
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Fission fragments are highly unstable because
they are so neutron rich.
Prompt neutrons are emitted simultaneously
with the fissioning process. Even after prompt
neutrons are released, the fission fragments
undergo beta decay, releasing more energy.
Most of the ~200 MeV released in fission goes
to the kinetic energy of the fission products, but
the neutrons, beta particles, neutrinos, and
gamma rays typically carry away 30–40 MeV of
the kinetic energy.
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Chain Reactions
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Because several neutrons are produced in
fission, these neutrons may subsequently
produce other fissions. This is the basis of the
self-sustaining chain reaction.
If slightly more than one neutron, on the
average, results in another fission, the chain
reaction becomes critical.
A sufficient amount of mass is required for a
neutron to be absorbed, called the critical mass.
If less than one neutron, on the average,
produces another fission, the reaction is
subcritical.
If more than one neutron, on the average,
produces another fission, the reaction is
supercritical.
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An atomic bomb is an extreme example of a
supercritical fission chain reaction.
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Chain Reactions
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A critical-mass fission reaction can be controlled by absorbing
neutrons. A self-sustaining controlled fission process requires
that not all the neutrons are prompt. Some of the neutrons are
delayed by several seconds and are emitted by daughter
nuclides. These delayed neutrons allow the control of the
nuclear reactor.
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Control rods regulate the absorption of neutrons to sustain a
controlled reaction.
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13.5: Fission Reactors
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Several components are important
for a controlled nuclear reactor:
1)
2)
3)
4)
5)
6)
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Fissionable fuel
Moderator to slow down neutrons
Control rods for safety and to
control criticality of reactor
Reflector to surround moderator
and fuel in order to contain
neutrons and thereby improve
efficiency
Reactor vessel and radiation shield
Energy transfer systems if
commercial power is desired
Two main effects can “poison”
reactors: (1) neutrons may be
absorbed without producing fission
[for example, by neutron radiative
capture], and (2) neutrons may
escape from the fuel zone.
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Core Components
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Fission neutrons typically have 1–2 MeV of kinetic energy, and because
the fission cross section increases as 1/v at low energies, slowing down
the neutrons helps to increase the chance of producing another fission.
A moderator is used to elastically scatter the high-energy neutrons and
thus reduce their energies. A neutron loses the most energy in a single
collision with a light stationary particle. Hydrogen (in water), carbon
(graphite), and beryllium are all good moderators.
The simplest method to reduce the loss of neutrons escaping from the
fissionable fuel is to make the fuel zone larger. The fuel elements are
normally placed in regular arrays within the moderator.
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Core Components
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The delayed neutrons
produced in fission allow the
mechanical movement of the
rods to control the fission
reaction. A “fail-safe” system
automatically drops the control
rods into the reactor in an
emergency shutdown.
If the fuel and moderator are
surrounded by a material with a
very low neutron capture cross
section, there is a reasonable
chance that after one or even
many scatterings, the neutron
will be backscattered or
“reflected” back into the fuel
area. Water is often used both
as moderator and reflector.
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Energy Transfer
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The most common method is to pass hot
water heated by the reactor through some
form of heat exchanger.
In boiling water reactors (BWRs) the
moderating water turns into steam, which
drives a turbine producing electricity.
In pressurized water reactors (PWRs) the
moderating water is under high pressure and
circulates from the reactor to an external
heat exchanger where it produces steam,
which drives a turbine.
Boiling water reactors are inherently simpler
than pressurized water reactors. However,
the possibility that the steam driving the
turbine may become radioactive is greater
with the BWR. The two-step process of the
PWR helps to isolate the power generation
system from possible radioactive
contamination.
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Types of Reactors
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Power reactors produce commercial electricity.
Research reactors are operated to produce high
neutron fluxes for neutron-scattering experiments.
Heat production reactors supply heat in some cold
countries.
Some reactors are designed to produce radioisotopes.
Several training reactors are located on college
campuses.
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Nuclear Reactor Problems
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The danger of a serious accident in which radioactive elements are
released into the atmosphere or groundwater is of great concern to
the general public.
Thermal pollution both in the atmosphere and in lakes and rivers used
for cooling may be a significant ecological problem.
A more serious problem is the safe disposal of the radioactive wastes
produced in the fissioning process, because some fission fragments
have a half-life of thousands of years.
Two widely publicized accidents at nuclear reactor facilities—one at
Three Mile Island in Pennsylvania in 1979, the other at Chernobyl in
Ukraine in 1986—have significantly dampened the general public’s
support for nuclear reactors.
Large expansion of nuclear power can succeed only if four critical
problems are overcome: lower costs, improved safety, better nuclear
waste management, and lower proliferation risk.
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Breeder Reactors
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A more advanced kind of reactor is the breeder reactor, which
produces more fissionable fuel than it consumes.
The chain reaction is:
The plutonium is easily separated from uranium by chemical means.
Fast breeder reactors have been built that convert 238U to 239Pu. The
reactors are designed to use fast neutrons.
Breeder reactors hold the promise of providing an almost unlimited
supply of fissionable material.
One of the downsides of such reactors is that plutonium is highly
toxic, and there is concern about its use in unauthorized weapons
production.
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13.6: Fusion
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If two light nuclei fuse together, they also form a nucleus
with a larger binding energy per nucleon and energy is
released. This reaction is called nuclear fusion.
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The most energy is released if two isotopes of hydrogen
fuse together in the reaction.
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Formation of Elements
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The proton-proton chain includes a series of reactions that
eventually converts four protons into an alpha particle.
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As stars form due to gravitational attraction of interstellar
matter, the heat produced by the attraction is enough to cause
protons to overcome their Coulomb repulsion and fuse by the
following reaction:
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The deuterons are then able to combine with 1H to produce
3He:
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The 3He atoms can then combine to produce 4He:
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Formation of Elements
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As the reaction proceeds, however, the temperature increases, and
eventually 12C nuclei are formed by a process that converts three 4He
into 12C.
Another cycle due to carbon is also able to produce 4He. The series of
reactions responsible for the carbon or CNO cycle are
Proton-proton and CNO cycles are the only nuclear reactions that can
supply the energy in stars.
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Hydrostatic Equilibrium
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A hydrostatic equilibrium exists in the sun between the gravitational
attraction tending to contract a star and a gas pressure pushing out
due to all the particles.
As the lighter nuclides are “burned up” to produce the heavier
nuclides, the gravitational attraction succeeds in contracting the
star’s mass into a smaller volume and the temperature increases. A
higher temperature allows the nuclides with higher Z to fuse.
This process continues in a star until a large part of the star’s mass
is converted to iron. The star then collapses under its own
gravitational attraction to become, depending on its mass, a white
dwarf star, neutron star, or black hole. It may even undergo a
supernova explosion.
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Nuclear Fusion on Earth
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Among the several possible fusion reactions, three of the
simplest involve the three isotopes of hydrogen.
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Three main conditions are necessary for controlled nuclear
fusion:
The temperature must be hot enough to allow the ions, for example,
deuterium and tritium, to overcome the Coulomb barrier and fuse their
nuclei together. This requires a temperature of 100–200 million K.
2) The ions have to be confined together in close proximity to allow the
ions to fuse. A suitable ion density is 2–3 × 1020 ions/m3.
3) The ions must be held together in close proximity at high temperature
long enough to avoid plasma cooling. A suitable time is 1–2 s.
1)
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Fusion Product
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The product of the plasma density n and the containment time τ must
have a minimum value at a sufficiently high temperature in order to
initiate fusion and produce as much energy as it consumes. The
minimum value is
This relation is called the Lawson criterion after the British physicist
J. D. Lawson who first derived it in 1957. A triple product of nτT
called the fusion product is sometimes used (where T is the ion
temperature).
The factor Q is used to represent the ratio of the power produced in
the fusion reaction to the power required to produce the fusion (heat).
This Q factor is not to be confused with the Q value.
The breakeven point is Q = 1, and ignition occurs for Q >> 1. For
controlled fusion produced in the laboratory, temperatures on the
order of 20 keV are satisfactory.
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Controlled Thermonuclear Reactions
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Because of the large amount of energy produced and the relatively small Coulomb barrier, the first
fusion reaction will most likely be the D + T reaction. The tritium will be derived from two possible
reactions:
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The problem of controlled fusion involves significant scientific and engineering difficulties. The two
major schemes to control thermonuclear reactions are magnetic confinement fusion (MCF) and
inertial confinement fusion (ICF).
Magnetic confinement of plasma is done in a tokomak, which has many confinement boundaries.
Heating of the plasma to sufficiently high temperatures begins with the resistive heating from the
electric current flowing in the plasma. There are two other schemes to add additional heat: (1)
injection of high-energy (40–120 keV) neutral (so they pass through the magnetic field) fuel atoms
that interact with the plasma, and (2) radio-frequency (RF) induction heating of the plasma (similar
to a microwave oven).
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Inertial Confinement
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The concept of inertial confinement fusion is to use an intense highpowered beam of heavy ions or light (laser) called a driver to implode a
pea-sized target (a few mm in diameter) composed of D + T to a density
and temperature high enough to cause fusion ignition.
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The National Ignition Facility at
Livermore will use 192 lasers to
create a thermonuclear burn for
research purposes.
Sandia National Laboratories has
used a device called a Z-pinch
that uses a huge jolt of current to
create a powerful magnetic field
that squeezes ions into implosion
and heats the plasma. Sandia
has proposed an upgrade that
may be a serious contender in
the fusion race.
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13.7: Special Applications
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A specific isotope of a radioactive element is called a
radioisotope.
Radioisotopes are produced for useful purposes by different
methods:
1) By particle accelerators as reaction products
2) In nuclear reactors as fission fragments or decay
products
3) In nuclear reactors using neutron activation
An important area of applications is the search for a very small
concentration of a particular element, called a trace element.
Trace elements are used in detecting minute quantities of trace
elements for forensic science and environmental purposes.
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Medicine
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Over 1100 radioisotopes are
available for clinical use.
Radioisotopes are used in
tomography, a technique for
displaying images of practically
any part of the body to look for
abnormal physical shapes or
for testing functional
characteristics of organs. By
using detectors (either
surrounding the body or
rotating around the body)
together with computers, threedimensional images of the body
can be obtained.
They use single-photon
emission computed
tomography, positron emission
tomography, and magnetic
resonance imaging.
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Archaeology
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Investigators can now measure a large number of trace elements in
many ancient specimens and then compare the results with the
concentrations of components having the same origin.
Radioactive dating indicates that humans had a settlement near
Clovis, New Mexico 12,000 years ago. Several claims have surfaced
in the past few years, especially from South America, that dispute
this earliest finding, but no conclusive proof has been confirmed.
The Chauvet Cave, discovered in France in 1995, is one of the most
important archaeological finds in decades. More than 300 paintings
and engravings and many traces of human activity, including hearths,
fiintstones, and footprints, were found. These works are believed,
from 14C radioactive dating, to be from the Paleolithic era, some
32,000 years ago.
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Art
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Neutron activation is a nondestructive technique that is
becoming more widely used to examine oil paintings. A
thermal neutron beam from a nuclear reactor is spread
broadly and evenly over the painting. Several elements
within the painting become radioactive. X-ray films
sensitive to beta emissions from the radioactive nuclei
are subsequently placed next to the painting for varying
lengths of time. This method is called an autoradiograph.
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It was used to examine Van Dyck’s Saint Rosalie
Interceding for the Plague-Stricken of Palermo, from the
New York Metropolitan Museum of Art collection and
revealed an over-painted self-portrait of Van Dyck
himself.
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Crime Detection
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The examination of gunshots by measuring trace
amounts of barium and antimony from the gunpowder
has proven to be 100 to 1000 times more sensitive than
looking for the residue itself.
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Scientists are also able to detect toxic elements in hair by
neutron activation analysis.
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Mining and Oil
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Geologists and petroleum engineers use radioactive sources routinely to
search for oil and gas. A source and detector are inserted down an
exploratory drill hole to examine the material at different depths. Neutron
sources called PuBe (plutonium and beryllium) or AmBe (americium and
beryllium) are particularly useful.
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The neutrons activate nuclei in the
material surrounding the borehole, and
these nuclei produce gamma decays
characteristic of the particular element.
36
Materials
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Natural silicon consists of 3.1% of the isotope 30Si, which
undergoes the reaction
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Phosphorus-doped silicon can be produced with fast-neutron
irradiation. Apparently the neutrons reduce the intrinsic resistivity
in the silicon substrate so that the extraneous ionization caused
later is much less likely to reset a bit.
Neutrons are particularly useful because they have no charge and
do not ionize the material, as do charged particles and photons.
They penetrate matter easily and introduce uniform lattice
distortions or impurities. Because they have a magnetic dipole
moment, neutrons can probe bulk magnetization and spin
phenomena.
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37
Small Power Systems
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Alpha-emitting radioactive sources have been used
as power sources in heart pacemakers.
Smoke detectors use 241Am sources of alpha
particles as current generators. The scattering of the
alpha particles by the smoke particles reduces the
current flowing to a sensitive solid-state device,
which results in an alarm.
Spacecraft have been powered by radioisotope
generators (RTGs) since the early 1960s.
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New Elements
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No transuranic elements—those with atomic number greater than
Z = 92 (uranium)—are found in nature because of their short half-lives.
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Reactors and especially accelerators have been able to produce 22 of
these new elements up to Z = 116.
Over 150 new isotopes heavier than uranium have been discovered.
Physicists have reasons to suspect from shell model calculations that
superheavy elements with atomic numbers of 110–120 and 184
neutrons may be particularly long-lived.
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39