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CHAPTER 1
Nuclear Radiation Review
Some Nuclear Units
Nuclear energies are very high compared to atomic processes, and need larger units
However, the sizes are quite small and need smaller units:
Nuclear masses are measured in terms of atomic mass units with the carbon-12
nucleus defined as having a mass of exactly 12 amu. It is also common practice to
quote the rest mass energy as if it were the mass. The conversion to amu is:
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Introduction
Relativistic Energy
The famous Einstein relationship for energy
includes both the kinetic energy and rest mass energy for a particle. The kinetic
energy of a high speed particle can be calculated from
The relativistic energy of a particle can also be expressed in terms of its momentum
in the expression
The relativistic energy expression is the tool used to calculate binding energies of
nuclei and the energy yields of nuclear fission and fusion.
Kinetic Energy
Kinetic energy is energy of motion. The kinetic energy of an object is the energy it
possesses because of its motion. The kinetic energy* of a point mass m is given by
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Kinetic energy is an expression of the fact that a moving object can do work on
anything it hits; it quantifies the amount of work the object could do as a result of
its motion. The total mechanical energy of an object is the sum of its kinetic energy
and potential energy.
For an object of finite size, this kinetic energy is called the translational kinetic
energy of the mass to distinguish it from any rotational kinetic energy it might possess - the total kinetic energy of a mass can be expressed as the sum of the translational kinetic energy of its center of mass plus the kinetic energy of rotation about
its center of mass.
*This assumes that the speed is much less than the speed of light. If the speed is
comparable with c then the relativistic kinetic energy expression must be used.
Rest Mass Energy
The Einstein equation includes both the kinetic energy of a particle and the energy
it has as a result of its mass. If the particle is at rest, then the energy is expressed as
which is sometimes called its rest mass energy.
Conservation of Energy
The relativistic energy expression is a statement about the energy an object contains
as a result of its mass and is not to be construed as an exception to the principle of
conservation of energy. Energy can exist in many forms, and mass energy can be
considered to be one of those forms.
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Introduction
Pair Production
Every known particle has an antiparticle; if they encounter one another, they will
annihilate with the production of two gamma-rays. The quantum energies of the
gamma rays is equal to the sum of the mass energies of the two particles (including
their kinetic energies). It is also possible for a photon to give up its quantum energy
to the formation of a particle-antiparticle pair in its interaction with matter.
The rest mass energy of an electron is 0.511 MeV, so the threshold for electronpositron pair production is 1.02 MeV. For X-ray and gamma-ray energies well
above 1 MeV, this pair production becomes one of the most important kinds of
interactions with matter. At even higher energies, many types of particle-antiparticle pairs are produced.
Relativistic Kinetic Energy
The relativistic energy expression includes both rest mass energy and the kinetic
energy of motion. The kinetic energy is then given by
This is essentially defining the kinetic energy of a particle as the excess of the particle energy over its rest mass energy. For low velocities this expression approaches
the non-relativistic kinetic energy expression.
Kinetic Energy for v/c<<1
The relativistic kinetic energy expression can be written as
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and the square root expression then expanded by use of the binomial theorem
given
substituting gives
Relative scale model of an atom and the solar
system
Do you perceive a gold ring to contain a larger fraction of solid matter than the
solar system?
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Introduction
On this scale, the nearest star would be a little over 10,000 miles away.
Data for Scale Model of Atom
Nuclear Size and Density
Various types of scattering experiments suggest that nuclei are roughly spherical
and appear to have essentially the same density. The data are summarized in the
expression called the Fermi model:
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Introduction
where r is the radius of the nucleus of mass number A. The assumption of constant
density leads to a nuclear density.
The most definitive information about nuclear sizes comes from electron scattering.
Nuclear Density and the Strong Force
The fact that the nuclear density seems to be independent of the details of neutron
number or proton number implies that the force between the particles is essentially
the same whether they are protons or neutrons. This correlates with other evidence
that the strong force is the same between any pair of nucleons.
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Introduction
Nuclear Forces
Within the incredibly small nuclear size, the two strongest forces in nature are pitted against each other. When the balance is broken, the resultant radioactivity yields
particles of enormous energy.
The electron in a hydrogen atom is attracted to the proton nucleus with a force so
strong that gravity and all other forces are negligible by comparison. But two protons touching each other would feel a repulsive force over 100 million times stronger! So how can such protons stay in such close proximity? This may give you
some feeling for the enormity of the nuclear strong force which holds the nuclei
together.
The Electromagnetic Force
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Introduction
One of the four fundamental forces, the electromagnetic force manifests itself
through the forces between charges (Coulomb's Law) and the magnetic force, both
of which are summarized in the Lorentz force law. Fundamentally, both magnetic
and electric forces are manifestations of an exchange force involving the exchange
of photons. The electromagnetic force is a force of infinite range which obeys the
inverse square law, and is of the same form as the gravity force.
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.
Nuclear Particles
Nuclei are made up of protons and neutrons bound together by the strong force.
Both protons and neutrons are referred to as nucleons. The number of protons is
called the atomic number and determines the chemical element. Nuclei of a given
element (same atomic number) may have different numbers of neutrons and are
then said to be different isotopes of the element.
Proton
Along with neutrons, protons make up the nucleus, held together by the strong
force. The proton is a baryon and is considered to be composed of two up quarks
and one down quark.
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Introduction
It has long been considered to be a stable particle, but recent developments of grand
unification models have suggested that it might decay with a half-life of about 1031
years. Experiments are underway to see if such decays can be detected. Decay of
the proton would violate the conservation of baryon number, and in doing so would
be the only known process in nature which does so.
When we say that a proton is made up of two up quarks and a down, we mean that
its net appearance or net set of quantum numbers match that picture. The nature of
quark confinement suggests that the quarks are surrounded by a cloud of gluons,
and within the tiny volume of the proton other quark-antiquark pairs can be produced and then annihilated without changing the net external appearance of the proton.
Neutron
Along with protons, neutrons make up the nucleus, held together by the strong
force. The neutron is a baryon and is considered to be composed of two down
quarks and one up quark.
A free neutron will decay with a half-life of about 10.3 minutes but it is stable if
combined into a nucleus. The decay of the neutron involves the weak interaction as
indicated in the Feynman diagram to the right. This fact is important in models of
the early universe. The neutron is about 0.2% more massive than a proton, which
translates to an energy difference of 1.29 MeV.
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The decay of the neutron is associated with a quark transformation in which a down
quark is converted to an up by the weak interaction.
The Strong Force
A force 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. Yukawa modeled the strong
force as an exchange force in which the exchange particles are pions and other
heavier particles. The range of a particle exchange force is limited by the uncertainty principle. It is the strongest of the four fundamental forces.
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Introduction
Nuclear Notation
Standard nuclear notation shows the chemical symbol, the mass number and the
atomic number of the isotope.
Example: the isotopes of carbon. The element is determined by the atomic number
6. Carbon-12 is the common isotope, with carbon-13 as another stable isotope
which makes up about 1%. Carbon 14 is radioactive and the basis for carbon dating.
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 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. Since the individual gluons and quarks are contained within the proton or neutron, the masses attributed to them cannot be used in
the range relationship to predict the range of the force. When something is viewed
as emerging from a proton or neutron, then it must be at least a quark-antiquark
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pair, so it is then plausible that the pion as the lightest meson should serve as a predictor of the maximum range of the strong force.
Isotopes
The different isotopes of a given element have the same atomic number but different mass numbers since they have different numbers of neutrons. The chemical
properties of the different isotopes of an element are identical, but they will often
have great differences in nuclear stability. For stable isotopes light elements, the
number of neutrons will be almost equal to the number of protons, but a growing
neutron excess is characteristic of stable heavy elements. The element tin (Sn) has
the most stable isotopes with 10, the average being about 2.6 stable isotopes per
element.
Information about the isotopes of each element and their abundance can be found
by going to the periodic table and choosing an element. Then take the link to
nuclear data.
Radioactivity
Radioactivity refers to the particles which are emitted from nuclei as a result of
nuclear instability. Because the nucleus experiences the intense conflict between
the two strongest forces in nature, it should not be surprising that there are many
nuclear isotopes which are unstable and emit some kind of radiation. The most
common types of radiation are called alpha, beta, and gamma radiation, but there
are several other varieties of radioactive decay.
Radioactive decay rates are normally stated in terms of their half-lives, and the
half-life of a given nuclear species is related to its radiation risk. The different types
of radioactivity lead to different decay paths which transmute the nuclei into other
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Introduction
chemical elements. Examining the amounts of the decay products makes possible
radioactive dating.
Radiation from nuclear sources is distributed equally in all directions, obeying the
inverse square law.
Alpha Radioactivity
Composed of two protons and two neutrons, the alpha particle is a nucleus of the
element helium. 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. It 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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Introduction
Alpha particle emission is modeled as a barrier penetration process. The alpha particle is the nucleus of the helium atom and is the nucleus of highest stability.
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.
The resolution of this dilemma came with the realization that there was a finite
probability that the alpha particle could penetrate the wall by quantum mechanical
tunneling. Using tunneling, Gamow was able to calculate a dependence for the halflife as a function of alpha particle energy which was in agreement with experimental observations.
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Introduction
Alpha Binding Energy
The nuclear binding energy of the alpha particle is extremely high, 28.3 MeV. It is
an exceptionally stable collection of nucleons, and those heavier nuclei which can
be viewed as collections of alpha particles (carbon-12, oxygen-16, etc.) are also
exceptionally stable. This contrasts with a binding energy of only 8 MeV for
helium-3, which forms an intermediate step in the proton-proton fusion cycle.
Alpha, Beta, and Gamma
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
Though 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
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Introduction
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.
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.
Graph of Radioactive Decay
The radioactive half-life gives a pattern of reduction to half in any successive halflife period.
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Introduction
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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Introduction
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 save direct particle interactions with 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.
One such method is called carbon dating, which is limited to the dating of organic
(once living) materials. 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 selfconsistent values for the times of formations of certain geologic deposits. These
clocks-in-the-rocks methods provide data for modeling the formation of the Earth
and solar system.
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. The high energy electrons have greater range of penetration than alpha particles, but still much less than
gamma rays. The radiation hazard from betas is greatest if they are ingested.
Beta emission is accompanied by the emission of an electron antineutrino which
shares the momentum and energy of the decay.
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Introduction
The emission of the electron's antiparticle, the positron, is also called beta decay.
Electron and Antineutrino
Early studies of beta decay revealed a continuous energy spectrum up to a maximum, unlike the predictable energy of alpha particles. Another anomaly was the
fact that the nuclear recoil was not in the direction opposite the momentum of the
electron. The emission of another particle was a probable explanation of this behavior, but searches found no evidence of either mass or charge. Pauli in 1930 proposed a particle called a neutrino which could carry away the missing energy and
momentum. With no charge and no mass, it was hard to detect, and not until 1953
was experimental detection of the neutrino achieved. For symmetry reasons, the
particle emitted along with the electron from nuclei is called an antineutrino. The
emission of a positron is accompanied by a neutrino.
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 churchless 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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Introduction
Beta Energy Spectrum
In the process of beta decay, either an electron or a positron is emitted. Because
either a neutrino or an antineutrino is emitted as well, 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.
Energy and Momentum Spectra for Beta Decay
Beta emission has a characteristic energy spectrum. It is accompanied by the emission of an electron antineutrino which shares the momentum and energy of the
decay.
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Introduction
This experimental energy spectrum is from G. J. Neary, Proc. Phys. Soc. (London),
A175, 71 (1940).
The emission of the electron's antiparticle, the positron, is also called beta decay.
Gamma Radioactivity
Gamma radioactivity is composed of electromagnetic rays. It 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 thicknesses of material.
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Introduction
Other Radioactive Processes
While the most common types of radioactive decay are by alpha, beta, and gamma
radiation, several other varieties of radioactivity occur:
Electron capture: A parent nucleus may capture one of its own electrons and emit a
neutrino. This is exhibited in the potassium-argon decay.
Positron or positive beta decay: Positron emission is called beta decay because the
characteristics of electron or positron decay are similar. They both show a characteristic energy spectrum because of the emission of a neutrino or antineutrino.
Internal conversion is the use of electromagnetic energy from the nucleus to expel
an orbital electron from the atom.
Electron Capture
Electron capture is one form of radioactivity. A parent nucleus may capture one of
its orbital electrons and emit a neutrino. This is a process which competes with
positron emission and has the same effect on the atomic number. Most commonly,
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Introduction
it is a K-shell electron which is captured, and this is referred to as K-capture. A typical example is
In the middle range of the periodic table, those isotopes which are lighter than the
most stable isotopes tend to decay by electron capture, and those heavier decay by
negative beta decay. An example of this pattern is seen with silver isotopes, with
two stable isotopes plus one of lower mass which decays by electron capture and
one of heavier mass which decays by beta emission.
Internal Conversion
Internal conversion is another electromagnetic process which can occur in the
nucleus and which competes with gamma emission. Sometimes the multipole electric fields of the nucleus interact with orbital electrons with enough energy to eject
them from the atom. 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.
An example used by Krane is that of 203Hg, which decays to 203Tl by beta emission, leaving the 203Tl in an electromagnetically excited state. It can proceed to the
ground state by emitting a 279.190 keV gamma ray, or by internal conversion. In
this case the internal conversion is more probable. Since the internal conversion
process can interact with any of the orbital electrons, the result is a spectrum of
internal conversion electrons which will be seen as superimposed upon the electron
energy spectrum of the beta emission. The energy yield of this electromagnetic
transition can be taken as 279.190 keV, so the ejected electrons will have that
energy minus their binding energy in the 203Tl daughter atom.
Electron emissions from the Hg-203 to Tl-203 decay, measured by A. H. Wapstra,
et al., Physica 20, 169 (1954).
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At higher resolution, the internal conversion electrons from the L, M and N shells
can be resolves. Z. Sujkowski, Ark. Fys. 20, 243 (1961).
At even higher resolution, the three L shells can be resolved. From C. J. Herrlander
and R. L. Graham, Nucl. Phys. 58, 544 (1964).
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Introduction
The resolution of the electron detection is good enough that such internal conversion electron spectra can be used to study the binding energies of the electrons in
heavy atoms. In this case, the measured electron energies can be subtracted from
the transition energy as indicated by the gamma emission, 279.190 keV.
Binding energies for T-203l
K: 85.529 keV
LI: 15.347 keV
LII: 14.698 keV
LIII: 12.657 keV
M: 3.704 keV
In addition to information from the internal conversion electrons about the binding
energies of the electrons in the daughter atom, the relative intensities of these internal conversion electron peaks can give information about the electric multipole
character of the nucleus.
Discovery of Radioactivity
Radioactivity was discovered by A. H. Becquerel in 1896. The radiation was classified by E. Rutherford as alpha, beta, and gamma rays according to their ability to
penetrate matter and ionize air.
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Introduction
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. Of particular note is the resonant
absorption of gamma rays in the Mossbauer effect. 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.
We can characterize the energetics 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”.
Some Nuclear Reactions
* The nuclear reaction in the atmosphere which produces carbon-14 for radiocarbon dating.
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Introduction
Data from C. W. Li, W. Whaling, W. A. Fowler, and C. C. Lauritson, Physical
Review 83:512 (1951)
Nuclear Cross Section
To characterize the probability that a certain nuclear reaction will take place, it is
customary to define an effective size of the nucleus for that reaction, called a cross
section. The cross section is defined by
The cross section has the units of area and is on the order of the square of the
nuclear radius. A commonly used unit is the barn:
A standard old story was that in the early days of the field, a particular cross section
turned out to be much bigger than expected. An experimenter exclaimed “Why,
that's as big as a barn!” and a unit name was born.
Scattering Cross Section
The concept of cross section, as its name suggests, is that of effective area for collision. The cross section of a spherical target is
In aiming a beam of particles at a target which is much smaller than the beam, as in
the Rutherford scattering experiment, the cross section takes on a statistical nature.
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Rutherford worked out the scattering cross section for alpha particles of kinetic
energy KE scattering off a single nucleus with atomic number Z. The cross section
for scattering at a greater angle than some chosen angle is
More detail is needed for the prediction of the number of scattering events to expect
above that angle. When the details about the beam and target are included, the fractional scattering rate is given by
The process for dealing with multiple targets is illustrated below
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Introduction
Scattering Cross Section
The concept of cross section, as its name suggests, is that of effective area for collision. The cross section of a spherical target is
The units of cross section are then area units, but for nuclear scattering the effective
area is on the order of the cross sectional area of a nucleus. For a gold nucleus of
mass number A=197, the radius determined from the nuclear radius relationship is
about 7 fermis.
The most common unit for cross section for nuclear scattering interactions is the
barn. The cross section in barns for alpha scattering above a selected angle is a standard part of the analysis of Rutherford scattering. In the case of 6 MeV alpha particles scattered from a gold foil, for example, you don't know the impact parameter
for any given alpha particle, so the calculation of the scattered fraction takes on a
statistical character. For alpha particles bombarding a gold foil of thickness 1
micrometer, less than 1 in 100,000 would meet the conditions for scattering at over
140°. The cross section for scattering at smaller angles will be larger, because the
alpha doesn't have to come as close to be scattered through the smaller angle. For
example, the cross section for scattering through 90° or above is 11.3 barns.
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For neutron scattering, there is no coulomb repulsion, so there is no appreciable
scattering unless the impact parameter is less than the effective radius for the strong
interaction. Therefore for a given target geometry the cross sections are smaller,
typically measured in millibarns.
The Value of the Cross-Section Concept
If you are firing projectiles which you cannot see at targets which are much smaller
than atoms, how can you make sense out of what you detect on the other side of the
target? This kind of scenario highlights the value of the concept of cross-section.
If you had a uniform beam of projectiles and encountered a target which intercepted
1% of the area of the beam, you would expect 1% of the projectiles to be scattered.
That basic concept can be extended to the calculation of the fraction of alpha particles scattered from a gold foil.
Suppose you had a beam of incident alpha particles with rate Ri = 10,000 /s on a
gold foil of thickness 10-6 meters and the effective area (cross-section) for each
gold nucleus was 100 barns. The fraction of those 10,000 particles scattered would
be the fraction of the beam area which is covered by one of the scattering gold
nuclei. The fraction of the beam covered can be calculated as follows
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Introduction
Multiplying the number of targets per square meter times the cross-section for each
target gives you the fraction of the area which is covered by target and therefore the
fraction of the beam which would be scattered:
For an incident rate of 10,000/s, an average of 5.88 particles/s would be expected to
be scattered.
To put this example more directly in the context of Rutherford scattering, you can
use the cross-section calculation to verify that for 6 MeV alpha particles incident
upon this gold film, the cross-section would be 100 barns for scattering above about
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37 degrees. Another context would be the calculation of scattering within an angular window. For example, suppose you start at 20 degrees, where the calculated
cross-section is 363 barns for scattering above that angle. The scattering cross-section for scattering at 23.4 degrees is about 263 barns, so the cross-section for scattering between 20 and 23.4 degrees is about 100 barns. Using finite detectors and
windows like this, the Rutherford team was able to compare the number of scattered alpha particles at different scattering angles and confirm that they followed
the calculated pattern for coulomb scattering. Then at higher energies, when they
detected a departure from the pattern, they could judge that they had interacted with
a different kind of force (the strong force) and could then imply a radius for the
nucleus.
Radiation Risk
Because the energies of the particles emitted during radioactive processes are
extremely high, nearly all such particles fall in the class of ionizing radiation.
Ionizing Radiation
The practical threshold for radiation risk is that of ionization of tissue. Since the
ionization energy of a hydrogen atom is 13.6 eV, the level around 10 eV is an
approximate threshold. Since the energies associated with nuclear radiation are
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Introduction
many orders of magnitude above this threshold, in the MeV range, then all nuclear
radiation is ionizing radiation. Likewise, x-rays are ionizing radiation, as is the
upper end of the ultraviolet range
All nuclear radiation must be considered to be ionizing radiation! In addition, the
upper end of the electromagnetic spectrum is ionizing radiation.
Activity of Radioactive Source
The curie (Ci) is the old standard unit for measuring the activity of a given radioactive sample. It is equivalent to the activity of 1 gram of radium. It is formally
defined by:
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Intensity of Radiation
The roentgen (R) is a measure of radiation intensity of x-rays or gamma rays. It is
formally defined as the radiation intensity required to produce and ionization
charge of 0.000258 coulombs per kilogram of air. It is one of the standard units for
radiation dosimetry, but is not applicable to alpha, beta, or other particle emission
and does not accurately predict the tissue effects of gamma rays of extremely high
energies. The roentgen has mainly been used for calibration of x-ray machines.
Absorbed Dose of Radiation
The rad is a unit of absorbed radiation dose in terms of the energy actually deposited in the tissue. The rad is defined as an absorbed dose of 0.01 joules of energy
per kilogram of tissue. The more recent SI unit is the gray, which is defined as
1joule of deposited energy per kilogram of tissue. To assess the risk of radiation,
the absorbed dose is multiplied by the relative biological effectiveness of the radiation to get the biological dose equivalent in rems or sieverts.
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Introduction
Biologically Effective Dose
The biologically effective dose in rems is the radiation dose in rads multiplied by a
“quality factor” which is an assessment of the effectiveness of that particular type
and energy of radiation. For alpha particles the relative biological effectiveness
(rbe) may be as high as 20, so that one rad is equivalent to 20 rems. However, for xrays and gamma rays, the rbe is taken as one so that the rad and rem are equivalent
for those radiation sources. The sievert is equal to 100 rems.
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Radiation Detection
Nuclear radiation and x-rays are ionizing radiation and they can be detected from
the ionizing events they produce.
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. If the voltage is high enough for the primary electron-ion pair to reach the
electrodes but not high enough for secondary ionization, the device is called and
ionization chamber. The collected charge is proportional to the number of ionizing
events, and such devices are typically used as radiation dosimeters. At a higher
voltage, the number of ionizations associated with a particle detection rises steeply
because of secondary ionizations, and the device is often called a proportional
counter. A single event can cause a voltage pulse proportional to the energy loss of
the primary particle. At a still higher voltage, an avalanche pulse is produced by a
single event in the devices called Geiger counters.
Scintillation Counters
Radiation detection can be accomplished by the use of a scintillator: a substance
which emits light when struck by an ionizing particle. The scintillation detectors
used in the Geiger-Marsden experiment were simple phosphor screens which emitted a flash of light when struck by an alpha particle. Modern scintillation counters
may use single crystals of NaI doped with thallium. 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.
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37
Introduction
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.
Interaction of Radiation with matter
You may click on any of the types of radiation for more detail about its particular
type of interaction with matter. The different parts of the electromagnetic spectrum
have very different effects upon interaction with matter. Starting with low frequency radio waves, the human body is quite transparent. (You can listen to your
portable radio inside your home since the waves pass freely through the walls of
your house and even through the person beside you!) As you move upward through
microwaves and infrared to visible light, you absorb more and more strongly. In the
lower ultraviolet range, all the uv from the sun is absorbed in a thin outer layer of
your skin. As you move further up into the x-ray region of the spectrum, you
become transparent again, because most of the mechanisms for absorption are
gone. You then absorb only a small fraction of the radiation, but that absorption
involves the more violent ionization events. Each portion of the electromagnetic
spectrum has quantum energies appropriate for the excitation of certain types of
physical processes. The energy levels for all physical processes at the atomic and
molecular levels are quantized, and if there are no available quantized energy levels
with spacings which match the quantum energy of the incident radiation, then the
material will be transparent to that radiation, and it will pass through
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Engineering Aspects of Food Irradiation
Introduction
Microwave Interactions
The quantum energy of microwave photons is in the range 0.00001 to 0.001 eV
which is in the range of energies separating the quantum states of molecular rotation and torsion. The interaction of microwaves with matter other than metallic
conductors will be to rotate molecules and produce heat as result of that molecular
motion. Conductors will strongly absorb microwaves and any lower frequencies
because they will cause electric currents which will heat the material. Most matter,
including the human body, is largely transparent to microwaves. High intensity
microwaves, as in a microwave oven where they pass back and forth through the
food millions of times, will heat the material by producing molecular rotations and
torsions. Since the quantum energies are a million times lower than those of x-rays,
they cannot produce ionization and the characteristic types of radiation damage
associated with ionizing radiation.
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39
Introduction
Infrared Interactions
The quantum energy of infrared photons is in the range 0.001 to 1.7 eV which is in
the range of energies separating the quantum states of molecular vibrations. Infrared is absorbed more strongly than microwaves, but less strongly than visible light.
The result of infrared absorption is heating of the tissue since it increases molecular
vibrational activity. Infrared radiation does penetrate the skin further than visible
light and can thus be used for photographic imaging of subcutaneous blood vessels.
Visible Light Interactions
The primary mechanism for the absorption of visible light photons is the elevation
of electrons to higher energy levels. There are many available states, so visible light
is absorbed strongly. With a strong light source, red light can be transmitted through
the hand or a fold of skin, showing that the red end of the spectrum is not absorbed
as strongly as the violet end.
While exposure to visible light causes heating, it does not cause ionization with its
risks. You may be heated by the sun through a car windshield, but you will not be
sunburned - that is an effect of the higher frequency uv part of sunlight which is
blocked by the glass of the windshield.
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Engineering Aspects of Food Irradiation
Introduction
Ultraviolet Interactions
The near ultraviolet is absorbed very strongly in the surface layer of the skin by
electron transitions. As you go to higher energies, the ionization energies for many
molecules are reached and the more dangerous photoionization processes take
place. Sunburn is primarily an effect of uv, and ionization produces the risk of skin
cancer.
The ozone layer in the upper atmosphere is important for human health because it
absorbs most of the harmful ultraviolet radiation from the sun before it reaches the
surface. The higher frequencies in the ultraviolet are ionizing radiation and can produce harmful physiological effects ranging from sunburn to skin cancer.
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41
Introduction
X-rays
Since the quantum energies of x-ray photons are much too high to be absorbed in
electron transitions between states for most atoms, they can interact with an electron only by knocking it completely out of the atom. That is, all x-rays are classified
as ionizing radiation. This can occur by giving all of the energy to an electron (photoionization) or by giving part of the energy to the photon and the remainder to a
lower energy photon (Compton scattering). At sufficiently high energies, the x-ray
photon can create an electron positron pair.
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Engineering Aspects of Food Irradiation