Principles
of Gamma-ray Spectroscopy and Applications in Nuclear Forensics
Introduction
Gamma-ray
(γ-ray) spectroscopy is a quick and nondestructive analytical
technique that can be used to identify various radioactive isotopes
in a sample. In gamma-ray spectroscopy, the energy of incident
gamma-rays is measured by a detector. By comparing the measured
energy to the known energy of gamma-rays produced by radioisotopes,
the identity of the emitter can be determined. This technique has
many applications, particularly in situations where rapid
nondestructive analysis is required.
Background
principles
Radioactive
decay
The
field of chemistry typically concerns itself with the behavior and
interactions of stable isotopes of the elements. However, elements
can exist in numerous states which are not stable. For example, a
nucleus can have too many neutrons for the number of protons it has
or contrarily, it can have too few neutrons for the number of protons
it has. Alternatively, the nuclei can exist in an excited state,
wherein a nucleon is present in an energy state that is higher than
the ground state. In all of these cases, the unstable state is at a
higher energy state and the nucleus must undergo some kind of decay
process to reduce that energy.
There
are many types of radioactive decay, but type most relevant to
gamma-ray spectroscopy is gamma decay. When a nucleus undergoes
radioactive decay by α or β decay, the resultant nucleus produced
by this process, often called the daughter nucleus, is frequently in
an excited state. Similar to how electrons are found in discrete
energy levels around a nucleus, nucleons are found in discrete energy
levels within the nucleus. In γ decay, the excited nucleon decays to
a lower energy state and the energy difference is emitted as a
quantized photon. Because nuclear energy levels are discrete, the
transitions between energy levels are fixed for a given transition.
The photon emitted from a nuclear transition is known as a γ-ray.
Radioactive
decay kinetics and equilibrium
Radioactive
decay, with few exceptions, is independent of the physical conditions
surrounding the radioisotope. As a result, the probability of decay
at any given instant is constant for any given nucleus of that
particular radioisotope. We can use calculus to see how the number of
parent nuclei present varies with time. The time constant, λ, is a
representation of the rate of decay for a given nuclei,
If
the symbol N0 is
used to represent the number of radioactive nuclei present at t = 0,
then the following equation describes the number of nuclei present at
some given time.
The
same equation can be applied to the measurement of radiation with
some sort of detector. The count rate will decrease from some initial
count rate in the same manner that the number of nuclei will decrease
from some initial number of nuclei.
The
decay rate can also be represented in a way that is more easily
understood. The equation describing half-life (t1/2)
is shown in
The
half-life has units of time and is a measure of how long it takes for
the number of radioactive nuclei in a given sample to decrease to
half of the initial quantity. It provides a conceptually easy way to
compare the decay rates of two radioisotopes. If one has a the same
number of starting nuclei for two radioisotopes, one with a short
half-life and one with a long half-life, then the count rate will be
higher for the radioisotope with the short half-life, as many more
decay events must happen per unit time in order for the half-life to
be shorter.
When
a radioisotope decays, the daughter product can also be radioactive.
Depending upon the relative half-lives of the parent and daughter,
several situations can arise: no equilibrium, a transient
equilibrium, or a secular equilibrium. This module will not discuss
the former two possibilities, as they are off less relevance to this
particular discussion.
Secular
equilibrium takes place when the half-life of the parent is much
longer than the half-life of the daughter. In any arbitrary
equilibrium, the ratio of atoms of each can be described
Because
the half-life of the parent is much, much greater than the daughter,
as the parent decays, the observed amount of activity changes very
little.
This
can be rearranged to show that the activity of the daughter should
equal the activity of the parent.
Once
this point is reached, the parent and the daughter are now in secular
equilibrium with one another and the ratio of their activities should
be fixed. One particularly useful application of this concept, to be
discussed in more detail later, is in the analysis of the refinement
level of long-lived radioisotopes that are relevant to trafficking.
Detectors
Scintillation
detector
A
scintillation detector is one of several possible methods for
detecting ionizing radiation. Scintillation is the process by which
some material, be it a solid, liquid, or gas, emits light in response
to incident ionizing radiation. In practice, this is used in the form
of a single crystal of sodium iodide that is doped with a small
amount of thallium, referred to as NaI(Tl). This crystal is coupled
to a photomultiplier tube which converts the small flash of light
into an electrical signal through the photoelectric effect. This
electrical signal can then be detected by a computer.
Semiconductor
detector
A
semiconductor accomplishes the same effect as a scintillation
detector, conversion of gamma radiation into electrical pulses,
except through a different route. In a semiconductor, there is a
small energy gap between the valence band of electrons and the
conduction band. When a semiconductor is hit with gamma-rays, the
energy imparted by the gamma-ray is enough to promote electrons to
the conduction band. This change in conductivity can be detected and
a signal can be generated correspondingly. Germanium crystals doped
with lithium, Ge(Li), and high-purity germanium (HPGe) detectors are
among the most common types.
Advantages
and disadvantages
Each
detector type has its own advantages and disadvantages. The NaI(Tl)
detectors are generally inferior to Ge(Li) or HPGe detectors in many
respects, but are superior to Ge(Li) or HPGe detectors in cost, ease
of use, and durability. Germanium-based detectors generally have much
higher resolution than NaI(Tl) detectors. Many small photopeaks are
completely undetectable on NaI(Tl) detectors that are plainly visible
on germanium detectors. However, Ge(Li) detectors must be kept at
cryogenic temperatures for the entirety of their lifetime or else
they rapidly because incapable of functioning as a gamma-ray
detector. Sodium iodide detectors are much more portable and can even
potentially be used in the field because they do not require
cryogenic temperatures so long as the photopeak that is being
investigated can be resolved from the surrounding peaks.
Gamma
spectrum features
There
are several dominant features that can be observed in a gamma
spectrum. The dominant feature that will be seen is the photopeak.
The photopeak is the peak that is generated when a gamma-ray is
totally absorbed by the detector. Higher density detectors and larger
detector sizes increase the probability of the gamma-ray being
absorbed.
The
second major feature that will be observed is that of the Compton
edge and distribution. The Compton edge arises due to Compton Effect,
wherein a portion of the energy of the gamma-ray is transferred to
the semiconductor detector or the scintillator. This occurs when the
relatively high energy gamma ray strikes a relatively low energy
electron. There is a relatively sharp edge to the Compton edge that
corresponds to the maximum amount of energy that can be transferred
to the electron via this type of scattering. The broad peak lower in
energy than the Compton edge is the Compton distribution and
corresponds to the energies that result from a variety of scattering
angles. A feature in Compton distribution is the backscatter peak.
This peak is a result of the same effect but corresponds to the
minimum energy amount of energy transferred. The sum of the energies
of the Compton edge and the backscatter peak should yield the energy
of the photopeak.
Another
group of features in a gamma spectrum are the peaks that are
associated with pair production. Pair production is the process by
which a gamma ray of sufficiently high energy (>1.022 MeV) can
produce an electron-positron pair. The electron and positron can
annihilate and produce two 0.511 MeV gamma photons. If all three
gamma rays, the original with its energy reduced by 1.022 MeV and the
two annihilation gamma rays, are detected simultaneously, then a full
energy peak is observed. If one of the annihilation gamma rays is not
absorbed by the detector, then a peak that is equal to the full
energy less 0.511 MeV is observed. This is known as an escape peak.
If both annihilation gamma rays escape, then a full energy peak less
1.022 MeV is observed. This is known as a double escape peak.
Example
of experiments
Determination
of depleted uranium
Natural
uranium is composed mostly of 238U
with low levels of 235U
and 234U.
In the process of making enriched uranium, uranium with a higher
level of 235U,
depleted uranium is produced. Depleted uranium is used in many
applications particularly for its high density. Unfortunately,
uranium is toxic and is a potential health hazard and is sometimes
found in trafficked radioactive materials, so it is important to have
a methodology for detection and analysis of it.
One
easy method for this determination is achieved by examining the
spectrum of the sample and comparing it qualitatively to the spectrum
of a sample that is known to be natural uranium. This type of
qualitative approach is not suitable for issues that are of concern
to national security. Fortunately, the same approach can be used in a
quantitative fashion by examining the ratios of various gamma-ray
photopeaks.
The
concept of a radioactive decay chain is important in this
determination. In the case of 238U,
it decays over many steps to 206Pb.
In the process, it goes through 234mPa, 234Pa,
and 234Th.
These three isotopes have detectable gamma emissions that are capable
of being used quantitatively. As can be seen in ,
the half-life of these three emitters is much less than the half-life
of 238U.
As a result, these should exist in secular equilibrium with 238U.
Given this, the ratio of activity of 238U
to each daughter products should be 1:1. They can thus be used as a
surrogate for measuring 238U
decay directly via gamma spectroscopy. The total activity of the 238U
can be determined by ,
where A is the total activity of 238U,
R is the count rate of the given daughter isotope, and B is the
probability of decay via that mode. The count rate may need to be
corrected for self-absorption of the sample is particularly thick. It
may also need to be corrected for detector efficiency if the
instrument does not have some sort of internal calibration.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVLCBVNhDv1gAWWWtcWBsbLI1OlqaUPbyf5Io5UB_knPjlmQigrrfLBUILpMWrqzKpRw1iIa2Mklzonn_KOfFn-RrRu6kWcKwhi2C_b2koHZgZZNJRAH9Z9kdmlLzonLIL75FCKfWVu_XX/s0/7.jpg)
Half-lives
of pertinent radioisotopes in the 238U decay chain
|
Isotope
|
Half-life
|
238U
|
4.5
x 109 years
|
234Th
|
24.1
days
|
234mPa
|
1.17
minutes
|
A
gamma spectrum of a sample is obtained. The 63.29 keV photopeak
associated with 234Th
was found to have a count rate of 5.980 kBq. What is the total
activity of 238U
present in the sample?
234Th exists
in secular equilibrium with 238U.
The total activity of 234Th
must be equal to the activity of the 238U.
First, the observed activity must be converted to the total activity
using Equation A=R/B. It is known that the emission probability for
the 63.29 kEv gamma-ray for 234Th is
4.84%. Therefore, the total activity of 238U
in the sample is 123.6 kBq.
The
count rate of 235U
can be observed directly with gamma spectroscopy. This can be
converted, as was done in the case of 238U
above, to the total activity of 235U
present in the sample. Given that the natural abundances of 238U
and 235U
are known, the ratio of the expected activity of 238U
to 235U
can be calculated to be 21.72 : 1. If the calculated ratio of
disintegration rates varies significantly from this expected value,
then the sample can be determined to be depleted or enriched.
As
shown above, the activity of 238U
in a sample was calculated to be 123.6 kBq. If the gamma spectrum of
this sample shows a count rate 23.73 kBq at the 185.72 keV photopeak
for 235U,
can this sample be considered enriched uranium? The emission
probability for this photopeak is 57.2%.
As
shown in the example above, the count rate can be converted to a
total activity for 235U.
This yields a total activity of 41.49 kBq for 235U.
The ratio of activities of 238U
and 235U
can be calculated to be 2.979. This is lower than the expected ratio
of 21.72, indicating that the 235U
content of the sample greater than the natural abundance of 235U.
This
type of calculation is not unique to 238U.
It can be used in any circumstance where the ratio of two isotopes
needs to be compared so long as the isotope itself or a daughter
product it is in secular equilibrium with has a usable gamma-ray
photopeak.
Determination
of the age of highly-enriched uranium
Particularly
in the investigation of trafficked radioactive materials,
particularly fissile materials, it is of interest to determine how
long it has been since the sample was enriched. This can help provide
an idea of the source of the fissile material—if it was enriched
for the purpose of trade or if it was from cold war era enrichment,
etc.
When
uranium is enriched, 235U
is concentrated in the enriched sample by removing it from natural
uranium. This process will separate the uranium from its daughter
products that it was in secular equilibrium with. In addition,
when 235U
is concentrated in the sample, 234U
is also concentrated due to the particulars of the enrichment
process. The 234U
that ends up in the enriched sample will decay through several
intermediates to 214Bi.
By comparing the activities of 234U
and 214Bi
or 226Ra,
the age of the sample can be determined.
In ,
ABi is
the activity of 214Bi,
ARais
the activity of 226Ra,
AU is
the activity of 234U,
λTh is
the decay constant for 230Th,
λRa is
the decay constant for 226Ra,
and T is the age of the sample. This is a simplified form of a more
complicated equation that holds true over all practical sample ages
(on the order of years) due to the very long half-lives of the
isotopes in question. The results of this can be graphically plotted
as they are in .
Ratio
of 226Ra/234U
(= 214Bi/234U)
plotted versus age based on .
This can be used to determine how long ago a sample was enriched
based on the activities of 234U
and 226Ra
or 214Bi
in the sample.
Exercise:
The gamma spectrum for a sample is obtained. The count rate of the
121 keV 234U
photopeak is 4500 counts per second and the associated emission
probability is 0.0342%. The count rate of the 609.3 keV 214Bi
photopeak is 5.83 counts per second and the emission probability is
46.1%. How old is the sample?
Solution:
The observed count rates can be converted to the total activities for
each radionuclide. Doing so yields a total activity for 234U
of 4386 kBq and a total activity for 214Bi
of 12.65 Bq. This gives a ratio of 9.614 x 10-7.
Using ,
as graphed this indicates that the sample must have been enriched
22.0 years prior to analysis.
References
G.
Choppin, J.-O. Liljenzin, and J. Rydberg. Radiochemistry
and Nuclear Chemistry, Elsevier
Press, Oxford (2006).
W.
Loveland, D. J. Morrissey, and G. T. Seaborg. Modern
Nuclear Chemistry, Wiley,
New Jersey (2006).
K.
Mayer, M. Wallenius, and I. Ray. Analyst,
2005, 130,
433.
J.
T. Mihalczo, J. A. Mullens, J. K. Mattingly, and T. E.
Valentine. Nucl.
Instrum. Meth. A,
2000, 450,
531.
J.
T. Mihalczo, J. K. Mattingly, J. S. Neal, and J. A. Mullens, Nucl.
Instrum. Meth. B,
2004, 213,
378.
K.
J. Moody, I. A. Hutcheon, and P. M. Grant. Nuclear
Forensic Analysis,
CRC Press, Boca Raton (2005).
C.
T. Nguyen. Nucl.
Instrum. Meth. B, 2005, 229,
103.
C.
T. Nguyen, and J. Zsigrai. Nucl.
Instrum. Meth. B,2006, 246,
417.
D.
Reilly, N. Ensslin, and H. Smith, Jr. Passive
Nondestructive Assay of Nuclear Materials,
National Technical Information Service, Springfield, VA (1991).
M.
Wallenius, A. Morgenstern, C. Apostolidis, and K. Mayer. Anal.
Bioanal. Chem., 2002, 374,
379.