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                        The Atomic Fingerprint:
                      Neutron Activation Analysis


                                   by
                             Bernard Keisch




                                CONTENTS


  INTRODUCTION                                                          4
  WHAT IS NEUTRON ACTIVATION ANALYSIS?                                  5
  THE SENSITIVITY OF NEUTRON ACTIVATION ANALYSIS                       10
  HOW AND WHERE TO USE IT                                              19
      In a Physics Laboratory                                          19
      In a Hospital                                                    28
      In a Plastics Plant                                              32
      In a Museum                                                      35
      In a Criminology Laboratory                                      42
  SUMMING UP: WHAT LIES AHEAD                                          46
  APPENDIX                                                             49
  READING LIST                                                         52
  MOTION PICTURES                                                      54

          U. S. Energy Research and Development Administration
                        Office of Public Affairs
                         Washington, D.C. 20545

           Library of Congress Catalog Card Number: 79-182556
                                  1972

               [Illustration: Photograph, spiral galaxy]

The U. S. Energy Research and Development Administration publishes a
series of booklets for the general public.

Please write to the following address for a title list or for
information on a specific subject:

    USERDA—Technical Information Center
    P. O. Box 62
    Oak Ridge, Tennessee 37830

              [Illustration: Photograph: shelf with china]

  A 19th century photograph restored by neutron activation. This
  picture, which is in the collection of the Smithsonian Institution,
  was exposed to neutrons in a nuclear reactor and then placed in
  contact with modern photographic film. The original, which had been
  taken by William Henry Fox Talbot who began his career in 1834, is
  badly faded.




                              INTRODUCTION


You are a physicist investigating the properties of semiconductors,
which are materials used to make transistors. The electrical properties
of one specimen are not quite like the others that you’ve studied. What
makes this specimen different?

                                   OR

You are a physician treating a patient who, because of a severe calcium
deficiency, has been suffering from osteoporosis (a softening of the
bones). Are you on the right track with your treatment?

                                   OR

You are an analytical chemist working for a plastics manufacturer. You
have been asked by the plant superintendent to determine why some of the
plastic coming from the plant has been discolored.

                                   OR

You are a curator working with the ancient coin collection in a large
museum. A donor has just given the museum a group of 50 gold coins
presumably about 1500 years old. Are they genuine?

                                   OR

You are a scientist working in the criminology laboratory of a large
metropolitan city. A detective brings you a minute sample of paint taken
from the clothing of a hit-and-run victim. He has a suspect whose
automobile paint seems to match that sample. Can you determine his guilt
or innocence?

Neutron activation analysis can be used to solve each of these problems
and many more. The solutions to these particular problems are explained
on pages 19-46.




                        The Atomic Fingerprint:
                      Neutron Activation Analysis
                           by Bernard Keisch




                  WHAT IS NEUTRON ACTIVATION ANALYSIS?


To understand neutron activation analysis, you should be acquainted with
a few basic concepts. The nuclei of atoms are stable only when they
contain certain numbers of neutrons and protons. The number of protons
in an atom’s nucleus determines an element’s identity; the number of
neutrons usually determines whether or not that atom is radioactive or
nonradioactive (stable).[1]

Thus, while all sodium atoms contain 11 protons, only those sodium atoms
that contain 12 neutrons are stable. A radioactive sodium atom contains
a different number of neutrons. For other elements, there may be more
than one number of neutrons that results in stability; for instance,
there are 10 stable atoms (isotopes) of tin, each containing a different
number of neutrons in their nuclei.

The fact that nuclei can absorb additional neutrons, which, in many
cases, results in the conversion of a stable nucleus to a radioactive
one, makes neutron activation analysis possible. Because radioactive
nuclei decay in unique ways and yield radiations that are often distinct
and can be measured even in very small amounts, measurements of these
radiations can determine the kind and the number of radioactive atoms
that are present.

In the most common type of activation analysis, the neutron bombardment
of a sample is performed in a nuclear reactor where the neutrons that
strike the target atoms have been slowed down so that they have very
little energy of motion. In this case, the usual reaction between the
target atoms and a neutron results in the capture of the neutron and
this creates a nucleus with an atomic weight of one more unit than it
started with. Thus for sodium as found in nature (symbol ²³Na)

     sodium-23 + a neutron → radioactive sodium-24 + gamma rays[2]

The numbers denote the atomic weight of the atom, which is the total
number of protons and neutrons in its nucleus.

In a nuclear reactor, there are many, many neutrons that can be used in
this reaction; approximately 10¹² to 10¹⁴ (10¹² is a million million;
10¹⁴ is a hundred times 10¹²) pass through each square centimeter of
target area every second. Not all these will strike the nuclei of sodium
atoms. Of those that do, not all will be captured. A mathematical
relationship that tells how many atoms of sodium-24 will be created in a
cubic centimeter of the target in one second is:

                              N₂₄ = N₂₃φσt

where N₂₄ is the number of sodium-24 atoms created during each second in
a cubic centimeter of the target; N₂₃ is the number of atoms of
sodium-23 in a cubic centimeter of the target; φ is the number of
neutrons crossing a square centimeter per second (called the neutron
flux); t is the time in seconds that the target is in the reactor; and σ
is a number that represents the probability that the conversion of
sodium-23 to sodium-24 will occur. This last number is called a “cross
section” and it is expressed in “barns”. One barn is equal to 10^{-24}
square centimeter, which is approximately the cross-sectional area of a
typical atomic nucleus.

In an activation analysis experiment, the analyst wants to determine the
number of target atoms (N₂₃ in the above example). He can measure how
long the target was in the nuclear reactor; there are ways of measuring
the neutron flux, φ; and the cross section is fixed and generally known
for each target nucleus. So, by measuring the number of radioactive
atoms created (N₂₄), he can calculate the number of target atoms. See
the figure on the next two pages.

Actually, to get the most accurate results, there are certain practical
tricks he can use that increase the accuracy. Some of these will become
apparent in later sections of this booklet.

The most important of these “tricks” is the use of a “standard” or
“comparator”. This comparator is similar in form and composition to the
sample to be measured but contains a _known_ quantity of the element to
be determined. The steps used for the analysis are simple.

1. Put the sample and comparator together into a reactor and bombard
them with neutrons.

2. Remove them and measure the radioactivity produced from the sample.

3. Compare the radioactivity of the sample and the comparator and
calculate the amount of the element in the sample as a proportion:

        (Radioactivity in sample)/(Radioactivity in comparator)
 = (Quantity of element in sample)/(Quantity of element in comparator)


Neutron Activation Analysis: Detecting Sodium in a Sample of Plastic

Step 1. Weigh a sample and a standard in quartz tubes.

     [Illustration: Piece of plastic; Standard = sodium carbonate]

Step 2. Seal tubes in package for reactor irradiation.

   [Illustration: Sealed aluminium can; Sealed quartz tubes; Sample;
                               Standard]

Step 3. Bombard with neutrons for about 3 hours in a reactor.

                        [Illustration: Neutrons]

Step 4. Remove sample and standard from tubes and place in separate
plastic containers to measure gamma rays.

[Illustration: Pulse height analyser; Sample; Standard; Gamma rays from
 Na-24; same container, distance, detector; Sodium iodide scintillator]

Step 5. Obtain gamma-ray spectrum for sodium-24 in both sample and
standard.

  [Illustration: (chart) Energy vs. Sample spectrum; Energy —→Standard
                               spectrum]

Step 6. Use standard to calculate 1.37 MeV gamma rays counted per minute
per gram of sodium (c/m/gNa).

      c/m/gNa = (counts/minute measured in 1.37 peak (shaded area
      above))/(grams of sodium known to be in standard (step 1.))

Step 7. Use c/m/gNa and 1.37 MeV gamma rays counted per minute in sample
to calculate grams of sodium in sample.

                          grams Na in sample =
         (counts/minute measured in sample)/(c/m/gNa (step 6.))

Step 8. Calculate percent sodium in sample.

                               % sodium =
 (grams sodium in sample (step 7.))/(weight of sample (step 1.)) × 100




           THE SENSITIVITY[3] OF NEUTRON ACTIVATION ANALYSIS


There are several factors that determine the sensitivity of the method.
Some are variable within limits and some, like the cross section, are
fixed. Time is variable to a degree, partially determined by the
half-life of the nuclide created and with an upper practical limit
determined by how long we want to wait for an analysis.

The crucial step in the analytical procedure is the measurement of the
number of radioactive atoms that were created.

  1. How do we measure how many radioactive atoms are present?

  2. Since there will usually be a mixture of elements in a target, and
  many of these will be made radioactive, how can we tell one from
  another?

  3. Since radioactive atoms are constantly “disappearing” by
  radioactive decay, how do we obtain the number of atoms created from a
  measurement made some time after the bombardment has taken place? And
  what of those atoms disintegrating while others are still being
  created in the reactor?

Radioactive atoms almost always decay by emitting negatively charged
beta particles usually accompanied by gamma rays. Instruments can detect
these kinds of radiation, and it is by measuring the radiation that we
determine how many radioactive atoms are present. To do this we have to
know the types of radiation emitted by the radioactive atoms we are
trying to measure. Fortunately each kind of radioactive atom decays with
a unique “pattern” scientists call a “decay scheme”. The figure on the
next page shows a simplified decay scheme for manganese-56, which is
produced by activation of manganese, and a diagram showing what the
decay scheme means.

Until a few years ago, it was difficult to measure the number of gamma
rays of a particular energy that were being emitted by a mixture of
radioactive isotopes unless there were only a few such gamma rays with
very different energies. Today instruments are available that can really
pick them out of a complex mixture. Thus it is usually possible to
“separate” with electronic instruments the radioactive element we are
interested in measuring. Some of the examples below will show how this
might be accomplished.

Each radioactive nuclide[4] also has a characteristic half-life,[5]
which is a measure of how fast the radioactive atoms change (transmute)
to atoms of another element. In a reactor, even while they are being
produced in the target, atoms of the radioactive nuclide are decaying
with the particular half-life of the nuclide. The mathematical laws that
govern this process tell us that the number of atoms determines the
amount of decay; i.e., the more atoms there are, the greater the amount
of decay in a given period of time. (The fraction that decays in that
time is constant.) As a result, the target eventually becomes
“saturated”, that is, the rate of production equals the rate of decay.
When the irradiation is first begun, the number of radioactive atoms
increases steadily. But eventually, this rate of increase slows down
until, at saturation, further irradiation no longer increases the number
of radioactive atoms present in the target.

    [Illustration: The energy of a gamma ray is equal to the energy
 difference between the two levels involved in the gamma-ray emission.]

  An _energy level diagram_. The slanted arrows indicate radioactive
  decay by beta-particle emission. In each case, manganese-56 decays to
  a certain energy level of iron-56. On the right the energy of each
  level is indicated. Following a beta emission to a high-energy
  (excited) state in iron-56, one or more gamma rays are emitted until
  the nucleus is de-excited to the level marked zero. The vertical
  arrows indicate gamma rays emitted during the de-excitation process.
  The energy of each gamma ray is the difference between the levels
  involved in the change. The numbers above the vertical arrows indicate
  the relative proportions of gamma rays of different energies emitted
  from that level.


The mathematical relationship that describes the irradiation process
exactly is:

                         A₀ = Nφσ (1 - e^{-λt})

where A₀ is the radioactivity produced (disintegrations per cubic
centimeter per second); N is the number of target atoms per cubic
centimeter in the sample; φ is the neutron flux (neutrons per square
centimeter per second); σ is the cross section for the reaction (square
centimeters); λ is the disintegration constant[6] for the radioactive
atoms produced (number per second); the number “e” is the base of
natural logarithms; and t is the irradiation time in seconds. Note that
for short irradiation times (t very small), 1-e^{-λt} approximates λt,
while for long irradiations (t very large), 1-e^{-λt} approximates 1.

          [Illustration: Graph: Decay scheme for manganese-56]

  Maximum Energy           % Betas
  2.84 MeV                      53
  1.03 MeV                      30
  0.720 MeV                     16
  0.30 MeV                       1
                          % Gammas
  0.847 MeV                     68
  1.811 MeV                     20
  2.110 MeV                     10
  Other Energies                 2
  2.543 MeV
  2.658 MeV
  2.957 MeV
  3.39 MeV

                      (avge~ 1.4 gammas per beta)

  This summarizes what the decay scheme or energy level diagram shows in
  terms of the relative amounts of betas and gammas emitted in the decay
  of manganese-56. Thus, you could observe more than three times as many
  gamma rays having an energy of 0.847 MeV than of 1.811 MeV, etc. Note
  that while one, and only one, beta is emitted in the decay of one atom
  of manganese-56, two gammas can sometimes be emitted in one decay.

Of course, when the target is removed from the reactor, the number of
radioactive atoms begins to decrease according to the characteristic
half-life of the nuclide. The mathematical expression that describes the
process of radioactive decay of a single nuclide is:

                           A_{t} = A₀e^{-λt}

where A_{t} is the radioactivity of an isotope at some time, t, after
the end of the irradiation, and A₀ is the radioactivity at the end of
the irradiation.

 [Illustration: Fraction of saturation sodium-24 activity _vs_ Time of
                          irradiation (hours)]

  The activation of sodium-23 to sodium-24, which has a half-life of 15
  hours. The horizontal line marked 1.0 represents the “saturation”
  activity level for a sample of sodium of a certain size in a constant
  neutron flux. Note that after about 120 hours, the activity of the
  sample is within 1% of the value at saturation, which is the most
  active that sample will ever become at a given φ. Note also that after
  the first 15 hours (1 half-life) the sample is exactly half way to its
  value at saturation. Thus long irradiations are useful to increase the
  sensitivity of the analysis, but only up to a certain point.

The result of all this is that the sensitivity of an analysis depends in
practice on a number of practical as well as theoretical factors:

  1. The cross section of the target element.
  2. The half-life of the radioactive isotope produced.
  3. The time available for irradiation.
  4. The flux of neutrons available for irradiation.
  5. The promptness with which we can begin measuring radioactivity and
          the efficiency of this measurement.
  6. Possible interferences due to the presence of elements yielding the
          same radioactive elements or those yielding very similar
          radiations.

In the next section of this booklet, there are several examples that
will show you how all this works in practice. But to summarize what
these factors mean in terms of sensitivity let us look at the chart in
the figure on page 18. Here all the elements are arranged in a periodic
table. The sensitivities are shaded in coded ranges representing
measurable quantities. They are calculated on the basis that there are
no interferences, that the neutron flux is 10¹⁴ neutrons per square
centimeter per second, and that we can measure 100 gamma rays per minute
without much difficulty assuming a gamma-ray detector efficiency[7] of
10%. The elements labeled β yield radioisotopes that emit few or no
gamma rays and can only be analyzed by neutron activation using
appropriate chemical separation procedures followed by beta
radioactivity measurements. Such chemical separation procedures (to
remove unwanted radioactive isotopes of other elements) are also
sometimes useful to improve the sensitivity of the analysis of gamma-ray
emitters if necessary.

  [Illustration: Graph: “Fraction of Sodium-24 remaining” vs. “Time of
                            decay (hours)”]

  The radioactive decay curve of sodium-24. The vertical scale is not
  _linear_ but _logarithmic_. Thus, each factor of two in radioactivity
  occupies the same distance along the vertical axis. When two samples
  are being analyzed for sodium by activation analysis, they must be
  compared at the same time after they have been removed from the
  neutron flux. If this period of time is different, then a correction
  must be applied to one of them, based on the decay curve shown here,
  to allow for the difference in decay time for the two. Waiting too
  long after the irradiation is completed results in much poorer
  sensitivity for the analysis depending on the half-life of the
  activation product. In this case, after 2 days it takes approximately
  ten times as much sodium to yield the same radioactivity as it would
  if the sample were measured when it was fresh out of the reactor.

It is not practical to determine a few elements, shown in black squares,
by activation analysis. Some others, like oxygen and nitrogen (labeled
HE), can be measured by using other projectiles like fast (more
energetic) neutrons, or protons or deuterons[8] produced in a device
called an accelerator. Other elements, those shown in white squares, can
be detected with such great sensitivity, that one can find some in
almost everything. For example, if you had a cube of “pure” aluminum
only 1 millimeter on a side, you could detect gold in it if there were
only one atom of gold for every fifty billion atoms of aluminum.

While it isn’t often that you would want to find a gold needle in an
aluminum haystack, the next section presents some practical
applications. Imagine yourself as the person with the problem in these
situations.

   [Illustration: Periodic table of elements, with sensitivity code]

* Th and U are radioactive but with such long half-lives that
neutron activation analysis can be used for their determination.

† µg = Microgram (one-millionth of a gram)




                        HOW AND WHERE TO USE IT


In a Physics Laboratory

_The Problem_

You are a physicist investigating the properties of semiconductors,
which are materials used to make transistors. When you apply a voltage
to one specimen of silicon (a semiconductor), it doesn’t behave quite
like the others that you’ve studied. The electrical properties of this
odd specimen are unusual and interesting and could lead to a new type of
transistor. What makes this specimen different from the others? Very
small amounts of impurities can cause large changes in the electrical
properties of semiconductors. You would like to obtain a chemical
analysis of the material, but your colleagues in chemistry tell you they
would have to dissolve a good size part of your sample to analyze it and
you are reluctant to give it up. How do you do it?

_The Solution_

You decide to try neutron activation analysis. You realize you won’t be
able to detect all the elements, but many of those that might affect
semiconductor performance could be detected quite easily.

What will you need? A source of neutrons to activate the material and a
gamma-ray spectrometer to measure the radiation from the material
afterwards. This spectrometer detects and measures gamma rays and sorts
them according to their energy. You find that your friend down the hall,
who is a nuclear physicist, has a gamma-ray spectrometer that
incorporates a lithium-drifted germanium crystal as a detector and a
pulse height analyzer. The germanium detector is a device that senses
the gamma rays that enter it and gives electrical signals related to the
energy of the gamma rays. It was invented only a few years ago and has a
very fine resolution. That is, it can easily “pick out” gamma rays that
are only slightly different in energy. For example, for gamma rays with
energies of approximately 1 MeV (million electron volts), it is not
unusual to distinguish between gamma rays that differ by only 2 or 3
tenths of a percent. The pulse height analyzer is an electronic device
that sorts the electrical pulses from the detector according to their
energy.

                   [Illustration: Gamma-ray detector]

  A lithium-drifted germanium-crystal gamma-ray detector. The large
  container is a reservoir of liquid nitrogen that keeps the detector
  cooled to a temperature of -196° Centigrade (321° below zero,
  Fahrenheit). The lead brick shield keeps out most of the gamma rays
  that come from naturally radioactive materials in the room. The
  plastic slots hold cards upon which the samples are mounted for
  counting. Sometimes the detector is arranged vertically and samples
  are placed on shelves above it.

                   [Illustration: Gamma-ray detector]

What about the neutrons for the irradiation? Although there isn’t a
suitable nuclear reactor[9] in your city, there is one at a university
only an hour away by jet. Since it may take a few hours to get the
sample to the counter after irradiation, you won’t be able to look for
short-lived activation products, i.e., those with half-lives of up to an
hour. However, this will exclude only a few elements from detection.

                 [Illustration: Pulse-height analyzer]

  A pulse-height analyzer used for gamma-ray spectrometry. A gamma-ray
  spectrum is displayed on the television screen. Data is printed out
  automatically on the electric typewriter and also may be plotted as a
  graph on the paper to the left. In other systems, data may be coded
  onto punched paper tape as well. Such tape may be “read” by a computer
  that can be programmed to use the data to calculate what radioactive
  isotopes are present and their quantities.

Now you are ready to begin the analysis. This will be a qualitative
analysis since you are merely looking for a significantly different
element in that silicon crystal. How much of it is present is only of
secondary interest. Therefore, if you find anything different, you will
rely on an approximate calculation to tell you “how much”.

                    [Illustration: Nuclear reactor]

  This is called a “swimming pool” reactor because the nuclear fuel,
  built into metal rods, is held in a framework at the bottom of a deep
  pool of water. The water serves as a shield to protect workers from
  the radiation and also helps the reactor “go” by slowing down neutrons
  to make them more likely to interact with the target atoms. “Swimming
  pool” reactors are frequently used for neutron activation analysis and
  typically provide neutron fluxes of over 10¹³ (10 million million)
  neutrons per square centimeter per second.

                    [Illustration: Quartz capsules]

  These sealed quartz capsules contain samples to be irradiated in a
  nuclear reactor. They are about to be placed in the aluminum can,
  which will be sealed and positioned at the end of an aluminum pole,
  close to the core of a “swimming pool” reactor. Often samples are
  placed in plastic tubes and are carried in and out of a reactor by air
  pressure in a pneumatic tube system.

You carefully scrape off a small amount of material, weigh it on a
sensitive balance, and put it into a short piece of pure quartz tubing.
You do the same with an ordinary piece of silicon for comparison and
then seal both tubes with an oxygen-gas torch. Although the tubes are
both ¼ inch in diameter and about 1 inch long, the first tube is just
slightly longer so you will be able to determine which is which after
the irradiation.

Off it goes to the reactor in a carefully wrapped package along with
instructions to irradiate the tubes for 12 hours in a neutron flux of
about 10¹³ neutrons per square centimeter per second and to return them
as quickly as possible after they are removed from the reactor.

The following week, the samples are delivered about 4 hours after they
were removed from the reactor. Working quickly but carefully, you note
that they are radioactive but easily handled by ordinary laboratory
techniques. You break the quartz tubes one at a time and attach each of
the two pieces of silicon to a card with self-sticking tape. Then you
place each card, in turn, on a holder close to the gamma-ray detector
for a period of 10 minutes. A spectrum, which is a graph of the quantity
of radiation recorded in each increment of energy over the range
observed for each of the samples, is plotted automatically at the end of
the counting period and you may now compare the compositions of the two
samples. (See the figure on the next two pages.)

The two spectra are virtually identical except that the suspect sample
has one obviously different peak in channel 157 and a somewhat smaller
peak in channel 183. Referring to an energy calibration curve for the
pulse height analyzer, you find that these channels correspond to 0.559
and 0.657 MeV respectively. A search of a table of nuclides, arranged by
gamma-ray energy, reveals that this combination is emitted by
arsenic-76, which would be the activation product for arsenic. Other
data also indicate that for arsenic there should be a number of smaller
peaks, including some corresponding to energies of 1.216, 1.228, 0.624,
and 1.441 MeV. A closer look at the spectrum of the suspect sample
reveals that these are also present.

Finally, noting that the half-life of arsenic-76 is approximately 27
hours, you wait a day and count the sample again in the same position as
the previous count. A decrease in the heights of the 0.559 and 0.657 MeV
peaks, by a little less than half in 24 hours, confirms that arsenic is
the unusual element in this sample. It may not be the only impurity
causing the peculiar behavior of this semiconductor, but it does seem a
likely candidate.

 [Illustration: Graph: “Counts in 20 minutes per 3.8 KeV channel” _vs_
                           “Channel Number”]

  Element                    Counts   Channel Number
  Gold                         1300              125
  Sodium                        900              140
  Antimony                      650              150
  Antimony                      550              160
  Scandium                      220              240
  Iron                          150              300
  Scandium                       60              310
  Cobalt                        110              320
  Iron                           45              350
  Cobalt                         50              360
  Sodium                        900              370
  Sodium                        140              425

                   (values estimated from the graph)

  The gamma-ray spectrum obtained after activation of a sample of “pure”
  silicon having “ordinary” properties of this type of semiconductor.
  Only very small quantities of various trace impurities are indicated.

 [Illustration: Graph: “Counts in 20 minutes per 3.8 KeV channel” _vs_
                           “Channel number”]

  Element                    Counts   Channel Number
  Gold
  Sodium
  0.559 Arsenic-75             1500              150
  Antimony
  0.624 Arsenic-75              190              165
  0.657 Arsenic-75              135              175
  Scandium
  Iron
  Scandium
  Cobalt
  1.216 Arsenic-75              100              330
  1.228 Arsenic-75               60              335
  Iron
  Cobalt
  Sodium
  1.44 Arsenic-75                25              380
  Sodium

                 (distinct values estimated from graph)

  The gamma-ray spectrum obtained after activation of a sample of
  silicon having “unusual” electrical properties. While most of the
  spectrum is identical with that obtained from the ordinary material,
  there is an interesting difference.

Using the equation given on page 12, the approximate known values for
half-life, sample weight, neutron flux, and periods of irradiation and
decay after irradiation, and an estimated value for the number of
arsenic-76 atoms measured by the gamma-ray spectrometer, you calculate
that the arsenic content of the sample is approximately 44 parts per
million (ppm). (See appendix.)

With this information as a starting point, you are now ready to proceed
with further research on the properties of your semiconductor, e.g., if
you double the concentration of arsenic, how will that affect its
properties?


In a Hospital

_The Problem_

You are a physician treating a patient who, because of a severe calcium
deficiency, has been suffering from osteoporosis (a softening of the
bones). You think you are on the right track with your treatment, but
you would like to be sure in order to know whether you should continue
the treatment or try something else. You would have your answer if you
knew that the calcium content of his skeleton had stopped decreasing.
How can you determine the amount of calcium in a living human being?

_The Solution_

You know that the usual techniques for determining calcium in the bones
are not very useful. They are either too inaccurate to show that your
patient’s calcium loss has been stopped or can only be used to measure
the calcium content of the bones in his extremities. The latter is not
satisfactory because these few bones may not be representative of the
rest of his skeleton.

Recently, however, there have been reports of neutron activation
analysis of whole persons, in which the calcium content of their bones
has been measured with unusually good reliability. This has been
accomplished by scientists and doctors working at the University of
Washington School of Medicine in Seattle.

You manage to obtain an appointment for your patient and you accompany
him to the hospital for the analysis. There he is placed on a rotating
platform with his head encircled by a plastic helmet and his arms and
legs submerged in a water-filled plastic container. See the photograph
on the next page. The platform is located in a beam of neutrons
emanating from a beryllium target 15 feet away, which is being bombarded
by deuterons from a 22-MeV cyclotron. The purpose of the water is to
surround the bones in that part of the subject’s skeleton with a neutron
moderator equivalent to the body tissue surrounding the rest of his
skeleton. (A neutron moderator slows down the neutrons and thus makes
them more likely to activate the calcium in the bones.) On each side of
the patient, there are two plastic containers permanently filled with a
solution containing a known quantity of calcium. These serve as
standards for the analysis.

The beam of neutrons is turned on for 35 to 40 seconds. It is then
interrupted while platform and patient are rotated 180 degrees. The
irradiation is resumed so that a uniform dose of neutrons bombards the
patient from both front and back.

During the irradiation your patient receives a dose of radiation
equivalent to approximately 10 ordinary chest X rays and one of the
calcium isotopes in his bones (calcium-48) is activated to calcium-49.
The latter has a half-life of only 8.8 minutes and so counting must
begin soon after the irradiation.

                        [Illustration: Patient]

  A patient in position for whole body irradiation with neutrons
  generated by an accelerator. His arms and legs are surrounded by
  plexiglas containers filled with water and his head is encased in a
  plexiglas helmet. On either side of him are containers, which serve as
  standards, filled with an aqueous solution of a calcium salt. The
  patient is standing on a turntable that is rotated 180 degrees after
  half the irradiation is completed so that the dose of neutrons is
  uniformly distributed to the front and the back of the patient.

                        [Illustration: Patient]

  A patient in position for whole-body gamma-ray spectrometry. The
  detectors are scintillation crystals that produce pulses of light
  proportional in intensity to the energy of the gamma ray absorbed in
  the crystal. The patient is scanned from head to foot in approximately
  12½ minutes at a rate that is varied to compensate for the gradual
  decay of the calcium-49 radioactivity during this period. Near the
  patient’s head are two calcium standard solutions in plexiglas
  containers.

The patient lies down in a padded aluminum box and, only 4 minutes after
the irradiation is concluded, a ring of 4 gamma-ray scintillation
detectors[10] begin to measure the gamma rays emitted by his body. These
detectors, which are each 4 inches thick and 9⅜ inches in diameter, pass
over his body from head to foot. This takes 12½ minutes and since the
calcium-49 is decaying with a half-life of 8.8 minutes, the detectors
are made to scan at a gradually decreasing rate to compensate for the
reduced radioactivity during the later parts of the counting period. The
figure on the next page shows the gamma-ray spectrum for the patient.
Notice the peak corresponding to an energy of 3.1 MeV. Because there are
small contributions to this energy peak from other activated products in
the body, repeat counts are taken later (after the calcium-49 has
decayed) so that these contributions can be measured and subtracted.

Twenty minutes after the irradiation period, the radioactivity of the
calcium standards is measured by the same instrument. The ratio of the
counts from your patient’s body to that of the standards is 0.210; this
serves as an index of the calcium content of his body on this day.
Because of the care taken to make the analysis repeatable, this index is
probably accurate to about 1 or 2%.

Your patient’s disease usually results in a decrease of approximately 3%
of the calcium in his body per year. Thus, by making the same
measurement a year from now, you will be able to tell if your treatment
is a success by noting that the calcium level in your patient’s bones
has stopped decreasing at a dangerous rate.


In a Plastics Plant

_The Problem_

You are an analytical chemist working for a company that makes plastic.
It is 11:30 a.m. and you have been called by the plant superintendent
because some of the plastic coming from the plant has been showing a
yellowish-brown discoloration. There seem to be only a few possible
reasons for it, but no easy way to tell which one is correct. One
possibility is that a copper tank, in which the plastic is prepared, is
somehow being corroded by excess acid in the raw material and minute
quantities of dissolved copper are discoloring the plastic. You could
prove that this is the cause if you could find copper in the plastic,
but the plant superintendent wants the answer immediately because a few
hours delay in production will jeopardize a valuable contract, and
ordinary chemical analysis would take several hours. How can you quickly
determine if there is copper present in the plastic?

  [Illustration: Graph: “Counts per 12.5 minutes/50 KeV channel” _vs_
                             “Channel no.”]

  Element                    Counts      Channel no.
  2.75 MeV Na-24               5000               10
  3.10 MeV Ca-49               3200               16
  3.85 MeV Cl-38                500               33
  4.0 MeV Ca-49                 100               39

                     (Values estimated from graph)

  A portion of the gamma-ray spectrum obtained after neutron activation
  of a human body. The area in the 3.10-MeV peak, which is above the
  background due to sodium and chlorine activities, is a measure of the
  quantity of calcium in the body of the subject. A computer may make
  the necessary corrections due to the background (which results from
  overlapping of part of the other gamma-ray peaks).

_The Solution_

One reason that ordinary analytical methods are so slow, in this case,
is because the amount of copper you are looking for is so small that you
would have to dissolve a large amount of plastic to get enough copper to
measure. You know that nearly all the plastic is carbon, hydrogen, and
oxygen and that none of these elements are easily made radioactive when
they are bombarded with low-energy neutrons. You look in a table to see
if copper is easily activated. You find that there are two stable
isotopes of copper having atomic weights of 63 and 65. Each of these is
easily activated, giving radioactive isotopes, copper-64 and copper-66.
The latter has a half-life of about 5 minutes and emits gamma rays with
energies of 1.039 MeV, which are easy to measure.

In the research building next door, there is a small reactor that can
irradiate encapsulated samples with low-energy neutrons at the rate of a
million million neutrons per square centimeter per second (10¹²
neutrons/cm²/sec). You calculate that if you irradiate only one tenth of
a gram of the plastic for 10 minutes, and if the plastic contains only
one part of copper in one million parts of plastic, then at the end of
the irradiation the radioactive copper formed will be emitting over 400
gamma rays per second. There is a pneumatic tube that can remove the
irradiated sample in 20 seconds, and you decide that it will take only a
minute or two to remove the sample from its capsule and get it into a
gamma-ray counter located nearby. The counter is a scintillation counter
that is connected to a pulse-height analyzer.

If you count for only 10 minutes you will detect about 1000 gamma rays
of the right energy (allowing for the inefficiencies of the detector
system). This sounds like it should do the job. But does the good
plastic contain copper too? And how much does it take to produce the
discoloration?

You decide to use neutron activation analysis and to analyze samples of
faulty plastic, normal plastic, and a small piece of copper foil, which
you have weighed and sealed in a small polyethylene bag as a standard.
Your results are shown in the table below.

  Sample                                     Counts in 10 minutes[11]
  0.1 grams faulty plastic                                    100,000
  0.1 grams good plastic                                        1,000
  0.1 milligrams of pure copper                             1,000,000

It worked! The faulty plastic contains 100 times as much copper as the
good plastic, specifically 100 parts per million. (If 0.1 milligrams of
pure copper gave 1,000,000 counts, then the 0.1 grams of faulty plastic
contains (100,000/1,000,000) · 0.1 milligrams or 0.01 milligrams of
copper. This is one ten thousandth of the weight of the plastic or 0.01%
or 100 ppm.) You relay the information to the plant superintendent
almost before he finishes his lunch. He now knows what to do and the
crisis is over.


In a Museum

_The Problem_

You are a curator working with the ancient coin collection of a large
museum. A donor has just given the museum a group of 50 gold coins
presumably about 1500 years old. After months of careful study, you have
satisfied yourself that most of those coins are genuine specimens of
that period. Judging from your experience, you decide that a small group
of five are definite forgeries.

However, there are three others that you suspect are also fakes, but you
are not quite certain. You know that both genuine minters and forgers
often tried to save money by diluting their gold with less expensive
metals such as silver and copper. Since the chances are slim that the
forger’s product has the same concentration of gold, silver, and copper
as the genuine coins, you realize that a chemical analysis would help
you decide if the doubtful pieces were real or fake.

An accurate chemical analysis would require a sample of such size that
the coin would be ruined as a museum specimen. You need an analytical
method that can be applied to an infinitesimal sample.

_The Solution_

You are not a scientist but you’ve heard about neutron activation
analysis. Therefore, you contact a radiochemist at a local university
who is an expert in this field.

He decides to use a sampling technique developed by scientists at
Brookhaven National Laboratory for sampling metal objects of
archaeological interest. You obtain from him a set of 50 quartz plates
that have been ground on one side. Following his instructions, you
carefully scrape away a small area on the edge of each coin. You then
rub each freshly cleaned area across the ground surface of one plate
leaving a minute streak of metal similar to a pencil mark.

At the scientist’s laboratory, each plate is carefully placed inside a
quartz tube. No attempt is made to weigh the tiny streak of metal since
you wish only to compare the ratios of the metal concentrations.
However, because the samples make a rather bulky package, the scientist
is concerned with the uniformity of the neutron flux that each sample
will “see”. He therefore also places in each tube an exactly equal
weight of a gold—silver—copper alloy wire (of known proportions) to act
as a standard neutron-flux monitor. The tubes are then sealed and taken
to a reactor to be irradiated for 12 hours.

After the samples are removed from the reactor, the scientist carefully
breaks open each of the quartz tubes and places the sample and the
standard piece of wire in separate numbered plastic capsules with lids.
For an accurate comparison, each capsule is prepared in the same manner.
About 4 hours after the samples are removed from the reactor, he begins
the radioactivity measurements.

The sample capsules are loaded into an automatic sample-changing
mechanism that places each one into an identical position above a
lithium-drifted germanium detector. (See the chapter beginning on page
19.) Gamma-ray spectra are collected all day, first from a sample, then
from its accompanying standard. Each count takes 2 minutes, and 3
minutes are required between counts for data printout and sample
changing. A typical gamma-ray spectrum looks like the one in the figure
on the next page. Notice that only gold (gold-198) and copper
(copper-64) show up in this short counting time. Later on, radioactivity
from silver (silver-110_m_) can be measured using a longer counting
time. This can be done because while the activation products from copper
and gold have relatively short half-lives (12.8 hours and 2.7 days,
respectively), that from silver has a half-life of 270 days. To increase
the sensitivity of the analysis for silver, the scientist repackages and
re-irradiates the samples and wires for 100 hours. Silver-110_m_ is one
of _two_ radioactive isotopes of silver that have the _same_ mass. In
this case, one has a higher energy than the other and decays in a
different way. This is known as an isomeric state and it occurs for many
other elements as well as for silver.

 [Illustration: Graph: “Counts in one minute per 3.1 KeV channel” _vs_
                               “Channel”]

  Element                  Counts    Channel number
  0.158 MsV Au-199            600                40
  0.412 MeV Au-198            800               120
  0.511 MeV Cu-64              50               150
  0.676 MeV Au-198             40               205

                     (Values estimated from graph)

  The spectrum obtained from a streak of metal on a quartz plate after a
  3-hour exposure to neutrons in a reactor and a 6-hour delay before
  counting. The activation products of gold and copper are obviously
  present and are easily measured in only 1 minute.

[Illustration: Graph: “Counts per 100 minutes per 3.2 KeV channel” _vs_
                           “Channel number”]

          Energy                Counts         Channel Number
       0.445 MeV                   230                    130
       0.657 MeV                  1200                    190
       0.687 MeV                   170                    200
       0.715 MeV                   220                    220
       0.760 MeV                   230                    225
       0.820 MeV                    60                    250
       0.884 MeV                   500                    260
       0.937 MeV                   190                    280

                   (Values are estimated from graph)

  The spectrum obtained from the same streak of metal after re-exposure
  to neutrons for 100 hours and a delay of approximately 2 months before
  counting. Activation products from gold and copper have decayed away
  and the gamma-ray spectrum of silver-110m is now observed. In this
  case the sample is closer to the detector than for the earlier
  measurement and the measurement takes 100 minutes.

Two months later, the scientist repeats the procedure of counting the
samples and standards, except that this time the plastic capsules are
closer to the detector, each count is for 100 minutes, and the sample
changer operates for about a week. A typical spectrum looks like that in
the figure on page 39.

The scientist can now compute ratios for the three elements in each
sample and compare them with the standard, but he decides that a
computer could do it faster and with fewer errors. The data collected
during the two series of counts are therefore sent to a data processing
center where, in a matter of minutes, a computer does the following for
each of 50 samples:

  1. Finds the 0.411-MeV gamma-ray peak for gold-198.

  2. Determines the total counts in the peak.

  3. Repeats the process for the corresponding wire standard.

  4. Corrects the total count for the wire for the small amount of
  radioactive decay that occurred in the few minutes between the sample
  count and the standard count.

  5. Computes the ratio: [total count for sample/total count for
  standard (corrected)]

  6. Repeats all the above for the 0.511-MeV gamma ray for copper-64 and
  (in the longer counts) for the 0.658-MeV gamma ray for silver-110.

  7. Computes the ratios: [sample to standard (for copper)/sample to
  standard (for gold)] and [sample to standard (for silver)/sample to
  standard (for gold)].

  8. Tabulates and prints the ratios found in Step 7.

     [Illustration: Graph: Number of coins at indicated ratios vs.
                           Copper/gold ratio]

  Radioactivity ratios for 50 “gold” coins. Above are the silver to gold
  ratios. There are two groups of genuine coins. Five known forgeries
  show considerably higher ratios than the genuine coins. Two of the
  suspect coins also show high ratios but the third, suspect A, shows a
  ratio that falls into one of the genuine groups. Below are the copper
  to gold ratios. Again there are two groups of genuine coins. (The same
  coins make up the two groups here as above.) The five known forgeries
  again show higher ratios than the genuine ones and again the same two
  suspects appear to be forgeries. Suspect A, however, shows a ratio
  similar to one group of the genuine specimens. One therefore concludes
  that suspect A is genuine and that B and C are not.

For example, suppose for _sample 1_ there are 20,000 counts in the
0.412-MeV peak (gold), 190 counts in the 0.511-MeV peak (copper), and
450 counts in the 0.654-MeV peak (silver). Suppose also that _standard
1_ yielded 10,000, 500, and 400 counts for these three peaks (corrected
for decay), respectively. Then the ratio for gold would be
(20,000/10,000) = 2.00, the ratio for copper would be (190/500) = 0.380,
and the ratio for silver would be (450/400) = 1.13.

Finally, the activity ratio of copper to gold would be (0.380/2.00) =
0.190, and the activity ratio of silver to gold would be (1.13/2.00) =
0.565.

Because each sample was irradiated with an identical standard, and
counted in an identical arrangement, the last two ratios will be the
same for different samples if, and only if, the concentrations of gold,
silver, and copper in those samples are in identical proportions. This
will be true no matter where in the reactor or for how long the
irradiation took place.

Now the scientist presents the data to you. You immediately see that (a)
the good coins fall into two groups, one with a silver to gold activity
ratio of approximately 0.56 and a copper to gold ratio of approximately
0.20 and a second group with these ratios approximately 0.51 and 0.18;
(b) the coins you were certain were forgeries have distinctly higher
ratios ranging from 0.60 to 0.65 for silver to gold and from 0.23 to
0.30 for copper to gold; and (c) of the three suspected coins, two have
ratios that fall into the range of the known forgeries, but one, with
ratios of 0.552 and 0.198, is probably genuine.

You present the result to the museum director in the form of a graph
(see the figure on page 41) and a few weeks later, 43 coins are added to
the permanent exhibits of the museum, while 7 are discarded.


In a Criminology Laboratory

_The Problem_

You are a scientist working in the criminology laboratory of a large
metropolitan city. A detective brings you a minute sample of paint taken
from the clothing of a hit-and-run victim. He has a suspect whose
automobile paint seems to match that sample. The suspect was found in
his parked automobile, not far from the scene of the accident. He seems
to fit the description given by two witnesses, and he is extremely
nervous. You scrape a small sample of paint from a recently damaged area
of the suspect’s car, and, (with the aid of a microscope) find that the
pigment content seems to be the same as that taken from the victim’s
clothing. But, are they really from the same paint?

_The Solution_

You know that paint, like almost everything else, contains very small
quantities of impurities that are present only by accident and do not
affect its properties as a useful material. The trace impurities, as
they are called, will vary from batch to batch of the same paint. Very
rarely will a match be obtained in both type and concentration of trace
impurities in two samples if they are not from the same batch.

By measuring a sufficient number of different elements, the probability
of accidentally matching two samples can be as rare as the duplication
of fingerprints in two individuals. Matching of trace impurities is
often called a “fingerprint” method.

With neutron activation analysis, you can obtain the “fingerprints” of
the two samples to see if they match. Although this kind of evidence may
be difficult to use as proof in court, a positive match will let the
detective know that he is on the right track. Also, the suspect might
confess if he is confronted with the evidence and realizes that he is
“caught”. On the other hand, a mismatch will clear the suspect
completely and the detective will know to look elsewhere for the
criminal.

You seal each sample in a tiny polyethylene bag about ½ inch square. One
sample is taken from the victim’s clothing and the second, about the
same size as the first, taken from the damaged area of the automobile.
In preparing these samples, you handle all the materials with clean
forceps because you realize that the most minute dirt from your fingers
will be detected in the analysis.

The two bags are irradiated together for 1 hour in a nearby reactor and
2 hours later you begin counting the samples with a high-resolution,
lithium-drifted-germanium, gamma-ray spectrometer. This will give you a
match (or mismatch) for elements that yield radioisotopes of fairly
short half-life such as manganese (2.56 hours), copper (12.8 hours),
sodium (15 hours), arsenic (27.7 hours), etc. You plan on “counting” the
samples again later on, if the first counts match, so that you can check
on radioisotopes with longer half-lives such as iron (45 days), chromium
(27 days), silver (270 days), cobalt (5 years), etc.

The two gamma-ray spectra you obtain look like those in the figure on
the opposite page. The gamma rays from the irradiated paint taken from
the victim’s clothing indicate the presence of the common elements
sodium, potassium, and copper, but gold, lanthanum, and europium are
also conspicuously present. The gamma rays from the other sample also
reveal sodium, potassium, and gold but in rather different proportions.
More striking is the absence of copper and the two rare earths, and the
presence of manganese and arsenic, which were not indicated in the first
sample.

The paint samples definitely do not match. Therefore, you inform the
detective that his suspect is innocent after all. You’ve solved your
problem, but he still has his. Perhaps the same technique will provide
positive proof when he finds the real culprit.

  [Illustration: Graph: “Counts/10 min per 3.3 KeV channel (arbitrary
                     scale)” _vs_ “Channel number”]

  Element                               Channel number
  .122 MeV Eu (Europium)                            35
  .328 MeV La (Lanthanum)                           95
  .344 MeV Eu                                       96
  .412 MeV Au (Gold)                               110
  .486 MeV La                                      120
  .511 MeV Cu (Copper)                             145
  .815 MeV La                                      240
  .837 MeV Eu                                      245
  .961 MeV Eu                                      290
  1.37 MeV Na (Sodium)                             410
  1.53 MeV K (Potassium)                           455
  1.60 MeV La                                      475

                      (channel numbers estimated)

  [Illustration: Graph: “Counts/10 min per 3.3 KeV channel (arbitrary
                     scale)” _vs_ “Channel number”]

  Element                               Channel number
  0.412 MeV Au (Gold)                              110
  0.511 MeV Na                                     145
  0.559 MeV As (Arsenic)                           160
  0.657 MeV As                                     195
  0.847 MeV Mn (Manganese)                         250
  1.21 MeV As                                      370
  1.37 MeV Na (Sodium)                             410
  1.53 MeV K (Potassium)                           455

                      (channel numbers estimated)

  Gamma-ray spectra of two samples of paint. These two spectra are
  obviously different and, therefore, could not have come from the same
  source.




                      SUMMING UP: WHAT LIES AHEAD


These five situations are intended to show why neutron activation
analysis is used, when it can be applied, and how it works.

In the real world, there are often many reasons _why_ this kind of
analysis is used. As in the situations described here, it may be the
only workable method. Sometimes there may be a choice of methods, but
activation analysis is used because it has certain peculiar advantages
or because it happens to be the most convenient. There are other times,
however, when other analytical methods can and should be used. Such
situations arise when the element sought is not easily activated, or
when a satisfactory alternative method exists that is more economical or
more convenient. The points to remember about the use of activation
analysis are that:

  1. In many cases, no elaborate sample preparation procedure is
  required.

  2. For many elements, it is the most sensitive analytical technique
  known.

The diversity of _applications_ in which activation analysis is used is
enormous and will probably continue to be. The examples given here
represent only a tiny fraction of circumstances in which the method has
been used. Consider that it has been used successfully:

  1. In the microscopic world of biology and medicine;

  2. For meteorites arriving from the vast reaches of space;

  3. In the production lines of consumer products;

  4. For precious samples of moon rocks;

  5. In the most “down-to-earth” business of hunting for new mineral
  sources;

  6. For exploring the causes of Napoleon’s death nearly 150 years
  earlier (see photograph on next page). Today, there is virtually no
  field of science and technology that is untouched by this method.

The illustrations of _procedures_ used in the situations described in
this booklet are typical of some in use today. There are many other
situations that require still other techniques. One of the most
exciting, which will be used with increasing frequency in the future,
involves the use of computers. It has been shown that data collected by
high-resolution gamma-ray spectrometers can be “fed” directly to a
computer. The computer can be programmed to identify unknown components
and to determine the concentrations of elements of interest to the
analyst. It is entirely possible to include corrections for radioactive
decay, possible interferences from other elements present, and many
other factors. It appears quite likely that the kinds of analyses
described here (as well as others) may someday be accomplished
automatically, with far smaller chances for error and probably more
economically.

                      [Illustration: Hair sample]

  Samples of Napoleon’s hair. Neutron activation analysis of these hairs
  revealed that he had been poisoned with arsenic. (He died, however,
  not from arsenic poisoning, but from acute mercury intoxication.)

Other newer techniques that may find increased usage in the future are
exemplified by the method for activation analysis of the whole human
body. The use of neutrons produced by nuclear machines (such as
cyclotrons or other particle accelerators) or produced by compact,
portable isotopic sources will make neutron activation analysis even
more versatile. Isotopic sources produce neutrons as the result of a
nuclear reaction. One such reaction uses alpha particles emitted by
polonium-210 (or some other alpha emitter) to bombard the element
beryllium. A different kind of isotopic source is the man-made
radioisotope californium-252 that decays by fissioning (splitting)
spontaneously and produces neutrons in the process. (One milligram of
californium-252 will spontaneously produce over 10⁹ neutrons per
second.) While californium-252 is quite expensive at present, it is
likely that production costs will be significantly reduced in the
future.

With computers, more convenient radiation sources, and continuing
improvements in the technology of gamma-ray detectors and nuclear
electronics, neutron activation analysis will become more and more a
routine tool of the analyst.




                                APPENDIX


Calculation of arsenic concentration with no standard for comparison.

1. Determination of arsenic-76 activity produced from _1_ microgram of
arsenic at the time it comes out of the reactor.

We use the equation from page 12:

                         A₀ = Nφσ (1 - e^{-λt})

where N is the number of target atoms. (One microgram of arsenic
contains (10^{-6} gram/75 grams per mole[12]) × 6.02 × 10²³ atoms per
mole which is 8 × 10¹⁵ atoms of arsenic.)

φ is the neutron flux. (This would be known to the reactor operator. It
is usually measured by inserting materials of known composition and
measuring their activation. In this case, φ = 10¹³ neutrons per square
centimeter per second.)

σ is the activation cross section. (Neutron cross sections have been
measured and tabulated by scientists. For the activation of arsenic-75
to arsenic-76, the cross section is known to be 4.2 × 10^{-24} square
centimeter.)

λ is the disintegration constant for arsenic-76. (Here, λ = (ln
2[13]/t_{½},(in hours); t_{½}, the half-life for arsenic-76, is 26.6
hours so λ = (0.693/26.6) = 0.026.)

t is the time of the irradiation. (Here t is 12 hours.)

Therefore: A₀, the activity of arsenic-76,

  = 8 × 10¹⁵ × 10¹³ × 4.2 × 10^{-24} × (1 - e^{-0.026 × 12})

  (Note: e is a physical constant, 2.71+)

  = 9 × 10⁴ disintegrations per second per microgram

2. Determination of activity of arsenic measured in the sample and
corrected back to the time of removal from the reactor.

We use the equation:

                        A₁ = (R)/(E × F) e^{λt}

where R is the measured count rate. (In this case, R is the number of
counts per second observed in the 0.559-MeV gamma-ray peak, which is
5300 counts in 20 minutes or 4.4 counts per second.)

E is the efficiency of the detector. (In this case, it is the number of
counts observed in the 0.559 peak for each 0.559-MeV gamma ray emitted
by a radioactive material at the sample distance. This is known for the
detector being used by making other measurements and, for the set-up
used here, is 0.010.)

F is the average number of 0.559-MeV gamma rays emitted in each
disintegration of arsenic-76. (This can be deduced from the decay scheme
of arsenic-76. See the decay scheme for manganese-56 on page 13. In the
decay of arsenic-76 the number of 0.559-MeV gamma rays emitted per
disintegration is approximately 0.41.)

λ is the disintegration constant for arsenic-76. (0.026, see page 49.)

t is the decay time. (This is the number of hours from the time the
sample was removed from the reactor to the time it was counted, or 5
hours.)

Therefore, A₁, the activity of arsenic-76 produced in the sample at the
time of removal from the reactor,

      = (4.4 counts per second)/(0.010 × 0.41) e^{0.026 × 5 hours}

                   = 1200 disintegrations per second

3. Calculation of arsenic concentration in the sample.

We use the equation:

         Concentration in parts per million = (A₁)/(A₀ × W) 10⁶

where A₁ and A₀ were determined above and W is the weight of sample
analyzed or 300 micrograms (0.0003 gram).

Therefore the concentration is

          (1200)/(9 × 10⁴ × 300) × 10⁶ = 44 parts per million.




                               FOOTNOTES


[1]There are exceptions. For a few elements there are no stable nuclei.
    In some cases, there are other differences that make certain atoms
    radioactive.

[2]These gamma rays (called prompt gamma rays because they are
    instantaneously produced when the neutron is captured) can also be
    used for analysis and sometimes are, but we will not be discussing
      this
    type of analysis in this booklet.

[3]Sensitivity in this case means how small an amount of an unknown
    element can be detected.

[4]Nuclide is a general term applicable to all atomic forms of elements.
    Whereas isotopes are the various forms of a single element (hence
    are a family of nuclides) and all have the same atomic number and
    number of protons, nuclides comprise all the isotopic forms of all
    the elements.

[5]The half-life of a radioactive nuclide is the time it takes for half
    the nuclei in a large sample to undergo decay. Note that after half
    of them are gone, a second half-life period will reduce the
    _remainder_ by one half, leaving one quarter of the original number.

[6]The disintegration constant is related to the half-life, T_{½}, by
    the expression: λ = natural logarithm of 2/half-life, or

                  λ = (ln 2)/(T_{½}) = (0.693)/(T_{½})

[7]The detector efficiency is the ratio of the number of gamma rays
    detected to the number emitted by the sample.

[8]A deuteron is the nucleus of a heavy hydrogen (deuterium) atom and
    consists of one neutron and one proton.

[9]Not all nuclear reactors are appropriate for this work. For example,
    reactors designed for electric power production do not have the
    means built into them for inserting and removing small samples for a
    “short” period of irradiation.

[10]A scintillation detector is a crystalline device, usually sodium
    iodide containing a small amount of thallium, which has the property
    of emitting light when energy is absorbed from nuclear radiation.

[11]After a 10-minute irradiation and a 3-minute delay before counting,
    corrected for decay to a common time.

[12]One mole is the atomic weight of an atom or molecule expressed in
    grams, or the weight of 6.02 × 10²³ atoms or molecules per mole.

[13]ln 2 is the natural logarithm of 2.




                              READING LIST


General Information About Nuclear Science

  _Secrets of the Nucleus_, Joseph S. Levinger, McGraw-Hill Book
  Company, New York, 1967, 127 pp., $0.50.

  _Working With Atoms_, Otto R. Frisch, Basic Books, Inc., Publishers,
  New York, 1965, 96 pp., $3.50.

  _The Atom and Its Nucleus_, George Gamow, Prentice-Hall, Inc.,
  Englewood Cliffs, New Jersey, 1961, 153 pp., $1.95.

  _Inside the Nucleus_, Irving Adler, The John Day Company, Inc., New
  York, 1963, 192 pp., $4.95.

  _Radioisotopes and Radiation_, John H. Lawrence, Bernard Manowitz, and
  Benjamin S. Loeb, Dover Publications, Inc., New York, 1964, 131 pp.,
  $2.50.

  _Sourcebook on Atomic Energy_ (third edition), Samuel Glasstone, Van
  Nostrand Reinhold Company, New York, 1967, 883 pp., $15.00.

  The Semiconductor Revolution in Nuclear Radiation Counting, J. M.
  Hollander and I. Perlman, _Science_, 154: 84 (October 7, 1966).


About Activation Analysis

Popular Level

  Neutron Activation Analysis, Vincent P. Guinn, _International Science
  and Technology, Prototype Issue,_ 74 (1961).

  Distribution of Arsenic in Napoleon’s Hair, Hamilton Smith, Sten
  Forshufvud, and Anders Wassen, _Nature_, 194: 725 (May 26, 1962).

  Nuclear Activation Analysis, Richard E. Wainerdi and Norman P. DuBeau,
  _Science_, 139: 1027 (March 15, 1963).

  Neutron Activation Analysis, W. H. Wahl and H. H. Kramer, _Scientific
  American_, 68: 210 (April 1967).

Technical Level

  _Activation Analysis Handbook_, Robert C. Koch, Academic Press, Inc.,
  New York, 1960, 219 pp., $8.00.

  Neutron Activation Experiments in Radiochemistry, K. S. Vorres,
  _Journal of Chemical Education_, 37: 391 (August 1960).

  Radioactivation Analysis, H. J. M. Bowen and E. Gibbons, Oxford
  University Press, London, England, 1963, 295 pp., $8.00.

  _Neutron Irradiation and Activation Analysis_, Denis Taylor, Van
  Nostrand Reinhold Company, New York, 1964, 185 pp., $8.95.

  _Guide to Activation Analysis_, William A. Lyon (Ed.), Van Nostrand
  Reinhold Company, New York, 1964, 186 pp., $5.95.

  _Advances in Activation Analysis_, Volume 1, J. M. A. Lenihan and S.
  J. Thomson (Eds.), Academic Press, Inc., New York, 1969, 233 pp.,
  $9.50.

  _Activation Analysis; Principles and Applications_, J. M. A. Lenihan
  and S. J. Thomson (Eds.), Academic Press, Inc., New York, 1965, 211
  pp., $8.50.

  _Modern Trends in Activation Analysis_, Volumes 1 and 2, J. R. DeVoe
  and P. D. LaFleur (Eds.), National Bureau of Standards Special
  Publication Number 312, U. S. Government Printing Office, Washington,
  D. C., 1969, 2005 pp., $8.50.

  _Pottery Analysis by Neutron Activation_, I. Perlman and F. Assaro,
  _Archaeometry_, 11: 21 (1969).

Bibliographies

  _Activation Analysis: A Bibliography_, G. J. Lutz, R. J. Boreni, R. S.
  Maddock, and W. W. Meinke (Eds.), National Bureau of Standards
  Technical Note 467, U. S. Government Printing Office, Washington, D.
  C., 1969, $8.50.

  _Forensic Science: A Bibliography of Activation Analysis Papers_, G.
  J. Lutz (Ed.), National Bureau of Standards Technical Note 519, U. S.
  Government Printing Office, Washington, D. C., 1970, $0.50.

  _Determination of Light Elements in Metals: A Bibliography of
  Activation Analysis Papers_, G. J. Lutz (Ed.), National Bureau of
  Standards Technical Note 524, U. S. Government Printing Office,
  Washington, D. C., 1970, $0.75.

  _Pollution Analysis: A Bibliography of the Literature of Activation
  Analysis Papers_, G. J. Lutz (Ed.), U. S. Government Printing Office,
  1971, $0.45.

  _14-MeV Neutron Generators in Activation Analysis: A Bibliography_, G.
  J. Lutz (Ed.), U. S. Government Printing Office, 1971, $1.00.

  _Oceanography: A Bibliography of Selected Activation Analysis
  Literature_, G. J. Lutz (Ed.), U. S. Government Printing Office,
  Washington, D. C., 1971, $0.50.


MOTION PICTURES

Available for loan without charge from the USERDA-TIC Film Library, P.
O. Box 62, Oak Ridge, TN 37830.

  _The Nuclear Witness: Activation Analysis in Crime Investigation_, 28
  minutes, color, 1966. This film illustrates the application of
  activation analysis to the investigation of criminal cases involving
  murder, burglary, and narcotics peddling.

  _Nuclear Fingerprinting of Ancient Pottery_, 20 minutes, color, 1970.
  Animated sequences are used to explain several of the analytical
  techniques. Part of the film shows how the research is actually done
  in the laboratory.

  _The Atomic Fingerprint_, 12½ minutes, color, 1964. The principles of
  neutron activation analysis are explained and the machines used in
  this work are shown. Some of its applications in crime detection,
  geology and soil science, analysis of art and archaeological objects,
  oil refining, agriculture, electronics, biology and medicine, and the
  space sciences are illustrated.

  _Neutron Activation Analysis_, 40 minutes, color, 1964. This film
  describes the nature, potentialities, and applications of neutron
  activation analysis. The kinds of neutron sources used and the
  counting techniques are shown. Examples of applications in crime
  detection, geology and geochemistry, agriculture, medicine, the
  petroleum and chemical industries, and the semiconductor industry are
  shown.

                   Photo Credits
  Cover            Federal Bureau of Investigation
  2                Smithsonian Institution
  30 & 31          University Hospital, University of Washington
  47               Dr. Sten Forshufvud

                     [Illustration: Bernard Keisch]


The Author

Dr. Bernard Keisch received his B.S. degree from Rensselaer Polytechnic
Institute and his Ph.D. from Washington University. He is now a Senior
Fellow at the Carnegie-Mellon Institute of Research at Carnegie-Mellon
University in Pittsburgh. He is presently engaged in a project that
deals with the applications of nuclear technology to art identification.
This is sponsored by the National Gallery of Art and in the past has
also received support from the U. S. Atomic Energy Commission and the
National Science Foundation. Previously he was a nuclear research
chemist with the Phillips Petroleum Company and senior scientist at the
Nuclear Science and Engineering Corporation. He has contributed articles
on art authentication to a number of journals. For ERDA, in addition to
this booklet, he has written _The Mysterious Box: Nuclear Science and
Art_, _Lost Worlds: Nuclear Science and Archaeology_, and _Secrets of
the Past: Nuclear Energy Applications in Art and Archaeology_.




                         A word about ERDA....


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improvement of oil drilling methods and of techniques for converting
shale deposits to usable oil.

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of underground heat sources to gas and electricity, and on fusion
reactors for the generation of electricity.

· ENVIRONMENT AND SAFETY—Investigation of health, safety, and
environmental effects of the development of energy technologies, and
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ERDA programs are carried out by contract and cooperation with industry,
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                       [Illustration: ERDA Seal]


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                        Office of Public Affairs
                         Washington, D.C. 20545




                          Transcriber’s Notes


--Retained publication information from the printed edition: this eBook
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End of Project Gutenberg's The Atomic Fingerprint, by Bernard Keisch