Undergraduate Research Projects in Atomic Collisions and
Gamma-ray Spectroscopy
J.M. SANDERS∗, S.L. VARGHESE∗ , D.W. HAYWICK† and M.L. FEARN†
∗
†
Dept. of Physics, University of South Alabama, Mobile, AL 36608
Dept. of Earth Sciences, University of South Alabama, Mobile, AL 36608
Abstract.
Research projects at University of South Alabama, an undergraduate physics department, have employed a 150-kV
Cockcroft-Walton accelerator for atomic collisions and sodium-iodide and high-purity germanium detectors for gamma-ray
studies. The atomic collision experiments dealt with electron capture and electron loss in collisions of protons and hydrogen
atoms with hydrocarbon molecules. Gamma-ray studies with NaI scintillators determined the potassium content of food using
40 K gamma-rays. Environmental studies of river sedimentation use a HPGe detector to determine 137 Cs and 210 Pb content.
Students learn the physics of the interactions of ionizing radiation with matter, while acquiring a familiarity with high-vacuum
technique, electronics, data acquisition and analysis, and reporting of results.
dx:
ATOMIC COLLISION EXPERIMENTS
df 0
= σc f 1 − σl f 0
(1)
dx
df1
= σl f 0 − σc f 1 .
(2)
dx
The students can then solve the equations to obtain the
final charge state fraction for a given length and pressure
of target gas [3]:
1
R
f0=
+
− f00 exp[−sc (1 + R) P ]
(3)
1+R
1+R
Electron capture and electron loss are processes of fundamental importance to the description of the passage
of beams through matter. In addition of the interest we
have in the processes themselves, the techniques used
to measure capture and loss cross sections find application in a wide variety of other measurements. Consequently, investigations of capture and loss cross sections
are well-suited as vehicles to teach basic principles of
beam/matter interactions and data acquisition.
At the University of South Alabama, we have used
a 150-keV Cockcroft-Walton accelerator to study collisions of 60- to 120-keV protons and hydrogen atoms with
hydrocarbon gasses [1, 2]. A diagram of the beam line is
provided in Figure 1. After magnetic momentum analysis, the protons pass through a differentially-pumped gas
cell containing a target gas– in our case, any of a variety of hydrocarbon gasses. The beam emerging from the
gas cell is charge-state analyzed by an pair of electrostatic plates, and the resulting proton and hydrogen atom
beams are detected by two surface barrier detectors. The
signals from the detectors are amplified, then they are
pulse-height analyzed by multichannel analyzers.
A two-charge-state model of the beam as it traverses
the target can be employed to obtain cross sections for
both electron capture by H+ and electron loss from H0
in a single measurement. Students are shown the coupled rate equations which govern the population in each
charge state as the beam goes through an areal thickness
where f 0 is the charge-state fraction for the neutral
species, f00 is the background neutral fraction, R is the
ratio of the cross section for loss to the cross section for
capture, sc is proportional to the cross section for capture
by H+ , and P is the pressure of the target gas. The capture
cross section is then given by σc = kTl sc and σl = R σc ,
where l is the effective length of the gas cell, k is the
Boltzmann constant, and T is the target gas temperature.
The capture and loss cross sections are obtained from
a non-linear least-squares fit of Eq. (3) to experimental
charge state fractions as a function of target pressure.
When performing the non-linear least-squares fit, f00 , sc ,
and R were the fitting parameters. This two-state model
does not include any contributions from H− , since the
fraction of the beam in the H− charge state at these energies is expected to be sufficiently small that contributions
from H− to the H+ and H0 charge state fractions may be
neglected [4, 5]. An example of a fit of Eq. (3) to experimental neutral fractions is shown in Fig. 2, and plots of
CP680, Application of Accelerators in Research and Industry: 17th Int'l. Conference, edited by J. L. Duggan and I. L. Morgan
© 2003 American Institute of Physics 0-7354-0149-7/03/$20.00
847
FIGURE 1. Schematic diagram of the experimental apparatus.
0.3
gamma-ray to determine the potassium content of a number of foods (bananas, red beans, black beans, powdered
milk, and potatoes). The apparatus consisted of a 2”×2”
NaI scintillator with pre-amplifier, amplifier, and multichannel analyzer. The NaI detector was shielded with
lead bricks to reduce the background of 40 K from the
surroundings.
In order to simplify analysis, the samples and the calibration source used the same type of holder. The calibration source was a container of Morton’s Lite™lowsodium salt obtained from the local grocery store. In
such salt, a portion of the NaCl is replaced with KCl.
The amount of K in the container was obtained from
the nutritional information chart on the side of the container. The samples were placed in a second Morton’s
Lite™container which had been emptied of salt and lined
with thin plastic. Spectra of the samples, calibration
source, and background were accumulated for 24 hours.
The potassium content of each sample was computed
using
Neutral Fraction
0.25
0.2
0.15
0.1
60 keV H+ on Acetylene
0.05
0
-10
0
10
20
30
40
Pressure (mTorr)
50
60
FIGURE 2. Neutral charge fraction versus pressure curve for
60 keV H+ on acetylene. The full curve is the result of a nonlinear least-squares fit of equation (3) to the data.
CK = (1 × 105 mg/100g)
capture and loss cross sections for acetylene and propylene targets are shown in Fig. 3.
These measurements allow the students to learn data
acquisition and analysis techniques, to learn about the
processes of electron capture and electron loss, and to
apply their knowledge of coupled differential equations
to solve for the charge state evolution as the beam traverses the target. In addition, students have learned electronic construction techniques as they have assisted in
the design and construction of Hall probe sensors, thermocouple gauge readouts, single-channel analyzers and
coincidence units. Much of the construction of the beam
line was done in-house and students were again active in
the design, construction, and testing of that apparatus.
N s − N b Mc
N c − N b Ms
(4)
where Ns was the number of counts in the 40 K peak in
the sample spectrum, Nc was the number of 40 K counts
in the calibration spectrum, Nb was the number of 40 K
counts in the blank (background) spectrum, Mc was the
mass of potassium in the calibration source, and Ms was
the total mass of the sample.
Results of this experiment are presented in Table 1
along with potassium content values from nutrition data.
It can be seen that the potassium content determined by
gamma-ray analysis is in fair to good agreement with the
accepted values. More careful shielding of the detector
would probably improve the quality of the results. Since
this project was performed, a similar measurement of
potassium in bananas, potatoes, and prune juice has been
reported by Hoeling et al.[9] Their technique differs
somewhat from the present experiment by using much
larger samples (about 3 kg compared to our samples
which were typically about 250 g) and by spiking the
samples with K in order to calibrate them.
POTASSIUM CONTENT OF FOOD BY
GAMMA ANALYSIS
Potassium-40 is a long-lived, naturally-occurring isotope
amounting to 0.0117% of natural potassium. It emits
a gamma-ray of energy 1461 keV. We have used this
848
-14
-14
10
10
10-15
2
Cross section (cm2)
a
Cross section (cm )
σl
10-15
10-16
σc
10-17
10-18
10-19
10-20
σl
b
10-16
10-17
σc
10-18
10-19
1
10
100
10-20
1000
Energy (keV)
100
1000
Energy (keV)
FIGURE 3. (a) Acetylene (C2 H2 ) target electron capture cross sections for H+ and electron loss for H0 . Capture data shown:
, present; , Ref. [6]; ^, Ref. [7]. Loss data shown: N, present. (b) Propylene (C3 H8 ) target electron capture cross sections for H+
and electron loss for for H0 . Capture data shown: , present; ^, Ref. [7]. Loss data shown: N, present.
SEDIMENTATION STUDIES USING
GAMMA-RAY SPECTROSCOPY
a 46.5 keV gamma ray. Although it is naturally a component of the soil as a member of the 238 U decay chain,
210 Pb is typically not in equilibrium due to the addition of
210 Pb fallout from 222 Rn in the atmosphere. This disequilibrium between 210 Pb and its precursors allows buried
layers (no longer receiving fallout) to be dated. The technique can yield dates for recent sediments up to one to
two hundred years [12].
Sediment cores have been taken from six sites in Dog
River whose watershed drains the city of Mobile, AL.
The sites were chosen to sample regions of the watershed where it is expected that sedimentation would vary
depending on the amount of urbanization in that part of
the watershed. Each core is extruded and sliced into 2 cm
samples. After the samples have dried, the relative 137 Cs
content is determined from a gamma-ray spectrum of
the sample taken with a high-purity germanium (HPGe)
detector. A comparison of the region of the 661.6 keV
gamma-ray of 137 Cs from samples near the top (2-4 cm)
and near the bottom (116-118 cm) of the core is shown in
Fig. 4. The deeper (older) sample clearly has little 137 Cs
content, while the more recent upper sample has a prominent 661.6 keV peak. A plot of the relative 137 Cs content
as a function of depth in the core is shown in Fig. 5 from
Rabbit Creek, a tributary of Dog River where little development has taken place. A clear onset of 137 Cs content marks the 1954 horizon, while the 1964 fallout maximum is also visible. This Cs profile is typical of regions
with steady sedimentation rates and little disturbance of
the sediment. Since the 1954 horizon is approximately
70 cm, we can conclude that the average accumulation
of sediment over the last 50 years is about 1.4 cm/yr.
Student activities associated with this project have
Short-lived radionuclides can be useful in providing
dates for recent sediment layers in lakes and streams.
Two isotopes in particular have found employment in
such dating: 137 Cs and 210 Pb. Cesium-137 has a halflife of 30.2 years and emits a 661.6 keV gamma-ray.
Fallout of 137 Cs began with atmospheric testing in 1953,
reached a maximum with a flurry of tests in 1962, then
declined rapidly after the Nuclear Test Ban Treaty of
1963 [10, 11]. Measurement of 137 Cs content as a function of depth in a sediment core can allow layers to be
associated with the years of significant change in fallout. Lead-210 has a half-life of 22.26 years and emits
TABLE 1. Potassium content of foods determined by 40 K
gamma-ray analysis compared with “accepted" values.
a
b
c
d
e
f
Sample
Present
(mg K/ 100 g)
Banana
Black Bean (dry)
Red Bean (dry)
Powdered Milk (dry)
NuSalt™
Potato (raw)
351 ± 47
1441 ± 38
1541 ± 39
1929 ± 160
46856 ± 1827
424 ± 47
Accepted
(mg K/ 100 g)
396a
1667b
1540c
1697d
53000e
407f
Ref. [8]
Ref. [8], value for raw beans corrected for moisture content.
Ref. [8], value for raw beans corrected for moisture content.
From product nutrition label.
From product nutrition label.
Ref. [8]
849
Dog River, Site C, Core 1
ACKNOWLEDGEMENTS
2-4 cm
116-118 cm
70
Several undergraduate students played leading roles in
these projects, namely, W.J. Harris, M. Byrne, G.A. Soosai, S.E. Gardner, C.H. Fleming, and M.D. Williams.
Their interest, enthusiasm, and work are gratefully acknowledged. We thank Dr. F.D. McDaniel of the University of North Texas for his original inspiration of the
potassium analysis of foods. This work has been supported in part by the USA Research Council, USA Committee on Undergraduate Research, and by a grant from
the U.S. Environmental Protection Agency STAR program.
137
60
Cs
Counts
50
40
30
20
10
0
620
REFERENCES
630
640
650
660
670
680
690
700
1.
Sanders, J. M., and Varghese, S. L., “Electron Capture
From Hydrocarbon Molecules by Proton Projectiles
in the 60–120 keV Energy Range,” in Applications of
Accelerators in Research and Industry: 15th International
Conference, edited by J. L. Duggan and I. L. Morgan, AIP
Conf. Proc., New York, 1999, vol. 475, pp. 70–72.
2. Sanders, J. M., Varghese, S. L., and Fleming, C. H.,
“Electron capture and loss cross sections for neutral
projectiles colliding with atoms and molecules,” in
Applications of Accelerators in Research and Industry:
16th International Conference, edited by J. L. Duggan
and I. L. Morgan, AIP Conf. Proc., New York, 2001, vol.
576, pp. 209–212.
3. McDaniel, E. W., Mitchell, J. B. A., and Rudd, M. E.,
Atomic Collisions: Heavy Particle Projectiles, John Wiley
& Sons, New York, 1993.
4. Toburen, L. H., Nakai, M. Y., and Langley, R. A., Phys.
Rev., 171, 114–122 (1968).
5. Stier, P. M., and Barnett, C. F., Phys. Rev., 103, 896–907
(1956).
6. Eliot, M., J. Phys. (Paris), 38, 21–27 (1977).
7. Varghese, S. L., Bissinger, G., Joyce, J. M., and Laubert,
R., Nucl. Instrum. Meth., 170, 269–273 (1980).
8. USDA Nutrient Database for Standard Reference,
Release 15, U.S. Department of Agriculture, Agricultural
Research Service (2002).
9. Hoeling, B., Reed, D., and Seigel, P. B., Am. J. Phys., 67,
440–442 (1999).
10. Ritchie, J. C., and McHenry, J. R., J. Environ. Qual., 19,
215–233 (1990).
11. Eisenbud, M., and Gesell, T., Environmental
Radioactivity: From Natural, Industrial, and Military
Sources, Academic Press, New York, 1997, chap. 9.
12. Appleby, P. G., and Oldfield, F., “Application of Lead210 to Sedimentation Studies,” in Uranium-series
Disequilibrium: Applications to Earth, Marine, and
Environmental Sciences, edited by M. Ivanovich and R. S.
Hardmon, Oxford Univ. Press, New York, 1992, chap. 21,
2 edn.
Energy (keV)
FIGURE 4. Comparison of 137 Cs gamma-ray spectra of sediment strata from Dog River, Mobile, AL. The dashed line is
the spectrum of the slice from 2 cm to 4 cm below the top of
the core, the solid line is the spectrum of the slice from 116 to
118 cm from the top of the core.
Dog River, Site E, Core 1
0
20
1964
Depth (cm)
40
60
1954
80
100
120
0
20
40
60
80
100
Relative Cs Yield (cts/g)
FIGURE 5. Cesium-137 yield as a function of depth in a core
from Rabbit Creek, Dog River, Mobile, AL. The onset of Cs
in 1954 and the fallout maximum of 1964 are indicated with
arrows.
been in the design and construction of the shielding for
the HPGe detector, taking the sediment cores, preparing
the samples for counting, and counting the samples. Ongoing projects will involve performing an efficiency calibration of the detector and analysis of 210 Pb data.
850