Status and Perspectives of a Forward Scattering Project for
the Multielemental Analysis of Liquids
J. A. Liendoa,b, A. C. Gonzálezb, N. R. Fletcherc and D. D. Caussync.
a
Departamento de Física, Universidad Simón Bolívar, Caracas,Venezuela
Centro de Física, Instituto Venezolano de Investigaciones Científicas, Caracas,Venezuela
c
Physics Department, The Florida State University, Tallahassee, FL, USA.
b
Abstract. A project based on low mass multielemental analysis of liquid samples by using forward elastic scattering is under
progress. Elastic cross section measurements for the reactions 13 MeV 6,7Li +A and 24 MeV 16O +A, A being any nucleus
lighter than Na, are necessary due to the existence of non-elastic processes. The non-Rutherford character of some of the
reactions quoted above has been established from experiments carried out at 12.45º, 16.45º, 20.45º and 28.0° where A = Be, C, O
and Si. The accuracy and precision of the measured cross sections have been tested. In the future, accurate cross section
determinations will be required for lighter target elements such as B, Li and H. The dilution of a liquid sample improves the
spectrum resolution. Efforts are currently concentrated on determining if the relative yields corresponding to various elements
present in a given sample remain constant as dilution changes.
is important because previous publications [3] show
remarkable improvements in the spectrum energy
resolution when a complex sample such as amniotic
fluid is diluted.
INTRODUCTION
An accurate determination of forward angle cross
sections and a quantification of the relationship
between sample dilution and elemental yield are
required in order to improve a method proposed
previously [1] for low mass multielemental analysis of
liquid samples. Differential cross sections relevant to
this method have been determined [2] from elastic
yields collected simultaneously at 12.45°, 16.45°,
20.45° and 28° for the reactions 6,7Li +9Be , 6,7Li + 12C,
6,7
Li + 16O, 6,7Li +28Si at Elab(6,7Li) = 13 MeV and 16O
9
+ Be, 16O +12C, 16O +16O and 16O +28Si at
Elab(16O)=24MeV.
In this work, we have tested the accuracy and
precision of the measured cross sections. Using
several targets, a set of three or four density values has
been obtained for each target element mentioned
previously by using elastic yields collected at different
angles and the corresponding cross sections reported in
a recent publication [2]. The consistency of the density
values obtained for each target element studied has
been used as the criterium to test the precision of our
measured cross sections. The cross section accuracy
has also been tested by comparing some of our density
results with target thickness nominal values supplied
by the target maker. In addition, we have carried out a
preliminary quantification of how amniotic fluid
elastic yields behave as sample dilution changes. This
EXPERIMENTS AND RESULTS
The experimental configurations used in this
research have been discussed in detail in a recent
publication [2]. In this work, for each target element of
interest (9Be,12C,16O and 28Si), we have carried out an
experiment where that element, contained in selected
targets made in the Florida State University
Accelerator Laboratory, has been bombarded with
three beams: 13 MeV 6Li, 13 MeV 7Li and 24 MeV
16
O. Elastically scattered data have been gathered
simultaneously at 12.45°, 16.45°, 20.45° and 28°.
The dominance of Rutherford scattering has been
assumed previously [1] to obtain density estimates for
several elements contained in amniotic fluid. However,
we have evidence for the existence of non-elastic
processes as shown in Fig. 1. The spectrum displayed
in this figure was collected at 28° when a target
containing carbon and gold was bombarded with a 16
MeV 7Li beam. The most prominent peaks, labeled in
Fig. 1a, are due to 7Li ions elastically scattered from
12
C and 197Au while the small peaks observed in the
region of the spectrum above channel 1050 (expanded
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
377
total charge, in µc units, collected during every
experiment in a Faraday cup attached to the scattering
chamber and located behind the target, and dσ/dΩ is
the measured differential cross section (in the
laboratory reference frame) whose precision is being
tested.
We have obtained dσ/dΩ values for 6,7Li-beam
reactions from 16O-beam reaction differential cross
sections by using the equation
in Fig. 1b) correspond to alpha particles produced in
12
C(7Li,α)15N reactions where the 15N nuclei are left
in several excited states labeled by their energies in
Fig. 1b.
Since Rutherford scattering is not the only process
available, we decided to measure elastic scattering
6,7
cross sections for reactions initiated with 13 MeV Li
(
Au + Li
5.28
5
200
0
100
1100
C + Li*
0
800
900
1000
1100
1200
1200
1300
1300
1400
1400
Channel Number
FIGURE 1. Elastically scattered particle spectra collected at
28° from the bombardment of a (C+ Au) target with a 16
MeV 7Li beam.
and 24 MeV 16O beams bombarding target elements
lighter than Na. The determination of accurate cross
sections is required to have confidence in the target
element density values obtained from the method
proposed previously [1]. The elastic scattering method
at forward angles is especially intended to analyze low
mass elements which cannot be detected by established
techniques such as Proton Induced X-Ray Emission
(PIXE) and Total Reflection X-Ray Fluorescence
(TXRF). The first set of cross section measurements
relevant to the method have been reported recently [2]
using 9Be, 12C, 16O and 28Si as target elements.
To test the precision of our cross section
measurements, the densities of 9Be, 12C, 16O and 28Si
present in several testing targets have been determined
at different scattering angles by using the formula
T ( µ g / cm
2
) =
0 . 266 A T Z P Y
dσ
Q ∆Ω
dΩ
dσ
dσ
Y Z Q
) Li = (
) O Li Li O
dΩ
d Ω YO Z O Q Li
(2)
where the indexes O and Li identify quantities
belonging to the reactions initiated with 16O and 6,7Li
beams respectively. It is obvious that the determination
of (dσ/dΩ )Li is possible if the corresponding (dσ/dΩ )O
is known. We have shown experimentally that the
reactions 16O+ 28Si , 16O+ 16O and 16O+ 12C are
consistent with the Rutherford predictions (at least in
the angular range used in this study). This has allowed
us to obtain (dσ/dΩ )Li values using equation (2) for
the corresponding reactions 6,7Li + 28Si, 6,7Li + 16O and
6,7
Li + 12C. Although the 24 MeV 16O + 9Be reaction
was proved to be a non-Rutherford process, we were
able to obtain target dependent cross section estimates
(at several scattering angles) for that reaction which
were then used to determined the 6,7Li + 9Be cross
sections by using equation (2).
Table 1 shows density values obtained in this
research for the target elements mentioned in the
previous paragraph. In most cases, for every targetprojectile combination, at least three density values
were obtained from elastic scattering data collected
simultaneously at 16.45°, 20.45° and 28.0°. The 12C
density values determined from the reactions 13 MeV
6
Li + 12C (using a formvar target) and 13 MeV 7Li +
12
C (using a target, labeled in Table 1 as SiO(c),
containing C, O and Si) show impressive agreements
within the errors. Similar consistent results were
obtained for the density determinations carried out for
9
Be (present in a BeO target bombarded with a 24
MeV 16O beam) and for 28Si (present in two different
SiO targets, labeled by (a) and (b), bombarded with a
24 MeV 16O beam). It is important to remark that the
nominal density value of silicon contained in target
SiO(b) was 8.4 µg/cm2 (given by the target maker)
which is very close to the value of (8.6 ± 0.6) µg/cm2
obtained in this work.
The 16O density values shown in Table 1 for a
formvar target (using the 13 MeV 6Li+16O reaction) are
consistent within the errors if they are calculated from
6.32
7.16
7.57
10
C + Li
300
b)
8.57
15
400
9.81
a)
9.16
Events / Channel
500
(1)
where AT is the target atomic mass number, ZP is the
beam average charge state as the beam passes through
the target, Y is the yield collected at a particular angle,
∆Ω is the detector solid angle in msr units, Q is the
378
TABLE 1. Density values obtained for 9Be, 12C, 16O and 28Si contained in several selected targets.
Target
Denomination
Target
Element
12
C
Projectile
13 MeV 6Li
Formvar
16
O
13 MeV 6Li
Densities
(µg/cm2)
0.23±0.02
0.21±0.02
0.21±0.02
0.074±0.006
0.073±0.009
0.076±0.009
0.078±0.007
0.059±0.006
0.053±0.005
Comments
The density values are obtained at 16.45°, 20.45°
and 28.0° by use of equation (1).
The 6Li+16O cross sections used for the density
determination (equation (1)), were determined by
using, in equation (2), the corresponding Mott
16
O + 16O cross sections.
The 6Li+16O cross sections used for the density
determination (equation (1)), were calculated by
using, in equation (2), the “overestimated” 16O
+16O cross sections.
23±1
9
Be
16
24 MeV O
21±1
23±1
103±3
BeO
135±8
16
O
24 MeV16O
Using Mott 16O +16O cross sections.
154±9
109±4
109±6
Using “overestimated” 16O +16O cross sections.
107±6
12.1±0.8
SiO
(a)
28
Si
16
24 MeV O
12.6±0.9
11.4±0.8
8.6±0.6
SiO
(b)
28
Si
16
24 MeV O
8.5±0.6
Nominal density = 8.4 µg/cm2 (given by the target
maker).
8.6±0.6
5.2±0.5
SiO
(c)
12
C
13 MeV 7Li
5.2±0.4
5.1±0.5
The density values are obtained at 12.45°, 16.45°,
20.45° and 28.0° by use of equation (1).
5.0±0.4
equation (1) with the 6Li + 16O cross sections, obtained
from equation (2), under the assumption that the
16
O+16O reaction is a Mott type process. It is
interesting to point out that although our measured 6Li
+ 16O cross sections were consistent with the results
published by Poling et. al [4], the corresponding 16O +
16
O cross sections do not follow the Mott curve.
However, from the analysis of the 16O+ 12C reaction,
which was proved to follow the Rutherford predictions,
we knew that the 16O + 16O reaction had to be a Mott
process. Using targets of different thickness, we
realized that the target used to determine the16O + 16O
cross sections was so thick that it did not allow us to
distinguish a contaminant contribution located very
379
close to the 16O elastic peak. This led to an
overestimation of the 16O+16O cross sections and,
consequently, to an overestimation, by virtue of
equation (2), of the corresponding 6Li + 16O cross
sections. Table 1 shows that the 16O density values
obtained for the formvar target are not consistent when
the overestimated 6Li + 16O cross sections are used in
equation (1). This clearly indicates that the formvar
target does not contain the contaminant contribution
mentioned above. An opposite situation occurs with
the 16O density determinations of the BeO target (using
the 24 MeV 16O+16O reaction) contained in Table 1. In
this case, the concentration values obtained show
consistency when the “overestimated” 16O+16O cross
sections are used in equation (1). This reveals the
presence of the contaminant in this BeO target. We
have determined 16O concentrations for several BeO
and SiO targets irradiated with 24 MeV 16O. The
results have been similar to those obtained for the BeO
target included in Table 1. In addition, the targets used
by Poling et. al [4] probably had the same type of
contamination since our “overestimated” 6Li + 16O
cross sections [2] are consistent with those reported in
that previous work.
We do not know if the
contamination observed in all these targets containing
oxygen (except the formvar target) is related to the
process of making the targets and/or the beams used
and/or any other reason. More research needs to be
done on this matter.
Recently, we have started the quantification of how
the dilution of amniotic fluid (AF) with distilled water
affects the elastic scattering yields produced by
different elements present in a given AF sample.
Scattering spectra obtained from the bombardment
(with a 13 MeV 6Li beam) of two AF samples prepared
with a relative dilution of 2.5, show that the yield
corresponding to the less diluted sample is
approximately 3 times that of the other sample for the
spectrum region above the elastic carbon peak.
However, a relative yield of 3/2 is obtained for the
region of the spectrum located below the 12C peak. The
discrepancies
obtained
in
this
preliminary
quantification between the relative yields measured for
different regions of the collected spectra (3 and 3/2)
and the nominal relative dilution of 2.5 need to be
understood. Currently, we are involved with the
analysis of
several spectra generated from the
irradiation (with 6Li and 7Li beams) of several AF
targets prepared from the same original AF but with
different dilutions. Our objective on this matter is to
obtain a quantitative relationship between AF dilution
and elastic yield per element contained in a sample.
This determination is important for the consolidation of
the forward scattering method because AF dilution has
been proved to improve the resolution of elastic
scattering spectra [3].
CONCLUSIONS
The consistency of the density values determined
for 9Be, 12C, 16O and 28Si (contained in several selected
targets) by use of cross sections measured in a recent
publication [2] has proved these dσ/dΩ measurements
are highly reliable for the application of the forward
scattering method proposed previously [1] for low
mass multielemental analysis. No explanatiom has
been found for the existence of a contaminant
contribution observed very close to the 16O elastic peak
in the spectra collected for targets containing oxygen
except the formvar backing. The agreement between
our overestimated 6Li + 16O cross sections measured
with thick targets and those reported by Poling et. al
[4] seems to indicate that the targets used by Poling
had a contamination similar to that observed in our
investigation. In the future, we will be carrying out
experiments to measure cross sections necessary for
the quantification of lighter elements such as boron,
lithium and hydrogen.
Preliminary results show no linear dependence
between the degree of dilution of an AF sample and the
elastic yield produced by its constitute elements when
the sample is bombarded with a 13 MeV 6Li beam.
Desorption under ion irradiation may be a factor
contributing to this. One of the goals of this project in
the near future is to analyze AF samples with different
dilutions to try to establish a quantitative relationship
between sample dilution and the elastic yield produced
by elements such as carbon and oxygen contained in
these samples.
ACKNOWLEDGMENTS
This research has been funded by project # S1-PNCB-401, Decanato de Investigación y Desarrollo,
Coordinación de Ciencias Básicas, Universidad Simón
Bolívar, Caracas, Venezuela, The Florida State
University and the National Science Foundation, USA.
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