**AVERAGE ATOMIC NUMBER OF HETEROGENEOUS MIXTURES
FROM THE RATIO OF GAMMA TO FAST-NEUTRON ATTENUATION **

**R. J. Rasmussen, W. S. Fanselow, H. W. Lefevre, M. S. Chmelik,
J. C. Overley,
A. P. Brown, G. E. Sieger, and R. M. S. Schofield **

*Department of Physics, University of Oregon, Eugene , Oregon
97403-1274 *

The attenuation of a continuous spectrum of fast neutrons by each pixel
in a luggage image can be used to detect plastic explosives in the presence
of other materials. The method involves deconvolution of the attenuations
into elemental compositions of H, C, N, O, and X, where X includes everything
other than these elements. To improve discrimination, one can also measure
the average atomic number, Z, of the mixture of materials in each pixel.
We have measured attenuations, by single-element samples, of prompt rays
produced from bombardment of a thick Be target with 4.2 MeV deuterons.
We report, in this regard, measured prompt gamma-ray spectra, whose median
energies indicate that associated attenuations are dominated by Compton
scattering. Attenuations were measured subsequently for several thicknesses
each of C, Al, Cu, Cd, Sn, and Pb. We have also investigated the attenuation
of the fast-neutron spectrum between 8.2 MeV and 5.5 MeV . We found that
the ratio of gamma-ray to neutron attenuation generally increases, albeit
not linearly, with Z. We apply these results to examine the effective Z
of heterogeneous mixtures of H_{2}O-C and C-Al, and have begun
to incorporate effective Z into explosives-detection algorithms.

**Keywords**: neutron attenuation, -ray attenuation, explosives detection,
atomic number

**Corresponding author**: R. J. Rasmussen, Department of Physics, University
of Oregon, Eugene, OR 97403-1274,

tel: (541) 346-4783, fax: (541) 346-5861, email: rjr@conch.uoregon.edu.

**INTRODUCTION **

It has been shown that many energetic materials possess distinct chemical signatures, particularly with regards to nitrogen and oxygen content [1]. Various analytical techniques which rely on these characteristics are currently under investigation to determine their efficacy for detecting concealed explosives in airline passenger luggage. We have developed a fast-neutron, time-of-flight (tof), technique for this purpose.

In part, the technique involves unfolding a neutron attenuation spectrum
based on individual contributions of the product of the projected number
densities, p_{i}, of hydrogen (H), carbon (C), nitrogen (N), and
oxygen (O) and their respective total neutron cross sections [2]. All other
elemental contributions are lumped together as a fictitious element, X,
which has been assigned an energy independent cross section. Based on the
results of deconvolution, each picture element, or pixel, of a scanned
luggage item addresses a bin in a 5-dimensional, orthogonal, space. The
coordinates which span this space are derived from superpositions of particular
p_{i}. Through numerous computer simulations, each of the 4x10^{6}
bins are assigned a probability, a so-called B-matrix value, that an explosive
signature has been encountered. For a complete description of the technique,
the reader is referred to the literature [3].

Although the technique has proven very effective, we have found restricting the spectral analysis to 5 basis elements problematic. In particular, when extraneous elements make a substantial energy-dependent contribution to the attenuation spectrum, the unfolding algorithm accounts for such contributions by erroneously adding or subtracting various amounts of H, C, N, and O. These complexities, in principle, can be circumvented by including additional appropriate elements in the analysis. Unfortunately, this approach involves considerably more computing time. At some juncture of the analysis, it would be advantageous to consider an additional parameter to warrant clearly the need to carry out a more complete analysis. We have found that the average atomic number, Z, can serve this purpose. To this end, we have developed a technique to approximate Z of any given material, or assemblage of materials, from the ratio of gamma-ray to fast-neutron attenuation.

**EXPERIMENTAL METHODS**

Prompt gamma-ray and neutron attenuations were evaluated from neutron tof spectra. Neutrons for these experiments were produced by bombarding a 3mm thick beryllium, Be, target with a 4.2-MeV deuteron beam from the University of Oregon 5-MV Van de Graaff accelerator. The beam was chopped at 1 MHz and klystron bunched; beam duration at the target was about 1.5 ns FWHM. Under these conditions, time-averaged beam currents were approximately 1 microampere.

Neutrons produced at 0^{o}, with respect to the deuteron beam,
were collimated to a fan beam by a 40-cm thick collimator of high-density
polyethylene. The collimator was sandwiched between 1-m diameter tanks,
filled with a water/lithium-carbonate mixture, which served as a target
shield. Sixteen neutron detectors, arranged in a linear array, were stationed
approximately 4m from the source. Each was constructed from a 6-cm square
plastic scintillator, 2.5-cm thick, coupled to a 12-stage Hamamatsu photomultiplier
tube, PMT, via a tapered acrylic light pipe.

Timing signals, derived from the deuteron beam and from each PMT, were
routed to a time-to-amplitude converter, TAC [4]. Corresponding events
were processed by quad analog-to-digital converters, ADCs, and stored as
8192-channel neutron tof spectra in histogramming memories; events were
accumulated for typically 80 C of total charge on target. Each raw spectrum
was then charge normalized and compressed into standardized 0.2 ns/m flight-time
bins. Such spectra exhibit a narrow prompt peak positioned at 3.4 ns/m
and several prominent kinematic edges which distinguish various neutron
groups characteristic of ^{9}Be(d,n) reactions.

Prompt gamma-ray and neutron attenuations were evaluated from the logarithm of the ratio of background-corrected sample-out (incident) to sample-in (transmitted) standardized spectra over an appropriate flight-time (energy) interval. For gamma rays, a single spectrum channel at 3.4 ns/m was used to evaluate the attenuation, while for neutrons, attenuations were averaged over a relatively high-energy regime (5.5-8.2 MeV) between 25-35 ns/m.

Systematic gamma-ray and neutron attenuation measurements were carried
out subsequently for various thicknesses of C, aluminum (Al), copper (Cu),
cadmium (Cd), tin (Sn), and lead (Pb). Additionally, attenuations from
binary heterogeneous mixtures of H_{2}O-C and C-Al were studied.
In each of the cases above, samples were placed directly at the exit slit
of the collimator. This provided improved signal to noise by allowing one
to average results over several shadowed detectors. For a more complete
description of the experimental design, the reader is referred elsewhere
[4].

We have also measured the thick-target, 0^{o}, gamma-ray, spectrum
from ^{9}Be + d reactions at 4.2 MeV. For these experiments, a
3"x3" NaI (Tl) scintillator was coupled to a PMT, as described
above, and positioned in front of the neutron-detector array, about 3.5
m from the source target. In this configuration, the TAC output was coupled
to a single-channel analyzer, SCA, which provided a gating signal for an
ADC. The linear input signal to the ADC was obtained from the PMT anode
after appropriate pulse-shaping amplification. Spectra were then acquired
by setting the SCA window on the prompt peak of the neutron tof spectrum.
Backgrounds were evaluated by moving the SCA window off the prompt gamma-ray
peak.

**RESULTS AND DISCUSSION **

The prompt gamma-ray spectrum observed for 4.2 MeV deuterons on ^{9}Be
is shown in Fig. 1. The spectrum has been corrected for background; however,
it has not** **been corrected for the energy dependence of detector
efficiency. Most of the prominent peaks have been identified and assigned
a label containing the letters

**FIGURE 1.** Thick-target, zero-degree gamma-ray spectrum
from ^{9}Be + d reactions at 4.2 MeV.

The peaks identified with **A** labels are associated with ^{9}Be(d,n)
reactions, and those identified with **B**

labels arise from ^{9}Be(d,p) reactions.

To investigate this prediction, gamma-ray attenuations, denoted g_{a}
, were measured for various single-element samples, as described above.
Several thicknesses of each sample type were employed to identify potentially
influential effects due to beam hardening. Representative data from these
experiments are shown for C by the filled circles in Fig. 2, wherein attenuations
are plotted against calculated projected number densities, p. For most
of the samples investigated, we found g_{a }simply proportional
to p. Slightly more complicated behavior, however, was observed for Pb.
In this instance, beam hardening and/or additional scattering mechanisms,
e.g. Compton plus pair production, were believed responsible. We have,
nonetheless, computed an effective attenuation coefficient, dg_{a}
/dp, for each set of sample data. Subsequent analysis revealed a power-law
dependence of the effective attenuation coefficients on Z, i.e. dg_{a}/dp
Z^{n}, where n=1.25.

**FIGURE 2.** Prompt gamma-ray (filled circles) and
fast-neutron (open circles) attenuations for various

projected number densities, i.e. thicknesses, of carbon.

Similar data were obtained for the attenuation of high-energy neutrons;
we refer to these attenuations as n_{a}. These results are also
illustrated in Fig. 2 by the open circles. In slight contrast to the previously
mentioned behavior of g_{a}, we found n_{a }~_{ }p
for each sample type. Since the n_{a} were evaluated at relatively
high energy, we expected the corresponding total neutron cross sections,
s_{t}, to be roughly equal to the geometric cross sections, s_{g}.
In this case, s_{g}^{1/2} depends linearly on A^{1/3},
where A is the atomic mass [7]. Consistently, we found that the values
of s_{t}, derived from dn_{a }/dp, indeed vary with A in
this manner. As evidenced below for additional single-element samples,
the agreement was less satisfying for light nuclei, where s_{t}
exhibits considerable resonant structure over the energy interval of interest.

The relationship between s_{t} and Z, unfortunately, can be
rather complicated. A semi-empirical treatment connects the atomic mass
of the most stable nuclei to the corresponding atomic number through the
following relation^{ }[7]: Z = A / {1.98 + 0.0155 A^{2/3}
}. For light elements, e.g. Z < 20, Z A/2; thus, one again obtains a
simple linear relation between s_{t}^{1/2} and, this time,
Z^{1/3}. For heavier elements, the full expression for A in terms
of Z must be incorporated into the formulation for the geometric cross
section. In either case one can express s_{g }as a continuous increasing
function of Z.

Based on the above results for g_{a }and n_{a}, we define
an additional explosives-detection parameter by the ratio of gamma-ray
to fast-neutron attenuation. Since both attenuations depend linearly on
projected number density, this quantity is independent of sample thickness.
Furthermore, to the extent that g_{a} and n_{a} are continuous
functions of Z , their ratio is also a continuous function of Z, at least
over the interval for which Z takes on physically meaningful values.

Thus, we summarize the results of gamma-ray and neutron-attenuation
measurements for all sample types and thicknesses in Fig. 3, where values
of g_{a }/n_{a} are plotted against Z. The attenuation
ratios for each sample thickness are depicted by the filled circles, and
their corresponding averages are shown by the open circles. The open circle
located at the origin was included for line fitting. Note that the deviations
in the data increase with Z. Computer-simulation studies indicate these
effects result from beam-hardening , manifested by a thickness dependent
absorption coefficient for gamma-ray attenuation. For simplicity, we describe
the locus of points corresponding to the averaged attenuation ratios by
2 line segments (solid lines) which intersect at Z=6. These line were obtained
simply by fitting separately the origin and the averaged carbon point and
the carbon point and the averaged lead point.

**FIGURE 3**. Ratio of gamma-ray to fast-neutron attenuations,
g_{a}/n_{a }, as a function of atomic number, Z.

The filled circles were obtained from attenuation measurements carried
out on samples of various thick-

nesses, cf. Fig. 2, the open circles are their corresponding averages,
the filled triangles were obtained from

samples of a single thickness, and the solid lines were obtained by fitting
separately the origin with the

averaged C point and the C point with the averaged Pb point.

In order to investigate the usefulness of this approximation, we have
measured attenuation ratios for several additional single-element samples,
including Be, N, O, calcium (Ca), and iron (Fe). These data are also shown
in Fig. 3. For the most part, these data are clustered around the 2 line
segments. As mentioned earlier, however, one expects some departure from
a smooth Z dependence, particularly for low-Z elements, where the geometric
approximation to _{t} is less than adequate. We have investigated
this effect further for several additional elements by analyzing total
cross-section data obtained from the National Nuclear Data Center at Brookhaven
National Laboratory. We averaged their values for _{t} over the
same energy interval specified above. We found that the _{t} obtained
in this way, generally increased with Z; however, the dependence was not
smooth. Although this behavior is presumably also mirrored in the data
of Fig. 3, the piece-wise linear approximation shown here was deemed a
sufficient measure of Z for our ultimate purposes. Obviously, more sophisticated
procedures could be invoked to represent the data more faithfully.

We have applied these results subsequently to investigate the effective
Z of various heterogeneous binary mixtures of H_{2}0-C and C-Al.
Results for the H_{2}O-C series are shown in Fig. 4, where Z_{eff}
was obtained from the appropriate line segment of Fig. 3, and <Z>
was computed from the number-weighted average for the mixture. As clearly
demonstrated by the linear fit to the data, Z_{eff} was essentially
equal to <Z> for each mixture. Although nearly identical results**
**were obtained for the C-Al series, we fully expect more complicated
behavior from mixtures whose end members do not lie on one of the line
segments.

**FIGURE 4.** Effective Z versus number-weighted average
Z for heterogeneous mixtures of H_{2}O-C.

The solid line is a least-squares fit to the data.

**CONCLUSIONS**

Notwithstanding, we have begun to incorporate the results of these analyses into an explosives-detection algorithm. In our experience, knowledge of Z greatly facilitates the associated decision process. Firstly, many so-called plastic explosives possess effective Z values which are somewhat larger than ordinary luggage items [8]; consequently, the probability of encountering an explosive is in some way related to Z of the sample in question. Currently, we are evaluating the inclusion of such a probability in a correlation analysis, which yields a single explosive probability from a 2-dimensional array of attenuation spectra corresponding to a given piece of luggage. Finally, Z has proven valuable in revealing various materials which may shield a concealed explosive from the analysis. These situations are almost always conspicuously marked by regions of elevated values of Z. Such cases signal the need to consider additional elemental contributions in the analysis of corresponding attenuation spectra.

**ACKNOWLEDGEMENTS **

In closing, the authors wish to acknowledge the many supporting efforts of Ms. Barbara Telecky. This work was supported by the Federal Aviation Administration Technical Center under Grant No. 94-G-020.

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