EPJ Web of Conferences 284, 17001 (2023)
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https://doi.org/10.1051/epjconf/202328417001
Experimental validation of thermal scattering evaluations
Yaron Danon1,∗ , Dominik Fritz1 , Benjamin Wang1 , Katelyn Cook1 , Sukhjinder Singh1 , Adam Ney1 , Peter Brain1 , Ezekiel
Blain1 , Michael Rapp2 , Adam Daskalakis2 , Devin Barry2 , Timothy Trumbull2 , Chris Chapman3 , and Goran Arbanas3
1
Gaerttner LINAC Center, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
Naval Nuclear Laboratory, P.O. Box 1072, Schenectady, New York 12301, USA
3
Nuclear Energy and Fuel Cycle Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA
2
In order to test the performance of new neutron thermal scattering law (TSL) evaluations it is
desirable to have experimental data that is highly sensitive to the TSL and provides high fidelity information
on the energy dependent performance of TSL evaluations. Three relevant experiments are discussed including:
accurate thermal total cross section measurements, thermal neutron die-away experiments, and neutron leakage
experiments. The experimental setups and results are reviewed and examples provided for some moderators
including polyethylene, Plexiglas, and YH x . For the experiments preformed thus far, there is generally good
agreement between the measured total cross section and simulations using current TSL evaluations, however
in certain energy ranges differences were observed. Similarly neutron die-away and leakage measurements
for samples at room temperature are in good agreement with data computed from TSLs, however leakage
measurements for polyethylene at 29K show discrepancies with TSL evaluations.
Abstract.
1 Introduction
In recent years there has been a resurgence in the field of
thermal scattering law (TSL) evaluations and experiments.
This comes after years that this field was dormant with
little updates or new ENDF evaluations. Evaluated TSL
is based on atomistic calculations that in most cases result
in a phonon spectrum that can be processed using a code
like NJOY [1] to create the scattering kernel for use in
applications. In the evaluation assumptions are made on
the material structure and crystalinity thus the experiments
are also validating such assumptions by comparing them to
real materials.
For neutron moderators such as water (H2 O) and
polyethylene (CH2 ) atomic mix of the nuclide cross sections will result in a very wrong scattering cross section
in thermal energies. TSL evaluations take into account
the change in relative velocity between the neutron and
atom that originate from molecular vibration and rotation
effects (primarily of H). A TSL evaluation is used to reproduce the thermal scattering cross sections and angular distributions below a few eV. In thermal reactor applications
where the neutron flux is mostly isotropic, the highest sensitivity to the scattering kernel is from the total cross section and much less from the angular distributions. Figure
1 shows the thermal total cross section of CH2 calculated
using free gas Doppler broadening and using a scattering
kernel in ENDF/B-8.0 [2], the large difference between the
two is evident as the incident neutron energy decreases.
Direct measurement of the scattering cross section is not
easy but measurement of the total cross section can be ac∗ e-mail: danony@rpi.edu
complished with high accuracy (1-2%) by inferring it from
neutron transmission measurements. Similarly the angular distribution of the scattered neutrons can be calculated
from the TSL and thus the neutron slowing down rate and
neutron leakage from a moderator are sensitive to this distribution.
TSL evaluations will affect results (multiplication factor) calculated for thermal criticality systems and criticality benchmarks, but these systems usually involve other
materials that contribute to the uncertainty of the calculated multiplication factor, thus experiments that are sensitive only to the TSL are preferred for validation. These experiments must have the sensitivity to resolve differences
between evaluations when they occur and cover the different physics of the TSL including temperature.
2 Experiments
Three types of experiments were developed and used, they
include: high-accuracy total cross section measurements
in the energy range from 0.0005 eV to 3 eV, neutron dieaway measurements, and neutron leakage measurements.
These experiments test different aspects of the TSL that
are relevant to applications. These types of experiments
are not new and were previously used, but in order to use
them for validation of modern evaluations, experimental
capabilities need to be re-developed and be available.
2.1 Total cross section measurements
Over the years many cross sections and other nuclear data
were measured at the Gaerttner LINAC Center at Rensse-
© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0
(https://creativecommons.org/licenses/by/4.0/).
EPJ Web of Conferences 284, 17001 (2023)
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1 5 0
1 4 0
P o ly e th y le n e - C H
1 3 0
σt [ b a r n / M o l e c u l e ]
https://doi.org/10.1051/epjconf/202328417001
S ( α, β)
F re e g a s
1 2 0
1 1 0
eV they differ. The ENDF/B-8.0 TSL evaluation is closer
to the measurement of Plexiglas G, but below 0.02 eV it
is higher then the experiment. Such experiments indicate
that the TSL can be reevaluated to achieve a better agreement.
2
1 0 0
1 2 0 0
9 0
8 0
1 0 0 0
6 0
8 0 0
7 0
4 0
0 .0 1
0 .1
N e u tro n E n e rg y [e V ]
σt [ b a r n ]
5 0
1
P le x ig la
P le
P le
E N
K .
G .
6 0 0
s
x ig
x ig
D F
D ro
S ib
la s G - U
la s G 0
/B -8 .0
z d o w ic
o n a e t
V T 0 .1 8 4 "
.1 2 1 "
z 1 9 8 9
a l. 1 9 9 1
4 0 0
2 0 0
Figure 1. Comparison of the total cross section of CH2 calculated using the scattering kernel in ENDF/B-8.0 vs. free gas
Doppler broadened cross sections
0
0 .0 0 1
0 .0 1
0 .1
1
E n e rg y [e V ]
3
Figure 2. The total cross section of Plexiglas comparing the RPI
measurements with others and the cross section generated from
the TSL in ENDF/B-8.0
laer Polytechnic Institute (RPI). The Center utilizes a linear electron accelerator (LINAC) that produces electron
pulses that are 6 ns - 4 µs wide with an energy of about
55 MeV. These electrons are directed to a stack of water
cooled tantalum plates to produce neutrons with an evaporation spectrum of average temperature of about 0.5 MeV
and a spectrum tail up to the maximum electron energy.
Different neutron production targets are used to moderate this spectrum and tailor it to the experimental needs
(for example [3]). To cover the thermal region, a so-called
enhanced thermal target (ETT) was previously developed
[4]. This neutron production target provided good signal
to background and energy resolution to enable resonance
measurements for incident neutron energies from 0.002 20 eV [5].
In order to improve the measurements capabilities at
RPI a cold moderator was recently designed and constructed as an add-on to the ETT and was named ETTC.
The moderator is 2.54 cm thick piece of polyethylene
operating at about 29K [6]. Below 0.01 eV the ETTC
provides a flux enhancement of up to a factor of 8 over
the ETT and thus enables measurement below the lowest
Bragg edge of most materials of interest like Be, YH x ,
ZrH x and others. The ETTC has a usable energy range
from 0.0005 - 3 eV where accurate neutron transmission
measurements can be performed.
Recently both ETT and ETTC were used for measurements of room temperature total cross sections for several
materials of interest to criticality safety applications including polyethylene, polystyrene, and Plexiglas. These
materials are part of one or more criticality benchmarks.
Other materials that are of interest to reactor applications
such as YHx and Be were also measured. To illustrate
the new capabilities, the ENDF/B-8.0 total cross section
of Plexiglas is shown in figure 2 and compared with new
RPI measurements and other experimental data found in
EXFOR [7]. For Plexiglas two types of common variety (G and G-UVT) were measured and below about 0.02
Another example is a measurement of YH1.85 plotted with other experimental data available in EXFOR and
the ENDF/B-8.0 evaluation in figure 3. This comparison
shows the ability to resolve all the Bragg edges at low energies and the wavy behaviors of the cross section between
0.1 and 1 eV. In general the evaluation is in good agreement with the experiment except for the Bragg edge structure between 0.002 to 0.02 eV. This illustrates the need to
use a TSL library that is tailored to the actual material intended to be used in an application and not an ideal material often used for the evaluation. The reasons for disagreement could be related to a different crystalline structure in
the measurements compared to the evaluation or inaccuracies in the physics embedded in the processing codes.
1 8 0
Y H
1 6 0
Y H
2 m m X
5 m m X
E N D F /B
V o r d e r w is c h &
B ra n d 1 9 7 0 (S
Y H
Y H
1 4 0
1 2 0
σt
x
1 .8 5
1 .8 5
1 .8 5
S
S
-V III.0 + Z & H S (a ,B )
W a s s e r r o th 1 9 6 9 ( S c a le d to H /Y = 1 .8 5 ) )
c a le d to H /Y = 1 .8 5 )
1 0 0
8 0
6 0
4 0
2 0
0 .0 0 1
0 .0 1
0 .1
E n e rg y [e V ]
1
3
Figure 3. The total cross section of YH1.85 comparing the RPI
measurements with others and the cross section generated from
the TSL in ENDF/B-8.0
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EPJ Web of Conferences 284, 17001 (2023)
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2.2 Neutron die-away measurements
The use of neutron die-away measurements is an established method for measuring the slowing down time of a
moderator [8]. It was used in the early days of reactor
physics to measure neutron diffusion coefficients of different materials. In this method a pulsed neutron beam
is entering a moderating material and the thermal neutron
population inside the medium, or leaking from it, are measured as a function of time. To understand the physics it is
useful to recall the fundamental mode solution of the time
dependent diffusion equation for the neutron density n(r, t)
in a large medium:
n(r, t) = A0 ψ0 (r)e−αt
Figure 4. A top view of the experimental setup used in this work
showing the DT neutron source on the right, He-3 thermal neutron detector, polyethylene cylindrical sample, and a Cd thermal
neutron return shield surrounding the sample and detector.
(1)
1 0
4
1 0
3
1 0
2
1 0
1
1 0
0
W a te r (3 0 0 m l, H = 7 .2 1 c m ,R a d iu s = 3 .6 4 c m )
E x p e r im e n t
M C N P E N D F /B -8 .0
C o u n ts
where α = v(Σa + DB2 ) and and ψ0 (r) is the spatial distribution. In these equations v is the average thermal neutron velocity, Σa is the average thermal macroscopic absorption cross section, D is the effective diffusion coefficient, and B2 is the geometric buckling which is inversely
proportional to the dimensions of the system. Thus a
large moderator will have a small value of B2 and thus α
is small and dominated by Σa resulting in a slower flux
decay. In a small (leaky) system additional terms are
needed in order to correct the diffusion coefficient and usually a diffusion cooling coefficient C is added such that:
α = v(Σa + DB2 + CB4 ). Measurements of the neutron
die-away α as a function of the buckling can provide information on the thermal diffusion coefficient and thermal
absorption cross section of the moderator [9].
Now-a-days it is more advantageous to compare a neutron die-away measurement to detailed time dependent
simulation using a code like MCNP [10] to check how a
TSL library is performing in a time dependent calculation.
The ability to use small samples of different geometries,
and the relatively low cost of the experiments are advantages of this type of experiment.
An a example of the geometry used for such experiments is shown in figure 4, the geometry is very compact
with flexibility on the sample size and geometry. The system was driven by a commercial pulsed DT source emitting 108 n/s with energy of about 14 MeV, operating at 100
Hz with a pulse width of 10 us.
An initial qualification of the system was performed
using two measurements with a water cylinder - one with
the sample, and one without it. The final result is the sample minus open spectrum. In figure 5 the experiment is
compared with MCNP simulation of the geometry and He3 detector using the ENDF/B-8.0 scattering kernel. The
simulation was for the geometry with the sample only and
did not include the surrounding room. The agreement between the slopes of the experimental and calculated dieaway curves seems very good and can be further quantified
by fitting the data.
Another experiment used a polyethylene cube sample
and is shown in figure 6. In this case it seems that the simulation result has a slightly faster die-away (larger α) compared to the experiment. It is important to note that careful subtraction of the right background is needed. In the
0
5 0
1 0 0
1 5 0
T i m e [ µs ]
2 0 0
2 5 0
3 0 0
Figure 5. Measurement of thermal neutron die-Away from a water cylinder, pulsed and measured from outside the cylinder and
compared with MCNP simulation using the scattering kernel in
ENDF/B-8.0.
region between 75-150 us where the background is negligible the agreement seems better. In this case (room temperature measurements) simulations with other available
scattering kernels gives the same result and such experiment is insensitive to the very small difference between
the evaluations.
2.3 Neutron leakage measurements
A neutron leakage experiment is similar to a die-away experiment. In a leakage experiment a moderator is placed
near a pulsed neutron source, and the detector is placed at
a long distance, about 15m for the experiment described
here. This measurement is thus similar to a time-of-flight
(TOF) experiment where the detection time is related to
the neutron energy. For the experiments reported here, the
RPI LINAC was used with the ETTC target mentioned in
section 2.1 and a polyethylene moderator was used as the
sample. This setup allowed us to test the concept and measure the leakage for a room temperature and cold polyethy-
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1 0
4
1 0
3
1 0
2
1 0
1
0
0
5 0
1 0 0
1 5 0
T i m e [ µs ]
2 0 0
2 5 0
8
F lu x p e r u n it le th a r g y [a r b .]
C o u n ts
P o ly e th y le n e (6 .3 5 c m c u b e )
E x p e r im e n t
M C N P E N D F /B -8 .0
1 0
1 0
https://doi.org/10.1051/epjconf/202328417001
3 0 0
1 0
7
1 0
6
1 0
Figure 6. Measurement of thermal neutron Die-Away from a
polyethylene cube, pulsed and measured from outside the cube
and compared with MCNP simulation using the scattering kernel
in ENDF/B-8.0.
5
0 .0 0 1
E T T
E T T
E T T
E T T
E T T
E T T
C
C
C
E x p
M C
M C
E x p e
M C N
M C N
0 .0 1
e r im e n
N P S im
N P S im
r im e n t
P S im u
P S im u
t 3 7 .5
u la tio
u la tio
(2 9 3 K
la tio n
la tio n
)
K
n 3 7 .5 K (E N D F /B -V III.0 )
n 4 0 .0 K (S p re v a k & K o p p e l (C A B ))
(E N D F /B -V III.0 )
(S p re v a k & K o p p e l (C A B ))
0 .1
E n e rg y [e V ]
1
3
Figure 7. Measurement of neutron leakage from the ETTC moderator at 29K with size of 17.78 x 17.78 x 2.54 cm3 (7 x 7 x 1
inch3 )
lene moderator. The moderator size was 17.78 cm x 17.78
cm and 2.54 cm thick and measurements were done at
two temperatures; 293K and 29K. The experimental and
simulation results with two different TSL evaluations are
shown in figure 7. The simulation in this case included
the evaporation neutron spectrum produced by the tantalum target and included the full geometry of the ETT
target and the added polyethylene moderator. The room
temperature measurement also serves as validation of the
simulation and shows excellent agreement with the experiment regardless of the TSL evaluation used (ENDF/B-8.0
or CAB [11]). The visible Bragg edge near 0.0025 eV
and 0.0008 eV are from lead (or its oxide) that was in the
beam between the moderator and detector. At low temperatures the two evaluations do not agree between them
and show a departure from the experiment. This example shows the high sensitivity of this type of setup to the
TSL evaluation. Because of the good agreement between
the simulation and experiment at room temperature, the
likelihood of a geometry mismatch between the them is
low. There could be several other reasons to the disagreement between the evaluations and experiment which could
relate to the models used and approximations that might
not be valid at such low temperatures or approximations
in the processing code NJOY [1] used to prepare the data
for MCNP.
tal cross section from 0.0008 - 3 eV using the neutron
time-of-flight methods. These measurements had accuracy of about 1.5% dominated by systematic uncertainties.
Knowledge of the exact composition and crystalline structure of the sample is very important for correct interpretation of the measured cross sections. It is also important to
note that accurate knowledge of the capture cross section
of elements in the sample is also needed, in many cases
the ENDF or other evaluations libraries can be used, especially for well know elements such as H and C (where
capture is very small). The die-away and leakage method
provide data that can be compared to time-dependent simulation that help test the performance of a TSL library by
looking at leakage of thermal neutrons at different time
scales.
All mentioned methods provide a comprehensive data
set that validates the TSL and also provide information
about discrepancies and informs the evaluation process on
where improvements are needed.
4 Acknowledgment
Part of this work was supported by the Nuclear Criticality
Safety Program, funded and managed by the National Nuclear Security Administration for the Department of Energy. Additionally, this material is based upon work supported under an Integrated University Program Graduate
Fellowship. Any opinions, findings, and conclusions or
recommendations expressed in this publication are those
of the author(s) and do not necessarily reflect the views of
DOE.
3 Conclusions
Experimental data is needed for validation of TSL evaluations, this data should be sensitive to the features of
TSL such as cross section, angular distribution, and temperature. Three types of experiments; total cross sections,
die-away, and leakage were discussed as possible experiments that can help validate TSL evaluations. The scattering cross section resulting from using the TSL is an important quantity for thermal systems and criticality applications thus accurate and energy detailed measurements
are needed. This was accomplished by measuring the to-
4
EPJ Web of Conferences 284, 17001 (2023)
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