Background
The NPDGamma Experiment, n + p  d +  , is a precision experiment designed to
test the weak nuclear force in a proton/neutron interaction by examining parity
violating asymmetry in produced gamma rays. As such, this experiment will test
the predictions of the Standard Model concerning interactions of the weak nuclear
force. To analyze the data that will be obtained in the experiment, the neutron flux
at SNS Beamline 13 must be known. The flux is required for modeling the beam
correctly, correcting the experimental data, and estimating the needed statistics for
the measurement. Accordingly, the purpose of this project was to measure the
actual flux, and to compare it with the theoretically predicted value.
Neutron Beam Intensity for the Spallation Neutron Source Beamline 13:
The NPDGamma Experiment
Analysis and Results
Jeremy Stewart
University of Tennessee at Chattanooga
Apparatus
The apparatus consisted of two cadmium apertures, a 6Li scintillator,
and a photomultiplier tube (PMT). The signals from the PMT were
conditioned and counted using Nuclear Instrumentation Modules
(NIM).
Discriminator Scan
A discriminator was used to exclude any cosmic rays, photoelectrons, and gamma ray bckground from the neutron signal. A
discriminator scan assisted in determination of the threshold voltage.
We decided to use a threshold of 30 mV (our lowest possible
setting). However, at this setting we might miss some of the
neutrons. Extrapolating the upward slope towards 0 mV resulted in a
correction of 7.9%
Horizontal Scan, Sx
Aperture 2
When a neutron travels through matter it interacts with the atoms
or molecules that comprise that target medium. In the case of a
neutron beam, the result is a reduction in intensity. There are two
ways that this can occur, absorption and scattering.
If a neutron is absorbed by the atom/nucleus there are two
reaction possibilities depending on the medium. One of the
reactions results in the emission of a gamma ray. In the second
reaction the target becomes activated; that is, an isotope of the
original nucleus.
In addition, a neutron can also be scattered by a target
nucleus. In this scenario, the target nucleus gains some of the
neutron's kinetic energy, and the neutron slows. Eventually, the
neutron can undergo enough scattering that it comes into thermal
equilibrium with the surrounding matter.
In order to correctly determine the flux at any point in the
NPDGamma target room the amount of attenuation due to air, and
other parts of the apparatus, must be taken into account. In this
particular measurement, we have attenuation due to air, the
aluminum windows in the NPDGamma apparatus, and the gas
contained in the NPDGamma monitors.
−σnx
F= F0e
where,
F = Total Flux
F0= Raw Flux
s = Cross Section
n = Target Particle Density
x = Target Thickness
Vertical Scan Data, Sy
For a mixture of gases such as air this becomes:
− (σ N n N + σ O nO) x
F= F0e
where,
sN= is the Cross Section for Nitrogen
sO= is the Cross Section for Oxygen
nN = is the density of Nitrogen at NTP
nO = is the density of Oxygen at NTP
The graph shows that the beam is NOT a Gaussian distribution in
the vertical direction. This was not expected! What could be the
cause?
Cross Section Calculation
Beam Attenuation Through Matter
We estimated our losses according to:
Divergent beam distributions should be Gaussian. As seen in
the above graph, this is what we get in horizontal data.
Neutron Flux Calculation
The neutron flux is found by integrating the horizontal and
vertical scans. This value is then multiplied by the step increment
in x and y. It is then divided by the peak neutron flux and the area
of Aperture 2. Finally, this value is multiplied by the ratio of the
area of the guide and the area of Aperture 1.
Aperture 1
Experimental Setup
Acknowledgments
I would like to thank my FaST Program
colleague Daniel Parsons, faculty
mentor Joshua Hamblen, and our
ORNL mentor Seppo Penttila. I would
also like to extend my thanks to David
Bowman, Paul Mueller, Mark McCrea,
Septimu Balascuta, and Zhaowen Tang.
Our Polarized Flux Compared To Previous Unpolarized Flux
Measurement
(Unpolarized flux data courtesy of Erik Iverson)
The cross section consists of two terms, the
exothermic reactions that are energy dependent and
the scattering cross section that, for cold neutrons,
is energy independent. Thus, the relation is,
σ = σ in  σ el
σ=
Et
σin  σ el
En
Et
En
Where,
is the correction for the cross sections
of thermal neutrons to SNS cold neutrons, s is the
total cross section, sin the energy dependent cross
section, and sel is the energy independent cross
section.
For air containing Nitrogen and Oxygen,
(300K)(1.381*1023 J  K 1 )
σΝ =
(0.075b  1.90b)  10.03b
22
(4.7298 *10 J)
σ N = 2.9592(1.975b)  10.03b
Percent Attenuation of Measured Neutrons
σ N = 15.875b
where sN and sO are the cross sections for nitrogen
and oxygen, respectively
(300 K )(1.381 *10 23 J  K 1 )
-3
sO =
(
0
.
19
x
10
b  0.0b)  3.761b
22
(4.7298 *10 J )
s O = 2.9592(0.19 x 10-3 b)  3.761b
s O = 3.7298b
Target Particle Density
At NTP the atmospheric air composition is
approximately 21% Oxygen and 79% Nitrogen. This
means that the attenuation must be weighted by
percentage. For gases this is not difficult. The first step
is to determine the density of the gas, n, which is easily
found in reference sources. The next step is to weigh
the densities. For Nitrogen with a density of 1.165
kg/m3,
g
mol
23 atoms
x
1
x
6.0222
x
10
cm3 14.007 g
1 mol
atoms
nN = 5.0088 x 1019
cm3
19 atoms
n N = (0.79)(5.0088 x 10
)
3
cm
19 atoms
n N = 3.9569 x 10
cm 3
nN = 0.001185
The calculation is the similar for Oxygen.
Source
Detector Efficiency
Air Attenuation
Aluminum Windows in NPDGamma
Apparatus
6Li Detector Edge Effect
Discriminator Threshold Level
NPDGamma beam Monitor 1 & Monitor 2
Total Beam Loss
Effect
0.1%
24% - 26%
9.2% - 9.8%
negligible
7.9 %
2.2%-2.7%, 1.5%-1.9%
39%
Results/Conclusions
* The calculated raw neutron flux was (2.78 ± 0.18) x 109 neutron/s
at 800kW power.
*The calculated intensity normalized to 1 MW and corrected for
losses was (5.70 ± 0.37) x109 neutrons/s/MW. This flux
measurement is comparable to the expected value.

*The structure seen in the Y distribution is likely due to Aperture 1
being installed 3.81 ± 0.16 cm below beam center, and the neutron
moderator being displaced approximately 1 cm in the vertical
direction. However, more study is needed.

*The ratio of the flux measured before the polarizer over the flux
measured after (Polarizer transmission ratio) was 28%. This result is
what we expect, and is consistent with other independent
measurements.
