Effect of Density and Nuclear mass on Spallation Output and
Energy spectra of Neutrons
Moiz Muddassir
May 22, 2023
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Central purpose
The central purpose of the experiment is to determine what specific material properties correlate
with different spallation energies and neutron output. specifically what we want to determine is
the trends relating to the energy spectra of spallation neutron beams from targets of different
elements, shapes, and geometries. The effect of increasing nuclear mass and atomic radii will be
specifically focused on.
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Target
Spallation is a phenomenon that occurs when a target nucleus is broken down into several parts
resulting in the emission the many particles such as free Neutrons, Protons, electrons, and gamma
radiation. For this study, we are looking to find trends in Neutron energies and their relation with
different properties of a material, Specifically how the spallation yield and subsequent neutron
energy spectra correlate with nuclear Mass and atomic density.
Nuclear mass Iron (Atomic number 26) and gadolinium (Atomic number 64) have similar densities 7.9 g/cm3 however their nuclear mass is very different subjecting these two to incident proton
beams of the same intensity will allow us to measure the effects of increased nuclear mass of the
target and its relation with neutron count and energy spectrum. Neodymium (atomic Number 60)
and zinc (Atomic number 30) can also serve as good candidates
Density To determine the effect of density we will take the opposite approach. since we can’t
have two substances with the same atomic number but different densities the approach we take is
to use the elements Indium (Atomic Number 49) and Cadmium (Atomic Number 48) as targets.
These two have respective densities of 7.31 g/cm3 and 8.65 g/cm3 . Silver (Atomic number 47) is
also a viable choice as its density is much greater at 10.49 g/cm3 .
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Detectors
Detectors will be a huge part of the entire setup. We hope to detect the beam energies and neutron
count. BF3 Bonner Sphere detectors are very good for general neutron detection, especially at high
energies. As for beam energies TOF (Time of Flight analysis) can be used to deduce the energies
of incident neutron beams. specifically, we will use a short pulse proton beam that will hit a target
that will be a known distance from the detector. to accurately measure the time taken from when
the proton beam hits the target we will use the accelerator data and then we will measure the time
taken between that and the detector pings.
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Beam energies
We will use proton beams of 4 different energies: 10 MeV, 50 MeV, 100 MeV, 200 MeV and 500 MeV.
This ensures that the trends hold up under different energies and test the highest possible spallation
yield under variable energies. Using different incident beams such as a lpha- particles can also help
broaden the horizons and see what types of outcomes we can get from that.
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0.8
Figure 1: Bonner Sphere Detector
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Theoretical Outcomes
All theoretical Outcomes were run using the FLUKA Monte Carlo Code/Simulation package Version 4.3.2. According to these simulations we can see that almost all substances irrelevant of their
Nuclear Mass and density have a peak neutron current of around 0.001 GeV. as for the theoretical
effects of Nuclear mass it correlates directly to a higher Neutron current overall however the effects are less pronounced when nearing the incident beams initial energy or the end of the energy
spectra. something to note however is that according to the simulation Iron has a peak at between
0.00001 and 0.0001 GeV which exceeds or closely matches the neutron current of Gadolinium at
that energy in all simulations. The simulations at those energies do have significant error margins,
however Upon a closer examination those peaks were still found to be present. another thing to
note is the errors in Gadolinium were significantly less than that of Iron even at the same energies.
also from the graphs we can infer that the monte-carlo code is not very effective at rendering low
energies in both flux and energies so It remains a mystery as to what we will observe there.
All in all we see that Nuclear mass has a greater impact on the spallation yield and produces
a larger variation in energy spectra than density.
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Setup and Overview
This section will explore the entire setup and overview of the experiment. Target Dimensions. All
Targets will be a cylinder of Radius 10cm and height of 10cm. These proportions are there to keep
the internal absorbance of neutrons within the spallation target to a minimum, Hence outputting
a high neutron current with regards to the incident Proton beam. All simulations have also been
done with these target dimensions.
Bonner Sphere. Bonner sphere detectors use a polystyrene layer to moderate the energy of
incoming neutrons which then allows a better probability of them being detected by a BF3 ionization detector at the core of the whole setup. the reason we use an 11 cm Polystyrene moderator is
to reduce the response time for the detector as much as possible while maintaining a high enough
cross-section to allow a good probability of detection.
the Tungsten Collimator will help focus stray neutrons towards the Bonner sphere to increase
the intensity and reduce ambient neutron flux. while the Ion and Gamma shielding (Steel) will help
decrease any non-neutron radiation going into the detector. Placing the shield close to the detector
will allow us to reduce the moderating sphere radius and that will result in a better time resolution
(useful in Time of Flight). Secondly, that will also help keep the neutron’s calculated energy as
close as possible to the actual energy as for the majority of the flight path neutrons will travel at
their original speeds/energies. this is because the lead barrier will result in a moderation effect
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of incoming neutrons. this is shown in the simulations below, the neutron beam is not scattered
much and holds its shape while the gamma radiation is much absorbed and scattered.
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Time Of Flight Analysis
to determine the energy spectra of the incoming proton beams we will be using Time of Flight
Techniques (TOF).
to apply these we must first figure out the velocity at which the particle is traveling which is
equal to the path length divided by time.
v = L/(t1 −t2 ) where L is path length and t1 is the time when the detector detects an event and
t2 is the time when the proton beam incidents the spallation target. using this we can substitute
the equation for kinetic energy for a relativistic particle that equals
K=
p
p2 c2 + m2 c4 − mc2
(1)
here m is the mass of the particle, p is the momentum, and c is the speed of light in a vaccum. for
a more accurate reading, we could use the relativistic momentum as well where
p=
qm0 v (2)
2
1− vc2
this K will give us the energy for a neutron however we must also take into account systemic errors
of the detector which include a non-zero response time. Other Systemic errors will include an
energy resolution limit of our detector however that is negligible in comparison to the response
time of our BF3 detector.
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Outcomes
we hope with the project to be able to develop a better understanding of how spallation works
and its underlying mechanisms. We also hope to be able to provide useful knowledge for better
neutron imaging devices and for radiation therapy through the data we collect for Spallation yield.
we also hope to be able to find a critical spot for spallation output where the number of neutrons
produced can be maximized all the while achieving a good energy output.
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Refrences and Acknowledgments
I would like to acknowledge Dr. Konstantin Batkov from the European Spallation Source (ESS)
for his immense help and time. None of this would have been possible without his support. I would
also like to thank Sir Markus Joos for his guidance in the early stages of the process and his help
in getting this team started.
1. : Antonio Brusegan, Gilles Noguere , Frank Gunsing (2002) The Resolution Function in
Neutron Time-of-Flight Experiments, Journal of Nuclear Science and Technology, 39:sup2, 685688, DOI: 10.1080/00223131.2002.10875192
2. BONNER SPHERE SPECTROMETER Cruzate, J.A.; Carelli, J.L. and Gregori, B.N.
3. On the nucleon effective mass role to the high energy proton spallation reactions Author
links open overlay panelB.M. Santos a d, A.R.C. Pinheiro c e, M. Gonçalves b, S.B. Duarte c, R.G.
Cabral 4.
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Figure 2: Neutrons and gammas traveling through steel of thickness 10 cm energy 50 MeV
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