Validation of Neutrons in Geant4 Using TARC Data- production, interaction and transportation

Alexander Howard, Gunter Folger, Jose Manuel Quesada, Vladimir Ivanchenko

Abstract—The TARC (Transumatation by Adiabatic Reso-nance Crossing) experiment has been simulated with the Geant4toolkit. The experiment measured neutron production from2.5 GeV/c and 3.5 GeV/c protons incident on high purity lead. TheGeant4 simulation utilised either the Bertini or Binary nuclear cas-cade models together with the low energy Neutron HP extension.The neutron time-energy correlation, absolute fluence spectrum,and radial fluences are compared between data and simulation.Recent improvements to the PreCompound and De-excitationmodules within Geant4 are presented and their influence on theTARC simulation demonstrated. Overall the Geant4 simulationreproduces the TARC data.

Index Terms—neutron, TARC, Geant4, PreCompound/De-excitation

I. INTRODUCTION

THE simulation of the production, interaction and trans-portion of neutrons is important for a number of applica-

tions including: background radiation studies; radiation effects(singe event upsets in electronics); background and spill-over(LHC experiments). The Geant4 toolkit offers the possibilityto simulate particle interactions and transportation from a veryhigh energy right down to thermal neutron energies [1], [2].

The high quality of data make TARC a good benchmark forvalidation of neutron physics in Geant4 over a broad energyand process range, specifically:

• Neutron production from ∼ GeV protons• Secondary neutron production• Thermalisation and capture• Absolute fluence measurement

TARC had the unusual capability of determining neutronenergies from higher energy evaporation (∼2 MeV) down tothermal energies. This is the first time that neutron validationof Geant4 across this energy range has been made.

A. The TARC Experiment

The TARC experiment took data in 1996-1997 in the CERNPS beam in order to study neutron driven nuclear Transmu-tation by Adiabatic Resonance Crossing [3], [4]. Protons of

Manuscript sent Novermber 13th, 2008. This was supported in part bythe Commission of hte European Commmunities under the 6th FrameworkProgramme “Structuring the European Research Area” contract number RII3-CT-2006-026126

A. Howard is with CERN and ETH Zuriche-mail: alexander.howard@cern.chcorrespondence: CERN, CH-1211 Geneve 23, SwitzerlandG. Folger is with CERNJ.M. Quesada is with the Departamento de Fısica Atomica, Molecular y

Nuclear, Universidad de SevillaV. Ivanchenko is with CERN

Fig. 1. The TARC geometry implemented within Geant4. The colours aregeometrically different blocks, high-purity lead is used throughout.

momentum 2.5 GeV/c and 3.5 GeV/c were incident on a largelead target. Fig. 1 shows the geometry as implemented withinGeant4. The target is approximately cylindrical in cross-section with a diameter of 3.3m and length 3m, comprising334 tons of natural lead. The colours correspond to differentgeometries of blocks, with pure lead used throughout.

High purity (99.99%) lead was used in order to maximisethe neutron elastic scattering, subsequent thermalisation and toreduce capture from impurities. The target volume was largeenough to stop the protons and contain ∼70% of the producedneutrons. The beam entered through a blind hole 1.2 m longwhich resulted in a secondary shower profile approximatelycentred in the volume. Twelve sample holes were located in theexperiment to allow the placement of detectors and materialsin order to measure the neutron fluence as a function of energyand to determine the capture cross-section on a selection ofisotopes of interest for nuclear waste management.

B. Geant4 Physics Modelling

To simulate the hadron interaction and production theGeant4 Bertini and Binary cascade physics models were cho-sen [5]. Both of these models include independent low energynuclear de-excitation models. The low energy (<20 MeV)Neutron HP package was used for neutron interaction, trans-poration, elastic scattering and capture. In addition, other“standard” Geant4 processes were included for hadron elastic,electromagnetic and stopping physics. The QGSP BERT HPand QGSP BIC HP physics lists were utilised.

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2008 IEEE Nuclear Science Symposium Conference Record N41-6

(a) A single proton interaction viewed side-on (b) A single proton interaction viewed end-on

Fig. 2. A single 3.5 GeV/c proton interacting in the lead volume from the side (a) and end-on (b) where the resulting neutron shower can be seen to bewell contained within the lead volume.

Fig. 3. The neutron energy vs. time correlation as simulated using the Bertininuclear cascade model within Geant4.

The simulation of the interaction of a single 3.5 GeV/cproton is shown in Fig. 2. The proton track is shown in blueentering from the left, the neutrons are black and gammas areshown in red.

II. GEANT4 COMPARISON WITH DATA

The Geant4 simulation was run with the two differentnuclear cascade models and compared against the TARCdata. Thin target comparison was also carried out across therelevant energy range in order to further understand the physicsmodelling in a more discrete manner.

A. Neutron Energy-Time Correlation

Due to the highly elastic nature of neutron scattering inlead it is possible to correlate the energy of a neutron with thetime of measurement. The energy time correlation assumesthat neutrons start with very high energy and only interactelastically. Below 20 MeV, the neutron transport in Geant4

using the Neutron HP model can thus be tested. A plot ofthe time (μs) vs. energy (eV) for neutrons produced from2.5 GeV/c protons using the Bertini cascade is shown in Fig. 3.Between 1μs and 1 ms a clear correlation can be seen withquite narrow distribution. The simulation results are plottedfor all neutrons crossing a fixed radius in the TARC volume.This results in some neutrons being sampled many times asthey re-cross the boundary, thus some excess off-correlationbackground is visible in the plot. The resulting distributionis very close to that produced from the original TARC studyusing FLUKA for hadronic interactions and custom-writtenneutron transport below 20 MeV [3], [4].

The neutron energy-time is correlated according to [6], [7]:

E(t)(t + t0)2 =√

K (1)

where E(t) corresponds to the energy of the neutron ata given time t. The off-set t0 is introduced in order tocompensate for the fact that the neutrons do not begin with in-finite energy. This correlation function is plotted for simulatedneutrons of energy 0.1-10000 eV in Fig. 4 for the two cascadesconsidered - Bertini (4(a)) and Binary (4(b)). A quasi-Gaussiandistribution is produced which can be fitted over a reducedrange to give the mean values of 167.2 and 168.6 for theBertini and Binary models respectively. The TARC experimentmeasured the correlation to be 173±2 using resonance capturewith eight different isotopes across the energy range 4.28-337 eV. The original TARC simulation confirmed this value.The smaller values for Geant4 indicate an under-production ofhigher energy neutrons from both cascade models. The slightlyhigher value with the Binary cascade can be attributed to aharder secondary neutron spectrum.

B. Absolute Neutron Fluence

The TARC experiment measured the neutron fluence ata number of positions in the target using a selection ofcomplementary techniques. The energy-time correlation onlithium and uranium detectors gave a natural way to assess

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742.2 / 22Constant 0.1217E+05 40.98Mean 167.5 0.6994E-01Sigma 25.42 0.6159E-01

Correlation, √K

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0 50 100 150 200 250 300 350 400

(a) Bertini Cascade

457.2 / 22Constant 7483. 32.57Mean 167.8 0.8718E-01Sigma 24.73 0.7642E-01

Correlation, √K

dN/d

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(b) Binary Cascade

Fig. 4. The correlation function (see text) fitted to a Gaussian distribution for Bertini (a) and Binary (b) cascades. The red line at 173 ± 2 corresponds tothe TARC experimental value.

precisely the neutron energy. Also direct measurements weremade via a fixed final-state 3He neutron capture and ionisationdetector.

For monoenergetic neutrons of velocity, V , and density, n,the neutron flux is defined as φ = Vn and is a quantity thatupon multiplying by the macroscopic cross-section (Σ), oneobtains the neutron reaction rate per unit volume. This quantityshould not be confused with the rate of particles crossinga surface element, which is a ‘current’ and depends on theorientation of the direction of the particles

Three procedures were used to determine the fluence:

1) dN/dSperp is the number of neutrons crossing a surfaceelement dS, with dSperp = dS cos θ wher θ is theneutron angle to the normal;

2) the average fluence in a volume element dV as dl/dV ,where dl is the total track length of neutrons in dV ;

3) Number of interactions in a detector and computingfluence as (1/Σ)dN/dV, where dN is the number ofinteractions ndV .

The first two were used in simulation and found to be ingood agreement with each other.

A plot of the simulation output is shown Fig. 5. The neutronfluence is plotted as a function of neutron energy from 0.01 eVup to 2 MeV. The energy bins were chosen to match those ofthe experimental data which are plotted in blue. The greendata points correspond to the +/− combined statistical andsystematic error of the experiment. The simulation data areplotted for the Bertini (magenta) and Binary (black) cascades.The experimental data lie in between the two cascade models,with Bertini over-producing and Binary underproducing theneutron fluence. However, both are within the systematic errorsof the experiment.

C. Radial Neutron Fluence

TARC measured the radial dependence of the neutronfluence in order to measure the slowing down within the lead

Fig. 5. The TARC absolute fluence compared to the Geant4 simulation withBertini (magenta) and Binary (black) cascades. The experimental data areplotted in blue with green for the +/- errors.

volume with protons at 3.5GeV/c (slightly higher than fluencedata). The detectors were moved along the holes in the set-upand measured at a number of different energies.

In the Geant4 simulation, a sequence of parallel shellvolumes were created at different radii according to the exper-imental measurements to increase CPU efficiency. Fermi AgeTheory predicts that the flux should be isotropic and TARCexperimental data (+/- z-values) supports this hypothesis overthe energy range investigated.

The agreement between experimental data and simulationis very good over all the measured energies with the Binary

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1000 events binary 3.5 GeV/c proton

Radial Distance/cm

dF/d

E n

/cm

2 /eV

/109 p

50 keV

10 keV

1 keV

480 eV

100 eV

18 eV

5 eV

1.5 eV

0.1 eV

1

10

10 2

10 3

10 4

10 5

10 6

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-200 -150 -100 -50 0 50 100 150 200

Fig. 6. The absolute fluence measured at different energies and differentradial positions within the TARC volume (blue) compared to the Binarycascade model (red).

Fig. 7. Previous situation: double differential cross sections for27Al(p,xn) at 22 MeV incident energy. BIC curve corresponds to Bi-nary cascade calculation; it includes as a later stage preequilibrium, cal-culated with G4PreCompound model. PRECO is the calculation withG4PreCompoundModel directly accessed to. BERT is the calculation withBertini cascade, which includes its own preequilibrium and equilibriumprocesses

cascade as displayed in Fig. 6. The Bertini cascade gaveslightly higher fluences in all cases.

III. IMPROVEMENTS TO THE

PRECOMPOUND/DE-EXCITATION MODULES WITHIN

GEANT4

The precompound stage a nuclear reaction, described inin the framework of the exciton model [8], is considered untilnuclear system is at equilibrium. Further emission of nuclearfragments or photons from excited nucleus is simulated using

Fig. 8. As previous figure with the improvements to the PreCompoundmodel (BIC and PRECO). The unchanged Bertini model (BERT is includedfor reference.

100 events binary 2.5 GeV/c proton

Energy/eV

EdF

/dE

n/c

m2 /1

09 p

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10 5

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103

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Fig. 9. The absolute fluence as simulated with the improvedPreCompound/De-excitation model from Geant4 (black) compared to data(blue).

the Weisskopf-Ewing [9] equilibrium theory , which by itsef isnot able to describe the high energy tails of emission spectra.

The inverse reaction cross section is a key ingredientin the calculation of particle emission probabilities. Initialformulation [10] was previous to the wealth of experimentaldata since the sixties. Therefore, several parameterizations,either of experimental cross sections [11] or of calculated crosssections from optical potentials in turn fitted to the availablenuclear reaction data sets [12]-[13], have been included asoptions. For light systems and low emission energies, nearthe Coulomb barrier, where no experimental data are usuallyavailable, additional refitting has been done in order to improvethe production of secondaries. These new cross sections carryby themselves the Coulomb barrier; therefore no additional

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Binary-v9.0-Ref01 G4 Shell 45.6cm

Energy/eV

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Dat

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(a) The previous PreCompound/De-excitation model

Binary G4 Shell 45.6cm

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(b) The new revised PreCompound/De-excitation model

Fig. 10. The ratio of simulation over data for the absolute neutron fluence simulated using the Binary cascade comparing the old and new PreCompound/De-excitation models.

explicit parameterization of this quantity is needed, as it wasformerly.

The emission probabilities, either for single nucleons or forcomplex fragments, have been calculated including combinato-rial factors Rj (which take into account the availability amongthe excitons of enough particles to form the one to be emitted);these factors were not included previously.

We have found that attention must be paid to the transi-tion from preequilibrium to equilibrium. In our MonteCarlosimulation a physically consistent condition has been directlyimplemented by means of the apropriate algorithm. Moreovera smooth transition from preequilibrium to equilibrium stage,which initially was set into the model (soft cutoff criterium),according to the proposal in [15] has proven not to benecessary in our case to enhance evaporation at the expenseof preequilibrium.

The improvement in thin target double differential cross-sections can be seen in Fig. 7 and Fig. 8 for the old and newmodels, respectively. The binary cascade is coupled to the pre-equilibrium and de-excitation models, whilst the preco valuesare directly using the pre-equilibrium/de-excitation models.

A more detailed explanation of these preequilibrium andequilibrium related aspects can be found in [16].

The affect of these improvements on the TARC absolutefluence is shown in Fig. 9 and Fig. 10.

IV. CONCLUSION

The Geant4 simulation using the Neutron HP modulegives good agreement with the TARC experiment for neu-tron transportation, in particular the energy-time correlationand number of neutrons exiting the set-up. The simulatedneutron fluence disagrees by ∼50% between the two nuclearcascade models, Bertini and Binary. With the improvementsto the PreCompound/De-excitation modules, absolute neutronfluence both radially and spectrally agree very weel betweenGeant4 and the experimental data.

ACKNOWLEDGMENT

Thanks go to John Apostolakis for many helpful discussionson the Geant4 simulation and Jean-Pierre Revol for assistingin understanding the TARC experiment.

REFERENCES

[1] S. Agostinelli et al., Nuclear Instruments & Methods A 506 (2003) 250-303.

[2] J. Allison et al., IEEE Trans. on Nucl. Sci. 53 No. 1 (2006) 270-278[3] A. Abanades et al. NIM A 478 (2002) 577-730[4] CERN Yellow report: ”The TARC Experiment (PS211):Neutron-Driven

Nuclear Transmutation by Adiabatic Resonance Crossing”Editor J.-P. Revol (CERN 99-11)

[5] More information on the Geant4 physics models can found in the PhysicsReference Manual:http://cern.ch/geant4/UserDocumentation/UsersGuides/PhysicsReferenceManual/html/PhysicsReferenceManual.html

[6] A.A. Bergman et al., Proc. Geneva Conf. IV (1955) 135-145.[7] M. Sawan and R.W. Conn, Nucl. Sci. Eng. 54 (1974) 127.[8] J. J. Griffin,Phys. Rev. Lett. 17(1966) 478.[9] V. E. Weisskopf and D. H. Ewing, Phys. Rev. 57(1940)472.[10] I. Dostrovsky, Z. Fraenkel and G. Friedlander, Phys. Rev.

116,vol.3(1959)683.[11] H. P. Wellisch and D. Axen, Phys. Rev. 54 (1996)1329.[12] A. Chaterjee, K. H. N. Murthy and S. K. Gupta, Pramana, vol. 16, No

5, May 1981, p.391-402[13] Kalbach, PRECO-2000 Exciton Model Preequilibrium Code with Direct

Reactions[14] S. Gupta,Z. Phys. A303(1981)329.[15] S. G. Mashnick, A. J. Sierk, K. K. Gudima and M. I. Baznat, Journal

of Physics, Conference Series 41 (2006) 340-351.[16] J.M. Quesada, M. A. Cortes, A. Howard, G. Folger and V. Ivantchenko,

“Improvements of Preequilibrium and Evaporation Models in Geant4 “,contribution sent to the Proceedings of 2008 Nuclear Science Symposium,19-12 October 2008, Dresden, Germany.

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