TECHNICAL NOTES

NEUTRON SCATTERING IN CONCRETE AND WOOD:PART II—OBLIQUE INCIDENCEA. Facure1, A. X. Silva2, J. C. Rivera3 and R. C. Falcao1,3,*1Comissao Nacional de Energia Nuclear, R. Gal. Severiano 90, sala 405, 22294-900 Rio de Janeiro,RJ, Brazil2[PEN/COPPE - DNC/EE]CT/UFRJ, Ilha do Fundao, PO Box 68509, 21945-970 Rio de Janeiro,RJ, Brazil3Laboratorio de Ciencias Radiologicas, Universidade Estadual do Rio de Janeiro, Rio de Janeiro,RJ, Brazil

Received September 20 2006, revised June 18 2007, accepted June 24 2007

The knowledge of neutron reflection coefficients is of practical interest when projecting the shielding of radiotherapy rooms,since it is known that about 75% of the neutrons at the maze entrance of these rooms are scattered neutrons. In a previouspaper, the energy spectra of photoneutrons were calculated, when reflected by ordinary, high-density concrete and wood bar-riers, using the MCNP5 code, considering normal incidence and neutron incident energies varying between 0.1 and 10 MeV.It was found that the mean energy of the reflected neutrons does not depend on the reflection angle and that these mean ener-gies are lower in wood and barytes concrete, compared with ordinary concrete. In the present work, the simulation of neutronreflection coefficients were completed, considering the case when these particles do not collide frontally with the barriers,which constitute the radiotherapy room walls. Some simulations were also made to evaluate how neutron equivalent doses atthe position of the room door is affected when the maze walls are lined with neutron absorbing materials, such as wood itselfor borated polyethylene. Finally, capture gamma rays dose at the entrance of rooms with different maze lengths were alsosimulated. The results were discussed in the light of the albedo concepts presented in the literature and some of these resultswere confronted with others, finding good agreement between them.

INTRODUCTION

It is known that high-energy accelerators producephotoneutrons isotropically because of giant dipoleresonance in the nuclear reactions between photonsand high Z target nuclei of the materials that consti-tutes the accelerator head(1). The treatment roomwalls are shielded to attenuate the primary and seco-ndary X-ray fluence, and this shielding is generallyadequate to attenuate the neutrons produced as acontaminant of the therapeutic beam. However,these neutrons are scattered through the maze of theroom and may result in a radiological problem atthe door entrance, a high occupancy area in a radio-therapy facility. Neutrons are also backscatteredto the patient and these particles can be responsiblefor an increase in the patient absorbed dose.Consequently, it is important to determine how neu-trons backscatter or stream through the room mazeand how the wall surface lining and compositioncan affect these processes.

In the recently published NCRP 151(1), a modifi-cation of the Kersey method is presented as a way tocalculate neutron equivalent doses at the mazeentrance of radiotherapy rooms, when linear

accelerators operate above 10 MV

Hn;D ¼ 2:4� 10�15wA

ffiffiffiffiffiS0

S1

r½1:64 � 10�ðd2=1:9Þ

þ 10�ðd2=TVDÞ� ð1Þ

In the above equation, Hn,D is the neutron doseequivalent at the maze entrance in sievert, per unitabsorbed dose of X-rays (gray) at the isocentre(Sv n21m2 ); wA is the neutron fluence at the isocentre,per unit absorbed dose of photons (m22 Gy21);S0/S1 is the ratio of the inner maze entrance crosssectional area to the cross sectional area along themaze (see Figure 1a). TVD is the tenth valuedistance (m) of neutron doses along the maze andd2 is the maze length. The modified Kersey methodis an empirical equation.

Another empirical equation to compute neutrondoses at the maze entrance of radiotherapy rooms isthe French and Wells method(2), where the conceptof dose albedo is used

a ¼ aðE0Þðcosu0Þ2=3ðcosuÞ ð2Þ

Here, u0 and u are the incidence and reflectedangles, respectively, measured with respect to the*Corresponding author: ross@cnen.gov.br

# The Author 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Radiation Protection Dosimetry (2008), Vol. 128, No. 3, pp. 367–374 doi:10.1093/rpd/ncm378Advance Access publication 1 August 2007

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normal of the reflecting surface (see Figure 1b). Thecoefficient a(E0) depends both on neutron incidentenergy and the wall composition, but, for practicalshielding purposes, a single value of 0.11 has beenused for ordinary concrete. If one considers equalangles of incidence and reflection, this dose albedocan vary from 0.1 (158) to 0.034 (608) and so, fornormal incidence, the coefficient a varies fromapproximately 0.1 (158) to 0.055 (608).

Since the albedo denotes the reflecting characteri-stics of a surface, the knowledge of neutron reflec-tion coefficients by the room walls can give atheoretical basis for the use of the coefficients pre-sented above—the numerical value 2.4 � 10215 inequation (1), relating neutron fluence at the isocentreto neutron dose at the room door, or the values fora in equation (2).

In a previous paper(3), it was found that whenneutrons coming from the accelerator head collidewith the room walls at normal incidence, they are

reflected mainly in large angles with respect to thesurface normal and that the scattered neutrons meanenergy is almost angle independent. It was alsofound that wood lined or barytes concrete wallsreflects neutrons with lower mean energies thanregular concrete, showing that the first two materialscan be considered as better neutron moderators.Since, as pointed above, due to isotropic emissionfrom the accelerator head, neutrons can collide withthe room walls coming from any direction, it is alsoimportant to know how they behave when collidingwith these surfaces in oblique angles.

In the present work, MCNP5 Monte Carlocode(4) and the ENDF/B-VI cross-section library, tosimulate neutron reflection by barriers of conven-tional and baryte concrete as well as a type of com-monly used Brazilian wood were again used,considering these oblique incidence. This libraryformat has several formalisms to describe correlatedsecondary energy-angle spectra. The results

Figure 1. (a) Typical room design in radiotherapy rooms. (b) Geometry of neutron scattering simulations.

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presented complement the simulation of neutronreflection coefficients of the previous paper(3).

In the present article, the neutron equivalent dosevariations at the maze entrance of various radiother-apy rooms were also simulated, when differentmaterials in lining the maze walls were used, inorder to analyse how is it possible to minimise thesedoses. Finally, in the case of ordinary concretemazes of different lengths, the dose due to neutronswere compared to that due to capture gamma rays.

NEUTRON SCATTERING—MONTE CARLOSIMULATION RESULTS

In order to study the reflection of the contaminantneutrons in typical radiotherapy rooms, the generalpurpose Monte Carlo code MCNP5(4) was used.MCNP permits the modelling of very sophisticatedgeometries, contains biasing and scoring options,and is now one of the most widely used codes forlow-energy neutron shielding and dosimetry.

Monoenergetic and monodirectional neutronbeams, with varying incidence angles (158, 308, 458and 608 with respect to the surface normal), on flatsurfaces of finite dimensions (50 � 50 � 50 cm3) ofconventional and barytes concrete and wood, weresimulated. In MCNP, directions and energies of alloutgoing particles from neutron collisions are deter-mined by sampling data from appropriated cross-section tables. Angular distributions are providedand sampled for scattered neutrons resulting fromeither elastic or discrete levels inelastic event; thescattered neutrons energy is then calculated fromtwo-body kinematics(4).

The F5 tally, which is a point detector tally, wasused in the present work to score reflected neutronflux per incident neutron at a point in (x, y, z) coor-dinates. The geometry of the simulations was thesame of that described in Figure 1b, since thedefault F5 tally assumes azimuthal symmetry. So, inall simulations the same hypothesis of French andWells was adopted, of isotropy of neutrons scatteringin the laboratory frame. Tallies can be divided intobins, subdivisions of the tally space into discrete andcontiguous increments such as cosine, energy ortime. So, the simulation output results were in dis-crete energy and cosine bins.

The calculations of reflected neutron flux wereperformed at 20 selected neutron energy bins(ranging from 0.1 to 10 MeV) and the number ofreflected particles and their mean energies were esti-mated at four reflecting angles, for each of the fourangles of incidence. The intensity and mean energiesof the reflected neutrons, for each reflection angle ur,were evaluated as a function of incident energy, forall the incident energies mentioned above.

The number of simulated histories in allcases was 108, which assures the estimated relative

statistical error of the scattered neutron flux to beless than 2%.

The walls compositions, by weight percent, as wellas their densities, are the same as in(3). It is knownthat the dose albedo of most materials varies accord-ing to its hydrogen content and that the H content isan absorptive process from neutron albedo stand-point. On the other hand, the SiO2 content actsinversely to the H content(5). This effect can be seenin Figure 2a, where one can note the neutron totalcross-sections, obtained through MCNP simulation.In the low energy range (E , 0.1 MeV), the totalcross section for wood (6% H content) is about twotimes greater that for barytes concrete (0.36 Hcontent and 1.05% Si), which, by its side, is twicegreater than the one for ordinary concrete (0.55% Hcontent and 31.36% Si). In Figure 2b, a comparisonbetween the total and the absorption cross sectionsin wood is shown. Although this comparison isshown only for wood, it was observed that for allmaterials studied, scattering is the predominantprocess when compared with absorption in neutroninteraction, and for all of them, the cross-sectionvalues increases with decreasing neutron energy.

Figure 2. (a) Total neutron cross-section for conventional,baryte concrete and wood. (b) Total and absorption

neutron cross-section in wood.

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Figure 3a, b and c show the reflection coeffi-cients, for monoenergetic incident neutrons onordinary concrete, barytes concrete and wood,when one considers equal incidence and reflectionangles. If one refers to the literature on neutronalbedos(5,6), what has been computed in thesesimulations is what Selph(6) calls a differentialalbedo of type 3, which relates the ratio of thereflected flux at fixed angles to the incident flux ata fixed energy and angle. It is to be observed thatthe number of reflected particles is integrated overall the energy range. Since the F5 tally was used,the units in the output were neutrons/cm2, normal-ised per incident neutron and the neutrons weredetected in a small solid angle about the reflectingangle. The reflection coefficients varied from 1026

(low energy, 608 reflected neutrons) to 1029 (highenergy, 158 reflected neutrons).

Figure 3 shows that there is a larger number ofreflected neutrons for higher values of the reflecting

angle, which means that there is a higher flux of neu-trons entering the maze, if compared with neutronsthat backscatter to the treatment room and, conse-quently, to the patient. This growth of neutron inten-sity for higher scattering angles occurs for allshielding materials studied and for all incidentenergy values, up to 8 MeV, and repeats the beha-viour observed when one studied the normal inci-dence. This fact is in accordance with(5), where it ispointed out that the albedo of water or hydrogenousmaterials, like concrete or wood, increases forincreasing angle of incidence. Chilton(5) also pointsout that the simple albedo formula of French andWells (see equation 2) is not adequate for the calcu-lation of neutron scatter from high hydrogen contentmaterials, specially at high angles of incidence. Infact, differently from the French and Wells a coeffi-cients presented in the introduction, the coefficientspresented in Figure 3 are greater for greater reflect-ing angles.

Figure 3. (a) Intensity of scattered per incident neutron, when equal angles of incidence and reflection are considered, forconventional concrete. (b) Intensity of scattered per incident neutron, when equal angles of incidence and reflection areconsidered, for barytes concrete. (c) Intensity of scattered per incident neutron, when equal angles of incidence and

reflection are considered, for wood.

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Another restriction in the use of French and Wellscoefficients is that they apply only to low energy neu-trons (E , 1 MeV), and neutrons coming from theaccelerator head have a broader spectrum. NCRP 51presents(7) reflection coefficients an for ordinary con-crete and iron, for neutron energies from 0.1 to14 MeV, considering the normal incidence and equalangles of incidence and reflection. Since their defi-nition of the reflecting angle is different from theone presented in this literature, it is not possible tomake a direct comparison between the data, but it ispossible to observe that the shape of the curves aresimilar. From the data it can be noticed that lowerenergy neutrons (0.1 , E , 4.5 MeV) are reflectedin greater intensity, then the reflected intensitycomes to a minimum value around 5–6 MeV,depending on the reflecting material, and starts togrow again around 8 MeV. This observation agreeswith the well-known fact that the scattering cross-section is greater for lower energy neutrons.

Finally, it was observed that, as it happened in thecase of normal incidence, for a given material,the shape of the reflected neutrons angular spectra isthe same for all sets of incidence/reflecting anglesstudied (158, 308, 458 and 608), indicating that,although the intensity of reflected neutrons for eachangle is different, the scattering pattern is nearly thesame, at least for incident neutron energies up to8 MeV. In a previous paper(8), one has foundthat the majority of neutrons that emerge from theaccelerator head are under this energy value, andthat their mean energies are of 0.4 MeV.

Figure 4a, b and c show the mean energies of thereflected neutrons, for the different reflecting angles(158, 308, 458 and 608), for four different values ofthe incident neutron energies—0.5, 1.0, 5.0 and10.0 MeV—and for the same materials studied pre-viously (conventional concrete, barytes concrete andwood). Although the simulations were performed forall four incident angles mentioned above, in thefigures shown, the incident angle was fixed at 608.From these data, one observes that the mean energyof the scattered neutrons are greater than 0.24 Edir(the incident energy), which is a relation proposedby NCRP 79(2). It can also be observed that theaverage energies of the reflected neutrons are almostindependent of the reflecting angle, but it is materialdependent. Higher energy neutrons (5.0 and10.0 MeV) lose more energy in barytes concrete,which is due to higher cross-section for neutron ofthis energy in high Z materials that compose thiskind of concrete. For example, a 10 MeV incidentneutron has its energy reduced by a factor of 4 inbarytes concrete, whereas in ordinary concrete theinitial neutron energy is reduced by a factor of 3.Intermediate energy neutrons, on the other hand,lose more energy in wood, which is related to thehydrogen content of this material.

Although not shown in the figures, it can beobserved that, analysing the present work and com-paring it with the previous one in(3), for fixed incidentangles, the energy of the reflected neutrons are almostthe same, independent of the reflecting angle. If, forexample, one considers 0.5 MeV neutrons, which isnearly the mean energy of neutrons coming out of theaccelerator head(8), incident on ordinary concrete, it isobserved that the neutrons reflected by an angle of 608or more and consequently stream to the room maze,have energies of about 200 KeV, which is in accord-ance to the values presented in the literature(9,10)

NEUTRON ATTENUATING MATERIALS

In a previous study of neutron attenuating materials,it is shown that the fluence inside the radiotherapyrooms can be greatly affected by the composition ofthe room walls(11). In order to illustrate this fact, inFigure 5, the behaviour of the fluence, which isgreatly attenuated in the presence of wood orborated polyethylene lined walls was reproduced,when compared with ordinary concrete walls.

In the present study, radiotherapy rooms weresimulated, with the layout presented in Figure 1a,and dimensions of 10 � 10 m of total area, the valueS0 of 3.5 m and S1 of 1.5 m. First, all the wallsmade of ordinary concrete were simulated. Then5 cm of wood was added to the maze walls andfound that the neutron dose equivalent at the posi-tion of the room door, simulated by MCNP, wasreduced by 33%, if compared with the dose of ordi-nary concrete room walls. Then, instead of wood,5 cm of 5% borated polyethylene was added to themaze walls, finding a reduction of 56% in neutrondose.

Lalonde(12) used a remmeter to evaluate dosesalong the maze of a 18 MeV Varian acceleratorroom, and found that the use of polyethylene alonefor lining the maze walls can reduce neutron dosesby no more than 27%, while in borated polyethylenewalls the doses were reduced to 50%, which is inaccordance with the simulations.

In NCRP 151(1), other methods to reduce theneutron equivalent doses at radiotherapy roomdoors are discussed, such as the use of an innerboron door, where a reduction of a factor of 4 wasfound.

CAPTURE GAMMA RAYS

Another important concern when operating highenergy (E . 10 MeV) medical linear accelerators isthe gamma dose at the room door caused byphotons generated along the maze, due to neutroncapture by the maze walls atoms or capture gammaray dose. According to(13), the average energyof capture gamma rays is about 3.6 MeV and

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Figure 4. (a) Mean energy of scattered neutrons vs. reflection angle, at four different neutrons energies—0.5, 1.0, 5.0 and10.0 MeV, for conventional concrete. Incidence angle is fixed at 608. (b) Mean energy of scattered neutrons vs. reflectionangle, at four different neutrons energies—0.5, 1.0, 5.0 and 10.0 MeV, for barytes concrete. Incidence angle is fixed at 608.(c) Mean energy of scattered neutrons vs. reflection angle, at four different neutrons energy—0.5, 1.0, 5.0 and 10.0 MeV,

for wood. Incidence angle is fixed in 608.

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McGinley(14) has showed that, for a 18 MeV accele-rator in rooms with maze lengths (d2 in Figure 1a)greater then 2.0 m, the capture gamma rays dose atthe door is more significant than the dose due to thescattered photons that come from the acceleratorhead. This happens because, while the tenth valuedistance (TVD) for the scattered photons is about1.4 m, the TVD for capture gamma rays is around6.4 m.

Using the same room dimensions and mazelengths described in the section above, and ordinaryconcrete as the walls material, the capture gammarays doses at the room door were calculated.Figure 6 shows a comparison between the valuesfound for neutron doses and capture gamma raysdoses, when the maze length were varied. Doses arenormalised per Gy of X-rays at the isocentre and itcan be observed that for maze lengths greater than

6.0 m, the capture gamma rays doses are greaterthan neutron doses at the room door.

CONCLUSION AND FUTURE WORK

In this work, the second and last part of a studywere presented, using MCNP Monte Carlo simu-lation, of the reflecting and attenuation behaviour ofneutrons produced by high-energy accelerators,when interacting with different materials of radio-therapy room walls. The energy range of neutronsanalysed covers all the spectra of neutrons producedby these machines and the materials studied were theones most commonly used in the shielding of radio-therapy facilities. Below the main results found aresummarized.

† Neutron reflection and attenuation is materialdependent. The relative intensity of neutronsreflected in concrete, for example, is greater thanthe one reflected by barytes concrete or wood.This happens for all neutron energies studied.

† The mean energy of reflected neutrons is alsomaterial dependent. For example, intermediateenergy neutrons lose more energy in wood,whereas neutrons of higher energy lose moreenergy in barytes. In general, mean energy ofreflected neutrons are greater than the 0.24 ofthe incident neutron energy proposed byNational Council on Radiation Protection andMeasurements(2).

† Neutron reflecting intensity varies with incidentangle. For a given material, the greater the inci-dent angle with respect to the surface normal,the higher is the number of reflected neutrons.This in accordance with what is presented in lite-rature(5), where it is shown that the albedo ofhydrogenous materials increases with the growthof incidence angle with respect to the surfacenormal.

† For fixed incident angles, neutrons reflect prefer-entially in higher angles, which means that theystream to the maze and the room door, ratherthan back to the room and, consequently, to thepatient. This happens for all materials studied.

† The use of attenuating materials, such as woodor borate polyethylene, in lining radiotherapyroom walls, can significantly reduce the neutrondose at the door. Our simulations showedreductions of 33% and 56%, respectively, inneutron equivalent doses. Since wood is abun-dant and cheap, at least in Brazil, this can be agood option for reducing neutron dose at radio-therapy facilities.

† The capture gamma rays dose at the door ofhigh energy radiotherapy facilities is usually ofthe same order of magnitude of neutronsdoses and can, for longer mazes, become more

Figure 6. Neutron and capture gamma rays doses at thedoor of rooms with different maze lengths.

Figure 5. Dependence of neutron fluence on the mazewalls lining materials.

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relevant than doses due to neutrons and scat-tered photons.

Although work is still to be done to fully correlatethe presented scattering coefficients with operationalneutron dose albedo values to be used in dose calcu-lations at maze doors, it was intended to have givenone more step towards a better understanding onneutron reflection and attenuation in shielding sur-faces. Presently, neutron equivalent doses measure-ments along mazes, using bubble detectors, arebeing done by some of the authors, in order toconfirm Monte Carlo calculations.

REFERENCES

1. National Council on Radiation Protection andMeasurements. Structural Shielding Design andEvaluation for Megavoltage X- and Gamma-RayRadiotherapy Facilities. NCRP Report No. 151 (2005).

2. National Council on Radiation Protection andMeasurements. Neutron contamination from medicalaccelerators. NCRP Report No. 79 (Bethesda, MD:NCRP) (1984).

3. Facure, A., Silva, A. X., Falcao, R. C. and Crispin,V. R. Neutron Scattering in concrete and Wood . Rad.Protect. and Dos. 119, 514–517 (2006).

4. X-5 Monte Carlo Team,. MCNP – A General MonteCarlo N-Particle Transport Code, Version 5, Volume I:Overview and Theory. LA-UR-03-1987. Los AlamosNational Laboratory (2003).

5. Chilton, A. B., Shultis, J. K. and Faw, R. E. Principlesof Radiation Shielding. Prentice Hall, Inc. New Jersey,1984

6. Selph, W. E. In: Reactor Shielding for NuclearEngineers. Schaeffer, N. M., Ed, Chap 7 (1973).

7. National Council on Radiation Protection andMeasurements. Radiation Protection Design Guidelinesfor 0.1-100 MeVAccelerator Facilities. NCRP ReportNo. 51 (1977).

8. Facure, A., Falcao, R. C., Silva, A. X., Crispin, V. andVitorelli, J. C. A Study of Neutron Spectra fromMedical Linear Accelerator. Appl. Rad. Isotop. 62,69–72 (2005).

9. Kase, K.R., Mao, X. S., Nelson, W. R., Liu, J. C.,Kleck, J. H. and Elsalim, M. Neutron Fluence andEnergy Spectra around the Varian Clinac 2100C/2300CMedical Accelerator. Health. Phys. 74(1), 38–47(1998).

10. Howell, R. M., Hertel, N. E., Wang, Z., Hutchinson, J.and Fullerton, G. D. Calculation of Effective Dosefrom Measurements of Secondary Neutron Spectra andScattered Photon dose from Dynamic MLC IMRT for6 MV, 15 MV and 18 MV beam energies. Med. Phys,33(2) (2006.)

11. Facure, A., Silva, A. X. and Falcao, R. C. MonteCarlo Simulation of Scattered and ThermalPhotoneutron Fluence inside a Radiotherapy Room.Rad. Protect. Dos. Advance access published on June30, 2006 doi 10.1093/rpd/ncl080.

12. Lalonde, R. The effect of Neutron-ModeratingMaterials in High Energy Linear Accelerator Mazes.Phys. Med Biol. 42, 335–344 (1997).

13. McGinley, P. H. Shielding Techniques for RadiationOncology Facilities. (Madison, Wisconsin: MedicalPhysics Publishing) (1998).

14. McGinley, P. H. and Huffman, K. E. Photon andNeutron Dose Equivalent in the Maze of a High EnergyMedical Accelerator Facility. Rad. Protec. Manag. 17,43–46 (2000).

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