Radiation Protection Dosimetry Advance Access published October 28, 2010 Radiation Protection Dosimetry (2010), pp. 1 8 doi:10.1093/rpd/ncq285 DIRECTIONAL DISTRIBUTION OF THE AMBIENT NEUTRON DOSE EQUIVALENT FROM 145-MeV 19 F PROJECTILES INCIDENT ON THICK AL TARGET C. Sunil 1, *, A. A. Shanbhag 1, M. Nandy 2, T. Bandyopadhyay 1, S. P. Tripathy 1, C. Lahiri 2, D. S. Joshi 1 and P. K. Sarkar 1 1 Health Physics Division, Bhabha Atomic Research Centre, Mumbai 400085, India 2 Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Kolkata 700064, India *Corresponding author: sunilc@barc.gov.in Received November 19 2009, revised August 11 2010, accepted September 16 2010 The directional distribution of the ambient neutron dose equivalent from 145-MeV 19 F projectiles bombarding a thick aluminium target is measured and analysed. The measurements are carried out with a commercially available dose equivalent meter at 08, 308, 608 and 908 with respect to the beam direction. The experimental results are compared with calculated doses from EMPIRE nuclear reaction code and different empirical formulations proposed by others. The results are also compared with the measured data obtained from an earlier experiment at a lower projectile energy of 110 MeV for the same target projectile combination. INTRODUCTION In positive ion accelerators, the major component of prompt radiation is the neutrons resulting from the beam losses during normal operations or accidental situations. For radiation protection purposes, the energy and angular distributions of thick target neutron yield are important parameters. But routine measurements are often carried out with conventional neutron dose equivalent monitors commonly known as rem meters as they provide an immediate measure of the ambient dose equivalent. These instruments are designed such that their count rate per unit fluence is proportional to the ICRP fluence to dose conversion coefficients for neutrons from thermal energy to 14 MeV. However, responses of conventional rem-meters are known to differ from the true ICRP response up to a factor of 5 (1,2). Also, since the highest neutron energy used for calibration is usually 14 MeV, incomplete knowledge of the response of the instrument for higher energies would introduce unknown errors when such instruments are used for measuring the dose above 14 MeV, unless extended range rem counters (3,4) are used. For accurate determination of the dose, the energy differential neutron yield is the primary invariant quantity that needs to be measured and consequently multiplied by the fluence to dose conversion coefficients. But if experimental data are unavailable, nuclear reaction model codes can be used to calculate the source terms such as the energy distribution, integral yield and the direction distribution of the dose equivalent. In this work, the EMPIRE (5,6) nuclear reaction code is used to calculate the double differential neutron yield, which is then folded with the ICRP fluence to dose conversion coefficients (7). The calculated results are then compared with the present experimental data. In routine radiation protection situations, it is convenient to calculate the dose and its directional distribution using simple empirical expressions compared with the nuclear reaction model calculations. In the case of heavy ions, a few empirical formulations have been proposed to calculate dose and they are generally derived by fitting the measured directional dose distribution data. The advantage of such empirical formulations for routine use is their simplicity and quick prediction of the dose values. However, unlike light ion projectiles, heavy ion projectiles can have charge and mass as additional variables apart from their energy, which should be taken into account. It is also important to know how well the measured dose values compare with the empirically estimated values. The present experimental data are compared with some of the empirical expressions reported in literature. Further, the experimental results are used to measure the variation in the prediction of an empirical expression as a result of the ambiguity in choosing the parameter value. In a similar experiment performed earlier, the neutron dose was measured from 110-MeV 19 Fprojectiles incident on a thick aluminium target (8). The present experimental data are also compared with those results for evaluating the trends of higher neutron and possible change in the directional distribution hardness of the energy spectra. The comparison will also help to quantify the dose # The Author 2010. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org
parameters like total neutron dose and the slope parameters in the exponential function based empirical expressions reported earlier. The present experiment is expected to provide additional dose distribution data as well as validate the empirical expressions at a different projectile energy. The experiment was carried out at the BARC TIFR superconducting linac booster of the Pelletron Accelerator Facility, Mumbai. Detailed description of the experimental setup can be found in our previous articles (9,10). UNCERTAINTIES IN MEASUREMENT The uncertainties in the measurement arise from the propagation of errors due to the calibration procedure, normalisation uncertainty in the total charge measurement and the room scattered contribution. Among these, the uncertainty associated with the calibration source is 10 %. The precision beam current integrator has 1 % associated error. The measurement of room scattered contribution using a shadow cone technique could not be carried out during the present experiment. To determine this contribution, simulations were carried out using the FLUKA (11,12) Monte Carlo code. In the simulations, the rem-meter was modelled as a cylinder of length 23 cm and diameter 21.5 cm. The beam hall geometry in the simulation consisted of concrete walls 3.0 m high and 1.0 m thick located at distances of 1.3 and 11.0 m in the lateral directions, 6.0 m in the forward direction and 4.2 m in the backward direction from the target location. This configuration closely approximates the actual experimental geometry. The source starting point in the simulation and the target location in the experiment are identical at 1.7 m above the floor. The neutron energy spectrum obtained from the EMPIRE calculations in the forward direction (see Figure 3) extending from 1 to 30 MeV was sampled using the SOURCE sub routine of the code. The track length estimator USRTRACK in FLUKA was used to score the neutron fluence inside the detector cell volumes. The dose equivalent inside a cell was then obtained by using the AUXSCORE card in the FLUKA input which folds the fluence with the fluence to ambient dose conversion coefficients. With an initial simulation, the total (direct and scattered) dose equivalent inside each detector volume was estimated at angles of 08, 308, 608 and 908. Later, simulations were carried out with truncated shadow cones placed between the source and the detector volume so as to cut-off the direct contribution. The shadow cones were kept at one angle at a time. Under such a condition, only the scattered contribution will reach the detector volume. The room scattered background contribution can then be estimated from the difference between the shielded and unshielded results. By C. SUNIL ET AL. simulating 10 7 histories, all the results were obtained with 1 % statistical error. The results of the simulation indicate that the room scattered contribution at 08 is 12 % while it is 10 % at other angles. The experimental results are reported after applying this correction. The overall uncertainty is estimated to be a 10 % at all the angles of measurements. The instrument response differs from the ICRP response by up to a factor of 5 as described before. This will also introduce an error that will depend on the extent of the neutron energy present. For the neutron spectrum emitted from a thick Be target bombarded by 19-MeV protons, this has been found to be 10 % (10). However, it is not incorporated in the uncertainty calculation here because generally the degree of deviation is unknown and the instrument is used as is available in routine operations. CALCULATED RESULTS Nuclear reaction model calculations In a thick target, the projectile interacts with the target nuclei at different continuously degrading energies and the observed emitted spectrum is a sum of emissions from all these projectile energies within the target (13,14). This is calculated from the thin target emission cross section for various projectile energies from the incident energy up to the Coulomb barrier. The thick target is considered to be made up of several thin slabs such that the projectile loses a specified energy in each slab. The projectile is assumed to interact with all target nuclei in its path within this thin slab with an average energy. The slowing down is thus considered in small discrete steps. The emitted spectra from all of these slabs are summed up to give the final spectra with correction applied at each step for the reduction in the projectile fluence due to nuclear interaction in the previous step. EMPIRE is a modular system of nuclear reaction codes comprising various nuclear reaction models and designed for calculations over a broad range of energies and incident particles. The projectile can be a neutron, proton, any ion (including heavy ions) or a photon. The energy range can extend from a few kilo electronvolts for neutron-induced reactions up to several hundreds of million electronvolts for heavy-ion-induced reactions. The code accounts for the major nuclear reaction mechanisms, including direct, pre-equilibrium and compound nuclear (CN). The compound nucleus (CN) decay is described by the Hauser and Feshbach (15) theory. In the present calculations, neutron emissions are considered from the CN decay only. Level densities are calculated using the dynamic approach in the case of heavy ion projectiles wherein collective enhancements due to Page 2 of 8
NEUTRON DOSE FROM 145-MeV 19 F ON THICK AL TARGET nuclear rotation and vibration are taken into account. Fusion cross section is calculated by the Bass model (16). Empirical relations The empirical formulations used in this work are briefly described in this section for the sake of completeness. The reader is referred to the respective original works for more details. respectively. The total neutron yield per ion, Y, is estimated from H AV using the following expression Y ¼ 1:41 10 8 H AV ð6þ The values of the parameters R b and R t are tabulated for certain elements by Guo et al., from which it is evident that they do not have any systematic dependence on the mass number of the element, but depend in some way on the neutron excess. Empirical formulations of Clapier Clapier and Zaidins (17) analysed data from heavy ion projectiles in the energy range of 3 86 MeV/amu and found that the total yield, Y (neutrons/ion), and the neutron dose rate at a distance of r cm from the target in the direction u are given by YðW; ZÞ ¼CðZÞW hðzþ HðW; Z; u; r; iþ ¼ YFðu; jþ r 2 i 0:72 msv h 1 ð1þ ð2þ where Z is the charge of the projectile and W is the projectile energy in MeV/amu, i is the beam current in particles per second, j is the slope parameter and F is the angular distribution function of the neutron yield. General formulations are given for estimating the values of j for a few typical cases of neutron spectra such as highly forward peaked and completely isotropic emissions. The major problem with this formalism, therefore, is to estimate the parameter j. Empirical formulations of Guo Guo et al. (18) have given an empirical relation for the directional distribution of neutron dose (msv h 21 ma 21 at 1 m) as follows:! ð1 þ SÞ 2 HðuÞ ¼2H AV ð1 þ e S expð SuÞ ð3þ Þ H AV ¼ð33:4R b R t Þ 2 E b CB 2 þ 0:35 ð4þ A b where H AV is the average dose rate calculated using certain parameters and beam energy, CB is Coulomb barrier and S is the slope of the ln[h(u)] versus u curve given by rffiffiffiffiffiffi A b E b S ¼ 0:5 ð5þ A b þ A t A b E b is the beam energy (MeV), A b, Z b, A t and Z t are the mass and charge of projectile and target, Formalism of Nandy et al. In order to fit the experimentally observed angular distributions of neutron dose obtained from 19 Fþ 27 Al, the following empirical relation, as a slight variant of the formalism of Guo et al. has been proposed by Nandy et al. (19). HðuÞ ¼ H tot 1 þ S 2 expð S uþ ð7þ 2p 1 þ e Sp where H tot and S* are, respectively, the total dose equivalent and the slope parameter. The numerical value of the slope parameter S* can be obtained as sffiffiffiffiffiffiffiffiffiffi S ¼ A b Eb CM ð8þ A b þ A t A b where, Eb CM is the centre of mass energy (MeV) of the projectile, and H tot can be approximated as H tot ¼ 4p H AV ð9þ The value of H AV is calculated using the formulation of Guo (see Equation (4)). This expression has been found to describe successfully (8) the angular dose distribution in the case of 110-MeV 19 F projectiles incident on thick Al target and is used in this study also. In the following discussions, S, S* and j are referred to as slope parameters while H AV and H tot are referred to as dose parameters. RESULTS AND DISCUSSIONS The experimentally measured angular distribution of neutron dose from the 19 Fþ 27 Al reaction at 145 MeV, the calculated values using the EMPIRE 2.19 code and using the empirical formulations are given in Table 1 as well as plotted in Figures 1 and 2. As has been mentioned, the formalisms of Guo et al. and Nandy et al. use the parameter R b to calculate H AV or H tot as defined by Guo. However, there is no systematic dependence of this parameter on the target or projectile properties. The parameter R b can be chosen based either on the neutron excess Page 3 of 8
C. SUNIL ET AL. Table 1. Experimental, empirical and computational results for 145-MeV 19 F projectiles incident on 27 Al. Angle Dose in msv h 21 na 21 at 1 m Degree Exp. Guo Nandy Clapier EMPIRE R b ¼ 1.2 R b ¼ 1.63 R b ¼ 1.2 R b ¼ 1.63 0 243+25 135 250 252 465 51 83 30 178+18 100 185 159 294 41 77 60 102+10 74 137 101 186 27 46 90 56+6 55 102 64 118 19 26 Figure 1. The experimental results compared with the calculated values from EMPIRE, and other empirical formulae. The value of R b used is 1.2. Figure 2. Experimental data and the results from the two formalism obtained using R b ¼ 1.63. or on the mass of the projectile. In this work, doses at different angles have been calculated using two values of R b based on these two assumptions and the results are given in Table 1. From Figure 1, it can be seen that the empirical expression of Nandy et al. agrees better with the present experimental results compared with other calculated results. The absolute value of dose as calculated by this formalism agrees with the measured data for R b ¼ 1.2 (Figure 1). It can be observed that with the formalism of Nandy et al. with R b ¼ 1.63 the measured data are over-predicted by a factor of about 1.8. The results obtained by the formalism of Nandy and Guo et al., with the value of R b taken as 1.63 are plotted in Figure 2 along with the experimental data. The formulation of Guo et al. does not reproduce the shape of the angular distribution of the measured dose because of the lower value of the slope parameter S in Equation (3). The calculated dose agrees with the experimental data at 908 with R b ¼ 1.2 and at 08 with R b ¼ 1.63. The slope calculated using Guo s technique (Equation (5)) is 0.57, while using Nandy s technique it is 0.87. The value of H AV (msv h 21 na 21, micro Sievert per hour per particle nano-ampere) calculated using Equation (4) with R b ¼ 1.2 is 76.03 and with R b ¼ 1.63 is 140.3. The corresponding H tot values are 954.9 and 1761.9 msv h 21 na 21, respectively. The results from Clapier s formalism underpredict the experimental data at all angles by a factor of 2 5. Calculated using this formalism, the neutron yield Y is 3.210 24 (ion 21 ), which is about three times lower than the neutron yield of 1.0710 23 (ion 21 ) obtained from the relation suggested by Guo et al. This discrepancy has also been observed previously (8,9,19). The slope parameter j is 0.29 as calculated from the present experimental values of H(0) and H(90). It is expected that a modified equation in Clapier s formalism that predicts a higher neutron yield will result in considerable improvement in its results. Since the projectiles involved are heavy ions, the yield should necessarily be a function of the properties of both projectile and the target. The formula for total neutron yield as suggested by Clapier et al. ignores the dependence on the target properties. Another drawback in Clapier s formalism is its inability to calculate the slope parameter independent of the measured dose at different angles. Page 4 of 8
NEUTRON DOSE FROM 145-MeV 19 F ON THICK AL TARGET The results obtained from EMPIRE calculations are about two to three times lower than the experimental results. Similar under-prediction was seen earlier (8) with a lower projectile energy of 110 MeV. The neutron energy spectra obtained from EMPIRE calculations for 110 MeV 19 Fþ 27 Al reasonably matched the measured energy spectra from a time-of-flight experiment in an earlier work (14). Since the experimental parameters are not drastically different here, similar agreement is expected in this case also. Hence the underestimation of results in the present case need to be further investigated. In Figure 3, the neutron doses per unit energy interval obtained by folding the EMPIRE calculated fluence with the ICRP fluence to dose conversion coefficients are shown. The neutron energies corresponding to the highest probable dose in these spectra are around 4 MeV. Hence the contribution from energies below 1 MeV, where the instrument responses has large variation, does not account for the large discrepancy between the experimental and EMPIRE results. The present results from EMPIRE calculations are obtained using the default level density and the fusion cross section options, considering neutron emission from a pure CN system. It is possible that some amount of pre-equilibrium emissions too can take place at this incident projectile energy. More importantly, EMPIRE requires in its input, the number of nucleons that has to be emitted in the CN decay process. Considering the large excitation energy of the system, this aspect also needs to be investigated. To understand the response of the instrument with respect to the energy fluence spectra, the ambient dose equivalent and fluence responses are shown in Figure 4. In the figure, the plots named ICRP and Wedholm, obtained from the user s manual of the instrument (20) have their ordinate on the left axis Figure 3. The energy differential neutron ambient dose equivalent obtained at different angles by folding the fluence calculated using EMPIRE code with the ICRP fluence to dose conversion coefficients. Figure 4. The fluence response of the instrument (left ordinate) along with the ratio of ambient dose equivalent of the instrument (H*(10) Inst ) to the ICRP ambient dose equivalent (H*(10) ICRP ), also known as the ambient dose equivalent response, on the right ordinate. (fluence response) while the ambient dose equivalent response ordinate named as instrument response (dotted line) is on the right axis. The horizontal line indicates a response that is equivalent to the ICRP response curve of the plot. A value above this indicates over-response while a value below it would mean an under-response. The instrument is seen to over-respond from 30 ev to 80 kev and from 1 to 5 MeV while under-responding at all other energies. The integral response of the instrument hence will be determined by the energy distribution being measured. To illustrate this point, the deviation of the instrument from the ICRP response is estimated using the neutron spectrum from a 252 Cf fission source and the neutron spectrum calculated using the EMPIRE code in the 08 direction (Figure 3). The fission neutron spectrum extends from thermal energy up to 10 MeV while the spectrum in Figure 3 begins at 1 MeV and extends up to 30 MeV. Since the instrument response extends up to 14 MeV, the folding process is also carried out up to 14 MeV only. The results indicate that the instrument over-responds by 10 % for the 252 Cf fission neutron spectrum while it under-responds by 18 % for the EMPIRE calculated neutron spectrum. Slope parameters In order to investigate the slope and the dose parameters, the experimental results are fitted to the expressions of Guo et al. and Nandy et al. Equations (3) and (7) are used to fit the experimental data in two ways: (i) by keeping the slope parameter S or S* fixed and the dose parameter free, and (ii) with both the slope and dose parameters free. In Figure 5, the results so obtained are shown along with the experimental data. In this case fixed values of the slope parameter S ¼ 0.57 and S* ¼ 0.87 are considered. Page 5 of 8
Figure 5. Fit results of the experimental results from 145 MeV 19 F projectiles incident on thick Al target. Table 2. Parameters obtained by fitting the experimental data with fixed and free slope parameters. Fitting technique Guo Nandy Free fit parameters H AV 123+6 H TOT 989+10 S 0.84+0.1 S* 0.83+0.1 Fit with calculated slope H AV 126+10 H TOT 958+37 Calculated slope parameter S 0.57 S* 0.87 Unit of H TOT and H AV is msv h 21 na 21 at 1.0 m. It can be seen that with the fixed slope parameter the fit by Guo s expression does not match the directional distribution trend of the experimental results. The results obtained using a free slope parameter and by keeping the slope fixed using Nandy s expression are the same. In Figure 5, these plots cannot be distinguished. Further, Guo s expression with both slope and dose parameters free, follow the fitted results using Nandy s formalism. These three curves cannot be distinguished in the plot. The values of the parameters obtained from the fitting procedures are shown in Table 2. Here it can be seen that using free parameter fits, the slope parameters in both the formalisms are identical to that obtained by the original equation of Nandy et al. Though this technique has yielded good results for the 19 Fþ 27 Al system at 110 MeV, it was found to predict lower values compared with the experimental results in the case of 100-MeV 19 F projectiles incident on a thick copper target (9). More work needs to be done for refining the present technique and to obtain a universal solution. C. SUNIL ET AL. MeV (8) and the results obtained in the present study are shown in Figure 6. From the figure it can be seen that 145 MeV projectiles give neutron doses that are about three to six times higher than that obtained from 110 MeV projectiles. The difference is higher in the forward directions compared with the backward angles, indicating a predominant forward emission of neutrons for the higher projectile energy. The slope of the plot obtained by a free fit procedure for incident energy of 145 MeV is 10 % higher than that obtained for 110 MeV, but agrees within the uncertainties. The values of the parameters obtained by fits of the two measured data using the formulations of Guo and Nandy are given in Table 3. It can be seen that the slope parameters obtained by both the formulations remain more or less constant for a given projectile. Comparison of yields A possible reason for the significant difference in the measured dose equivalent values from the same target (Al) and projectile ( 19 F) at 110 and 145 MeV could be due to the difference in the respective neutron yields. This is investigated by comparing the neutron yields obtained from different empirical formulations as well as the EMPIRE calculations. The results so obtained are shown in Table 4. It can be seen that the empirical formalisms predict two to three times more neutron yield from 145 MeV when compared with 110 MeV, whereas EMPIRE predicts a much lower ratio from these two projectile energies. The higher yield alone does not explain the difference in the dose values obtained from the two projectile energies. The contribution of high-energy neutrons to the ambient dose equivalent is also investigated from the calculated neutron spectra from the EMPIRE nuclear reaction codes. Table 5 gives the angle integrated Comparison of results from 110 and 145 MeV projectiles The results obtained from the same projectile target combination but at a lower incident energy of 110 Figure 6. The experimentally measured directional neutron dose equivalent from 110 and 145 MeV 19 F projectiles incident on a thick Al target. Page 6 of 8
Table 3. Free parameter fit results obtained from the experimental data of 110 and 145 MeV 19 F projectiles incident on thick aluminium target. Projectile energy in MeV Guo Nandy H AV S H TOT S* 145 123+6 0.84+0.1 989+10 0.83+0.1 110 23.5+0.3 0.76+0.04 210+12 0.78+0.07 Table 4. Energy and angle integrated neutron yield obtained by the empirical relations and from EMPIRE calculations. Projectile energy in MeV Neutron yield in ion 21 110 MeV (Y1) 145 MeV (Y2) Ratio (Y1/Y2) Guo 5.3E24 1.1E23 2.1 Clapier 1.16E24 3.18E24 2.7 EMPIRE 5.98E24 7.38E24 1.2 Table 5. The angle integrated neutron yields for different energy bins calculated using EMPIRE nuclear reaction code for 110 and 145 MeV 19 F projectiles incident on thick Al target. Projectile energy 145 MeV 110 MeV Ratio Neutron energy bin in MeV NEUTRON DOSE FROM 145-MeV 19 F ON THICK AL TARGET Neutron yield in MeV 21 sr 21 ion 21 (Y1) (Y2) (Y1/Y2) 1 5 4.12E206 3.35E206 1.23 6 10 2.04E206 1.40E206 1.46 11 15 9.52E207 5.66E207 1.68 16 20 4.31E207 2.02E207 2.13 21 25 1.82E207 6.47E208 2.82 yield for the energy bins in steps of 5 MeV from 1 to 25 MeV for 110 and 145 MeV projectiles incident on an Al target. From the ratio it is clear that while the yield of low-energy neutrons (,15 MeV) are about 1.5 times higher for 145 MeV projectiles when compared with 110 MeV projectiles, neutrons of energy.15 MeV are higher by about 2.2 times. An increase in the total yield and a relatively higher contribution to the dose from high-energy neutrons could be the reasons for the three to five times increase in the experimental ambient dose equivalent obtained from 145 MeV projectile energy. CONCLUSIONS The directional distribution of the neutron ambient dose equivalent resulting from the bombardment of a thick aluminium target by 145 MeV 19 F projectiles has been measured. The results are analysed with the help of three empirical formalisms and the results from the EMPIRE nuclear reaction code. While the empirical formalism of Nandy et al. is found to predict the present experimental results with reasonable accuracy, Guo s and Clapier s empirical techniques and the results obtained from the EMPIRE calculations are found to underpredict these values. The dose equivalents resulting from 145 MeV projectiles are found to be three to five times higher compared with 110 MeV, indicating higher neutron emissions. REFERENCES 1. International Atomic Energy Agency. Radiological safety aspects of the operation of proton accelerators. Technical Report Series No. 283. IAEA (1988). 2. Bartlett, D. T., Tanner, R. J., Tagziria, H. and Thomas, D. J. Response characteristics of neutron survey instruments. NRPB-R333(rev) November 2001, Available on http://www.hpa.org.uk/web/hpawebfile/hpaweb_c/ 1194947364968 (last accessed 19 May 2010). 3. Birattari, C., Ferrari, A., Nuccetelli, C., Pelliccioni, M. and Silari, M. An extended range neutron rem counter. Nucl. Instrum. Methods 297, 250 257 (1990). 4. Olsher, R. H., Hsu, H. H., Beverding, A., Kleck, J. H., Casson, W. H., Vasilik, D. G. and Devine, R. T. WENDI: an improved neutron rem meter. Health Phys. 70, 170 181 (2000). 5. Herman, M., Capote, R., Carlson, B. V., Oblozinsky, P., Sin, M., Trkov, A., Wienke, H. and Zerkin, V. EMPIRE: Nuclear Reaction Model Code System for Data Evaluation. Nucl. Data Sheets 108, 2655 2715 (2007). 6. Herman, M. EMPIRE-II statistical model code for nuclear reaction calculations (2.18 Mondovi), IAEA 1169/06. IAEA (2002). 7. International Commission on Radiological Protection. Conversion coefficients for use in radiological protection against external radiation. ICRP Publication 74. Ann. ICRP 26(3 4). Elesevier Science (1996). 8. Sunil, C., Maiti, M., Nandy, M. and Sarkar, P. K. Thick target neutron dose evaluation for 19 FþAl system. Radiat. Prot. Dosim. 123, 277 282 (2007). 9. Sunil, C., Nandy, M., Bandyopadhyay, T., Maiti, M., Shanbhag, A. A. and Sarkar, P. K. Neutron dose equivalent from 100-MeV 19 F projectiles on thick Cu target. Radiat. Meas. 43, 1278 1284 (2008). 10. Sunil, C., Shanbhag, A. A., Nandy, M., Maiti, M., Bandyopadhyay, T. and Sarkar, P. K. Direction distribution of ambient neutron dose equivalent from 20 MeV protons incident on thick Be and Cu targets. Radiat. Prot. Dosim. 136, 67 73 (2009). 11. Battistoni, G., Muraro, S., Sala, P. R., Cerutti, F., Ferrari, A., Roesler, S., Fasso, A. and Ranft, J. The FLUKA code: description and benchmarking. In: Proceedings of the Hadronic Shower Simulation Workshop 2006, Fermilab, 6 8 September 2006. Albrow, M. and Raja, R., Eds. AIP Conf. Proc. 896, 31 49 (2007). Page 7 of 8
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