A Practical Method for Evaluating the Neutron Dose

Transcription

1 Journal of NUCLEAR SCIENCE and TECHNOLOGY, 3[11], p.473~478 (November, 1966) 473 A Practical Method for Evaluating the Neutron Dose Equivalent Rate* Yoshikazu YOSHIDA**, Hatsumi TATSUTA**, Hiroshi RYUFUKU**, Kyoshiro KITANO** and Seiji FUKUDA** Received July 7, 1966 A practical method applicable to field monitoring with survey instruments is presented, which permits evaluation of the dose equivalent rate for neutrons, the spectrum of which is unknown but with energy ranging from epithermal to fast. The detectors employed consist of a BF3 proportional counter with paraffin moderators 6.5 cm and 1.0 cm thick, sheathed in 0.5 mm thick Cd, and a scintillation (ZnS and plastic) counter. The dose equivalent rate D(mrem/hr) of neutrons with a broad spectrum is determined from the equation D=DB+Ds, where DB is the dose equivalent rate determined from the effective neutron flux and the effective neutron energy through the counting rates obtained with the BF3 proportional counter with paraffin moderators, and Ds the dose measured with the scintillation counter, the sensitivity of which is nearly proportional to the dose equivalent rate for neutrons above 2 MeV. The error in evaluating the dose equivalent rate by the present method has been calculated to be at most 60% for typical neutron spectra, in the energy range from epithermal to 10 MeV. I. INTRODUCTION Measurement of the dose equivalent rate of neutrons is very difficult, particularly when the spectrum is unknown but with energy ranging from intermediate to fast, such as in the case of neutrons leaking from nuclear reactors. Detectors(1)~(3) and circuits(4)(5) have been developed that show a response nearly proportional to the tissue-absorbed dose rate; and methods have been devised for evaluating the dose equivalent rate from the neutron flux and the effective energy, using either two different detectors(6), or a detector employed with moderators of several thicknesses(6)~(8). However, these devices are not suitable for intermediate neutrons. More recently, various instruments have been developed to evaluate the dose equivalent rates of neutrons, including those of intermediate energies(9)~(11), but they are not necessarily portable. In this paper is described a practical method for field monitoring in the vicinity of reactors with survey instruments. This is used for evaluating the dose equivalent rate of neutrons, the spectrum of which is unknown but with energy ranging from epithermal to fast. The detectors employed are a BF3 proportional counter with two paraffin moderators, 6.5 and 1.0 cm thick, sheathed in 0.5 mm thick Cd, and a scintillation (ZnS and plastic) counter. The error incurred in evaluating the dose equivalent rate by this method is also discussed for typical neutron spectra, in the energy range from epithermal to 10 MeV.. DETECTORS II The main characteristics of the detectors used are given in Table 1, and Photo. 1 is a photograph of the survey instrument set with these detectors. Figure 1 shows the response curves of the detectors, measured with a 2 MeV Van de Graaff and 20 MeV Linac in the Japan Atomic Energy Research Institutec(12)(13)***. The response of the BF3 proportional counter covered by 6.5 cm-paraffin is nearly constant in the energy range below about 4 MeV, but decreases rapidly beyond this energy level, whereas * A summary of this paper was presented to the First International Congress of the International Radiation Protection Association in Rome, September ** Division of Health Physics and Safety, Japan Atomic Energy Research Institute, Tokai-mura, Ibaraki-ken, * The response curve of the ** BF3 counter covered with 6.5 cm-paraffin is revised on the basis of a recent experiment by some of the present authors(14). 19

2 474 J. Nucl. Sci. Technol. Table 1 Description of Detectors with the counter covered by 1.0 cm-paraffin, the response only starts to decrease at about 5 ev. The ratio between the responses of the counter covered by 1.0 cm- and 6.5 cm-paraffin is shown in Fig.2 as a function of neutron energy; it is seen that the ratio decreases with energy between 20 ev and 3 MeV, and is nearly constant below 5 ev and above 3 MeV. Accordingly, if the neutron spectrum is monoenergetic, the energy of the neutrons can be obtained from the counting rate ratio. In the energy range of 2 to 10 MeV, the error in the response of the scintillation counter Photo. 1 Survey Instruments Set, with BF3 Proportional Counter Covered by Paraffin Moderator and Scintillation (ZnS and Plastics) Counter is within +-20% of the curve relating the tissue absorbed dose rate to the energy, shown in Fig. 3(15), and below this range the counting efficiency is impaired. Fig. 1 Responses of the BF3 Proportional Counter Covered with 6.5 cm-paraffin and 1.0 cm-paraffin, (represented by curves marked g1(e) and g2(e)), and Response of Scintillation (ZnS and plastics) Counter (represented by gs(e)) Fig. 2 Ratio between Response of BF3 Proportional Counter Covered by 1.0 cm- and 6.5 cm-paraffin 20

3 Vol.3, No.11 (Nov. 1966) 475 Fig.3 Dose Equivalent Rate per Unit Flux Density as Function of Neutron Energy (from NBS Handbook, 63, 1957.) III. METHOD FOR EVALUATING THE DOSE EQUIVALENT RATE In the present method, for neutrons with energies ranging from epithermal to fast, the dose equivalent rate D=DB+Ds, where DB(mrem/ hr) is the dose equivalent rate mainly for epithermal and intermediate neutrons, determined from the counting rates obtained by paraffin-moderated BF3 proportional counter, and Ds(mrem/hr) is the dose equivalent rate mainly for neutrons in the energy range above about 2 MeV, measured by scintillation counter. 1. Determination of DB For neutrons general, the dose equivalent rate D=Sh(E)p(E)dE (mrem/hr) (1) where h(e): Dose equivalent rate per unit neutron (see Fig.3) p(e)de: Neutron flux density in the energy interval (E, E+dE) (n/cm2,sec). The counting rates N1 and N2(cpm) for the BF3 proportional counter, covered by 6.5 cmand 1.0 cm-paraffin moderators, respectively, are given by Ni=Sgi(E)p(E)dE, (i=1, 2) (2) BF3 proportional counter with 6.5 cm- and 1.0 cm-paraffin moderators respectively (see Fig 2). If the neutron spectrum is monoenergetic, it can be expressed by Dirac's delta function: (E)=p0d(E-E0), where E0 is the p neutron energy. Hence Eq.(2) can be transformed to and Eq.(1) (E0)p0 (i=1, 2), (3) Ni to where the neutron energy E0 is obtained from the equation The function f(e) is shown in Fig.2. In general, the neutron flux density p0=ni/gi(e0) should be determined from N1 rather than N2, because g1(e) is larger than g2(e) and moreover nearly constant in the energy range below about 4 MeV. Hence Eq.(4) is transformed to The present method for evaluating the dose equivalent rate for neutrons with a broad energy spectrum with the use of BF3 proportional counter is based on the method just described for monoenergetic neutrons. In the case of a broad neutron spectrum, if we take Eq.(5) to be the definition of the effective energy Eeff, then (4) (5) (4') So that, as described in Appendix, the approximate dose equivalent rate (5') (6) 21

4 476 J. Nucl. Sci. Technol. The contribution of fast neutrons to N1 and Eeff, and hence to DB is very much smaller than that of the slow neutrons owing to the characteristics of the counter, represented by the curves g1(e) and g2(e) shown in Fig Determination of Ds The dose equivalent rate for the neutrons in the energy range above about 2 MeV is nearly proportional to the counting rate Ns(cpm) of the scintillation counter, because the response gs(e)(cpm/n/cm2,sec) is nearly proportional to h(e) in this energy region, as seen from Figs. 1 and 3. Hence for neutrons mainly in this range above 2 MeV, the dose equivalent rate Ds=K,Ns (mrem/hr), (7) where K is a calibration constant*, and Ns=Sgs(E)p(E)dE. (8) IV. CALCULATION OF ERRORS FOR TYPICAL NEUTRON ENERGY SPECTRA The errors incurred in evaluating the dose equivalent rates by the present method were calculated for the following four typical neutron spectra: (1) The 1/E neutron spectrum expressed by the equation (2) The energy spectrum for thermal fission of 235U, expressed by(16) where K is a constant; (3) Energy spectrum calculated for a homo- Fig.4 Ratio between Dose Equivalent Rate (DB, DB+Ds) obtained by the Present Method and Actual Rate (D), Calculated for a Neutron Spectrum of the form SEmxlev1/edE(Emax<=10MeV) Table 2 Ratio between Dose Equivalent Rates (DB, DB+Ds) obtained by the Present Method and Actual Dose Equivalent (D) calculated for Typical Spectra geneous light water reactor core(17); (4) The energy spectrum of Ra-g-Be neutrons(18). The counting rates of the two kind of detectors used were calculated with Eqs. (2) and (8) respectively. The ratios between the dose equivalent rates calculated by the present technique and those by Eq.(1) were obtained. The results obtained for the 1/E neutron spectrum are shown in Fig.4 and summarized in Table 2. The results prove that: (1) The errors in the approximate dose equi- * K=1.82x10-2mrem/hr,cpm for the neutrons from a RaD-Be source. 22

5 Vol.3, No.11 (Nov. 1966) 477 valent rate for the broader 1/E spectra are within 60%. (2) The values obtained solely with the BF3 proportional counter with paraffin moderator err on the lower side, but the errors are smaller for neutron spectra of lower energy range. (3) The errors incurred by the present method for typical energy spectra are within 60%. V. CONCLUSION The errors incurred in evaluating the dose equivalent rates by the present method were calculated to be at most 60% for the typical spectra in the energy range from epithermal to 10 MeV. The method using survey instruments has been applied to field monitoring around the nuclear reactors and other facilities. It has been shown that this method is useful for radiation protection against neutrons having a broad spectrum such as those leaking from reactors and accelerators. APPENDIX] [ Theoretical Discussion on Evaluation of the Dose Equivalent Rate with Two Detectors (1) Theoretical Derivation of the Method using Two Detectors Equation (1) can be transformed to where the symbol < >n1, specifies averaging with the weight function n1(e)=g1(e)p(e): (9) (10) Now, the ratio g2(e)/g1(e) is a function of neutron energy: From Eqs. (2) and (11), (15) If the effective energy of a neutron spectrum is defined by Eq.(5'), from Eqs. (12), (14) and (15), (16) Using Eq.(16), Eq.(9) can be transformed to (17) Equation (16) is generally satisfied when Eq. (13) holds. (2) Discussion on the Error incurred by the Method using Two Detectors This method introduces some error because Eq.(13) cannot always be satisfied for neutrons having a broad energy spectrum. Taking up to the second power term in Taylor's expansion of F[f-1(R)] with (R- <R>n1), where a0-=f[f-1(<r>n1)] (18) Hence, using Eqs. (13) and (14), the error in <h(e)/g1(e)>n1 is expressed by (19) Then the error in the dose equivalent rate DD is expressed by (11) Since f(e) is a monotonic function, as shown in Fig.2, we derive the relation (12) If the relation <F[f-1(R)]>n1=F[f-1(<R>n1)], (13) is satisfied, from Eqs.(12) and (13), (14) (20) where sr is the standard deviation of R. Equation (20) indicates that the error depends upon both a2 and s2r, and for monoenergetic neutrons, the error is zero because R=<R>n1. The curve of F[f-1(R)]-which is the relation of h(e)/g1(e) and R-is shown in Fig.5; the responses of the BF3 proportional counter, covered with 6.5 cm- and 1.0 cm-paraffin, are 23

6 478 J. Nucl. Sci. Technol. REFERENCES Fig.5 Relation between F[f-1(R)] (=h(e)/ g1(e)) and R(=g1(E)/g2(E)) as a Parameter of Neutron Energy utilized for g1(e) and g2(e), respectively. The neutron energies are shown in Fig.5. From Fig.5 and Eq.(20), it is seen that the error is zero for neutrons of energies up to 10 kev irrespective of the spectrum, since the curve is linear in this region, and it is negative if the range of neutron energy exceeds 10 kev, that is, the estimated values are lower than actual, since the second differential coefficient as is positive*. This agrees with the results calculated in Chap.IV. * If the effective energy Eeff of a neutron spectrum including neutrons of energies above 10 - kev - is under 10 kev, the estimated value is much smaller than actual, because a straight line linking 2 ev and 10 kev is substituted for the curve in Fig.5. (1) HURST, G.S., RITCHIE, R.H., WILSON, H.N.: Rev. Sci. Instr., 22, 981, (1951). (2) SKJOLDEBRAND, R.: J. Nucl. Energy, 1, 299 (1955). (3) DENNIS, J.A., LOOSEMORE, W.R.: AERE-EL/ R-2149, (1957). (4) WAGNER, E.B., HURST, G.S: Rev. Sci. Instr., 29, 153 (1958). (5) HURST, G.S., RITCHIE, R.H.: Health Phys., 8, 117 (1962). (6) WALLACE, R., HANDLOSER, J.S., MOYER, B.J., et al.: A/Conf., 15/P/1882, (1964). (7) DEPANGHER, J.: Nucl. Instr. Mesh., 5, 61 (1959). (8) POHLIT, W., POHLIT, H.: Nukleonik, 2[5], 13 (1960). (9) DENNIS, J.A.: Nucleonics, 20, 76 (1962). ) HANKINS, D.E.: Health Phys., 9, (10 31 (1963). (11) ANDERSSON, I.O., BRAUN, J.: Nukleonik, 6[5], 237 (1964). TATSUTA, (12) H., YOSHIDA, Y., MINAMI, K.: Oyobutsuri, (in Japanese), 32, 367 (1963). (13) TATSUTA, H., KATOH, K., YOSHIDA, Y.: J. Appl. Phys., 4, 321 (1965). (14) RYUFUKU, H., TATSUTA, H., SHIROTANI, T.: "The Sensitivity of a Paraffin Moderated BF3- proportional Counter", to be published. NBS Handbook, 63, (1957). (15) (16) WATT, B.E.: Phys. Rev., 87, 1037 (1952). (17) KATSURAGI, S., MORIGUCHI, K., KUGE, Y.: Fast Neutron Spectrum and Group Constant Code 7044 UGMG, JAERI-1104, p. 28 (1966). HANSON, A.O.: "Fast Neutron (18) Physics", p. 37 (1960), Intersci. Publ., Inc. 24