Tritium Breeding Ratio in Li, Pb-Li, Pb-Li-C, Be-Li, Be-Li-C, Spheres Measured with Li2CO3 Pellets and/or LiF TLDs Version 1.0 compiled on March 8, 1994 Authors T. Iguchi(i), M. Nakazawa(i), J. Cetnar(i), K. Sugiyama(ii), A. Takahashi(iii) and K. Sumita(iii) Organizations (i) Department of Nuclear Engineering, University of Tokyo 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan Tel 03-3812-1800 Fax 03-5800-6861 (ii) Department of Nuclear Engineering, Tohoku University Aoba, Aramaki, Aoba-ku, Sendai, Miyagi 980, Japan (iii) Department of Nuclear Engineering, Osaka University 2-1 Yamada-oka, Suita, Osaka 565, Japan Tel 06-877-5111 Fax 06-877-3264 Facility OKTAVIAN, Osaka University Date Experiments with lithium pellets -1987 TLD experiments: February 1990, November 1990 Measured Quantities Local tritium production rate by lithium carbonate pellets (Li2CO3) was measured. Responses of LiF TLDs namely UD136N combined with UD137N were measured and then used to estimate local tritium production rate (TPR). The Nb foil activity was measured to determine the neutron source strength by means of the 'Large Solid Angle Activation Foil Method' 1). Experimental Method Several experiments were carried out to measure tritium breeding ratio (TBR) in various lithium spheres combined with lead or beryllium neutron multiplier and optionally graphite reflector. The tritium production rate distributions inside the lithium spheres were measured with lithium carbonate pellets (Li2CO3) or with LiF TLDs. Determination of TBR from TLD measurements was done using the least squares method employing covariance matrixes of nuclear data. The measured values of TBR were compared with theoretical ones obtained by neutron transport calculation using the ANISN code with the nuclear library JENDL-3. The direct measurement of local TPR by lithium carbonates pellets is widely known. This technique was applied to bare Li(50cm) assembly as well as to Pb(10cm)+Li(40cm) one. Derivation of TBR by integrating the local TPR over the whole lithium zone was assisted by its theoretical distribution to overcome problems with step space dependencies of measured values. In case of TLD application to TBR measurements, additional effort is necessary to obtain local TPR from TLD measurements. This technique was used for remaining systems. Now this method will be briefly described. Idea of the measurement is based on the fact that TLDs UD-136N and UD-137N consist of the same material apart from isotope of lithium. In the former case it is 6Li, in the latter 7Li. Detectors of 6Li are sensitive for neutrons mainly due to reaction 6Li(n,a)T, thus the response function to neutrons is similar to tritium production cross section. Both detectors has the same sensitivity for gamma radiation. If we take difference of responses from UD-136N and UD-137N, it will be the response only for neutrons. In this case the presence of gamma radiation will not disturb the measurement. But since the difference response function of TLDs (TLDD response function) differs from the tritium production cross section an influence of a neutron spectrum uncertainty on the TPR derivation from TLD responses must be of concern. For this purpose the neutron spectrum is treated as a variable. When the neutron flux and cross sections are presented in the group structure one can write equations: TPR=SIGMA(fai*sigma(sub)TP) (1) TLDD=SIGMA(fai*f(sub)TLDD) (2) where f is the neutron flux at measured point,sigma(sub)TP is the macroscopic tritium production cross section and f(sub)TLDD is the difference of TLDs response function. To solve the equations (1) and (2) the general least squares method was used. Generally, it minimizes function (3) conserving side equations (1) and (2) expressing TPR and TLDD responses at each point of measurement. M=[y-ym]t*Gy*[y-ym] (3) where y and ym denote true and measured values vectors, Gy is the weight matrix equal to reverse covariance matrix of measurements. During the experiment, TLD responses in lithium zone and source strength were measured. Measured values of TLD response functions with their covariance matrixes were prepared from direct measurements 2,3). Macroscopic tritium breeding cross section and its covariance matrix were prepared from 6Li(n,a)T and 7Li(n,n'a)T cross section and uncertainty data from 4). Neutron flux obtained from transport calculation is treated as a measured one but uncertainty of these data was chosen large since direct measurement of flux is not performed. This treatment gives us an information about the impact of flux spectrum uncertainty on the final uncertainty of TBR. It can be also noticed that this method imposes some correlation of TPR measured in different points what is physically understandable due to a fact that mean free path of neutrons in the system is comparable with the size of the lithium zone. The neutron spectrum is treated as uncertain to take into consideration errors imposed by differences between shape of TLDD response function and tritium production cross section. Condition of the positive value of neutron spectrum sets limit on relative standard deviation. It was chosen equal to 80% and correlations between group values were set at the level leading to TBR uncertainty obtained only from transport calculation equal to about 40%. This way final TBR uncertainty derived from TLD measurements is not strongly affected by additional a priori information concerning neutron spectrum. Neutron Source Characteristics In the first experiments (with Li pellets) the pulse beam line was used with the neutron source strength of order 1011 n/s. In this case angular distribution of source neutron increases errors of strength estimation. In next series experiments (with TLD) the neutron strength was of order 109 n/s, with improved angular distribution and reduced size of the target. Material / Geometry / Configuration Calculations and measurements of TBR were carried out for the following structures of the spherical assemblies: 1. Li(50cm) 2. Li(50cm)+C(20cm) 3. Pb(10cm)+Li(40cm) 4. Pb(10cm)+Li(40cm)+C(20cm) 5. Be(11.65cm)+Li(40cm) 6. Be(11.65cm)+Li(40cm)+C(20cm). Figure 1.1 presents the systems with the neutron multiplier and the graphite reflector. Experimental Data with Errors Experimental data with errors are shown in Tables 1.1 - 1.16. For experiments applying TLD units are: TLD responses; [Co-60 equivalent Roentgen/ source neutron] and TPR; [1/ source neutron/cm3]. For experiments with carbonate pellets and foil activation method TPR and reaction rate are given as a reaction rate per source neutron. Error Assessment In experiments with lithium carbonate pellets the given errors of local TPR consist of an uncorrelated statistical error of measured production rates and here called systematic error from source strength estimation. In case of TLD experiments local TPR errors are correlated not only by source measurements but also TLD response function, TPR cross sections, and neutron spectrum uncertainty. Correlation matrixes are attached with experimental data. Importance of each source of errors can be deduced from Table 1.1 and 1.2 calculated for total TBR integrated over the lithium zone. In the latter experiments improved neutron strength error consist of: error of the Nb cap position; c.a. 2%, counting statistics less than 1%, others errors including cross section of Nb about 1%. Example of Experimental Analysis Experimental analysis can be made in the similar method described in the next chapter. One-dimensional transport codes such as ANISN may be used. References 1) Iguchi T. and Nakazawa M.: "New Large Solid Angle (4p) Activation Foil Method for Absolute Measurement of D-T Neutron Source Intensity," Journal of Nuclear Science and Technology, Vol. 24, No. 11 (1987). 2) Hashikura H., Haikawa K., Tanaka S. and Kondo S.: "Calculation of Neutron Response of Thermoluminescent Dosimeters," Journal of the Faculty of Engineering, the University of Tokyo (B) Vol. XXXIX, No. 1 (1987). 3) Private communication on TLD UD136N, UD137N response function measurements. 4) Furuta K., Oka Y. and Kondo S.: "Evaluation of Covariance Data for 6Li and 7Li Cross Section in JENDL3-PR1," UTNL-R-0167 (VIII 1984). 5) Cetnar J. et al.: "Tritium Breeding Ratio in Li, Li-C, Pb-Li, Pb-Li-C, Be-Li, Be-Li-C, Spheres Measured by TLD or Li Pellets", Proc. of the Sec. Spec. Meeting on Nucl. Data for Fusion Reactors, JAERI-M 91-062, (March 1991). List of Tables ( also compiled in files of T1-*.txt ) Table 1.1 Comparison of TBR experimental and theoretical values. Table 1.2 Partial errors forming uncertainty of total TBR [%]. Table 1.3 Experimental and calculational data for Pb(10)-Li(40)-C(10) system. Table 1.4 Experimental and calculational data for Pb(10)-Li(40)-C(10) system. R.S.D of TLDD (Difference between UD136N and UD137N) and correlation matrix. Correlated part results from neutron strength estimation, uncorrelated part is. Table 1.5 Experimental and calculational data for Pb(10)-Li(40)-C(10) system. R.S.D of TPR (derived from TLDD) and correlation matrix. Increased correlations result from response function and TPR cross section uncertainty. Table 1.6 Experimental and calculational data for Be(10)-Li(40)-C(10) system. Table 1.7 Experimental and calculational data for Be(10)-Li(40)-C(10) system. R.S.D of TLDD (Difference between UD136N and UD137N) and correlation matrix. Correlated part results from neutron strength estimation, uncorrelated part is originated from random error of TLD readings. Table 1.8 Experimental and calculational data for Be(10)-Li(40)-C(10) system. R.S.D of TPR (derived from TLDD) and correlation matrix. Increased correlations result from response function and TPR cross section uncertainty. Table 1.9 Experimental and calculational data for Be(10)-Li(40) system. Table 1.10 Experimental and calculational data for Be(10)-Li(40) system. R.S.D of TLDD (Difference between UD136N and UD137N) and correlation matrix. Correlated part results from neutron strength estimation, uncorrelated part is originated from random error of TLD readings. Table 1.11 Experimental and calculational data for Be(10)-Li(40) system. R.S.D of TPR (derived from TLDD) and correlation matrix. Increased correlations result from response function and TPR cross section uncertainty. Table 1.12 Experimental and calculational data for Li(50)-C(20) system. Table 1.13 Experimental and calculational data for Li(50)-C(20) system. R.S.D of TLDD (Difference between UD136N and UD137N) and correlation matrix. Correlated part results from neutron strength estimation, uncorrelated part is originated from random error of TLD readings. Table 1.14 Experimental and calculational data for Li(50)-C(20) system. R.S.D of TPR (derived from TLDD) and correlation matrix. Increased correlations result from response function and TPR cross section uncertainty. Table 1.15 Measured reaction rates (R.R.) in Li(50 cm t) sphere. Units are [x10-24 reactions/ source neutron/ atom] for R.R and [%] for error. Table 1.16 Measured reaction rates (R.R.) in Pb(10 cm t)+Li(40cm t) sphere. Units are [x10-24 reactions/ source neutron/ atom] for R.R and [%] for error. List of Figure Fig.1.1 Pb(Be)-Li-C combined spherical system. ---------------------------------------------------------------- Table 1.1 Comparison of TBR experimental and theoretical values. Exp. Theor. C/E RSD TBR TBR ------------------------------------- Li 0.685 0.672 0.98 5.6 % LiC 1.13 1.03 0.91 16. % PbLi 0.530 0.527 0.99 6.0 % PbLiC 1.16 1.11 0.96 8.5 % BeLi 0.848 0.935 1.1 16. % BeLiC 1.51 1.45 0.96 9.1 % Table 1.2 Partial errors forming uncertainty of total TBR [%]. Source Detectors TPR TLD Neutron strength meas. cross sec. resp. funct. spectrum Li 5.3 1.0 LiC 2.6 8.0 1.5 7.0 10.0 PbLi 5.3 2.0 PbLiC 3.0 2.0 1.0 5.0 6.0 BeLi 2.6 9.0 1.0 6.0 9.0 BeLiC 2.5 3.5 1.0 4.5 6.0 Table 1.3 Experimental and calculational data for Pb(10)-Li(40)-C(10) system. Position TLDD calc. TLDD exp. UD136N exp. UD137N exp. TPR calc. TPR exp. [cm] ------------------------------------------------------------------------------------------------- 20.55 1.407e-13 1.406e-13 4.580e-13 3.167e-13 2.955e-06 2.940e-06 26.00 9.613e-14 7.645e-14 2.589e-13 1.830e-13 1.809e-06 2.021e-06 31.45 7.705e-14 8.804e-14 1.880e-13 9.990e-14 1.752e-06 1.602e-06 36.90 6.113e-14 6.211e-14 1.400e-13 7.760e-14 1.277e-06 1.250e-06 42.40 5.466e-14 5.114e-14 1.020e-13 5.110e-14 1.068e-06 1.108e-06 47.85 5.005e-14 4.420e-14 8.205e-14 3.780e-14 9.250e-07 1.007e-06 52.30 5.075e-14 5.694e-14 9.430e-14 3.730e-14 1.138e-06 1.020e-06 53.35 5.160e-14 4.950e-14 8.024e-14 3.070e-14 1.020e-06 1.038e-06 54.35 5.295e-14 5.223e-14 9.030e-14 3.810e-14 1.073e-06 1.067e-06 56.45 5.771e-14 6.970e-14 1.070e-13 3.730e-14 1.398e-06 1.171e-06 57.20 6.044e-14 8.129e-14 1.177e-13 3.631e-14 1.603e-06 1.233e-06 58.50 6.900e-13 9.538e-14 1.310e-13 3.540e-14 1.939e-06 1.448e-06 58.85 7.796e-14 8.709e-14 1.140e-13 2.730e-14 1.960e-06 1.733e-06 59.40 1.468e-13 1.790e-13 2.065e-13 2.740e-14 5.286e-06 4.486e-06 Table 1.4 Experimental and calculational data for Pb(10)-Li(40)-C(10) system. R.S.D of TLDD (Difference between UD136N and UD137N) and correlation matrix. Correlated part results from neutron strength estimation, uncorrelated part is. ----------------------------------------------------------------------------------------------------------- r.s.d [%] Correlation (upper part of a symmetric matrix) 21.0 1.0 .05 .07 .07 .07 .08 .06 .08 .08 .07 .07 .07 .10 .08 22.1 1.0 .07 .06 .07 .07 .06 .08 .08 .07 .07 .07 .10 .08 13.2 1.0 .09 .10 .11 .09 .12 .12 .10 .10 .11 .14 .12 14.0 1.0 .10 .10 .0.9 .12 .11 .09 .10 .11 .14 .12 12.3 1.0 .10 .10 .09 .12 .10 .11 .11 .15 .13 11.3 1.0 .10 .14 .13 .11 .11 .12 .16 .14 11.9 1.0 .11 .11 .09 .09 .10 .13 .11 9.82 1.0 .15 .12 .13 .13 .18 .16 9.14 1.0 .12 .12 .13 .18 .15 10.9 1.0 .10 .11 .14 .12 10.3 1.0 .11 .15 .13 9.68 1.0 .14 .16 7.95 1.0 .19 8.12 1.0 Table 1.5 Experimental and calculational data for Pb(10)-Li(40)-C(10) system. R.S.D of TPR (derived from TLDD) and correlation matrix. Increased correlations result from response function and TPR cross section uncertainty. ----------------------------------------------------------------------------------------------------------- r.s.d [%] Correlation (upper part of a symmetric matrix) 24.8 1.0 .43 .41 .37 .35 .30 .21 .24 .23 .16 .15 .13 .15 .07 23.8 1.0 .42 .38 .36 .31 .22 .26 .25 .17 .16 .14 .16 .07 16.9 1.0 .38 .37 .33 .24 .27 .26 .19 .17 .16 .17 .08 15.8 1.0 .35 .32 .24 .27 .26 .19 .18 .16 .17 .09 14.3 1.0 .32 .25 .28 .28 .20 .19 .17 .19 .09 12.6 1.0 .24 .28 .28 .21 .20 .19 .20 .09 11.7 1.0 .23 .24 .19 .18 .17 .17 .08 10.5 1.0 .27 .22 .21 .20 .21 .10 9.88 1.0 .22 .22 .21 .22 .10 10.5 1.0 .19 .18 .18 .08 9.88 1.0 .19 .19 .08 9.38 1.0 .22 .11 8.85 1.0 .20 11.9 1.0 Table 1.6 Experimental and calculational data for Be(10)-Li(40)-C(10) system. Position [cm] TLDD calc. TLDD exp. UD136N exp. UD137N exp. TPR calc. TPR exp. 2.03e+01 2.01e-12 1.670e-12 1.900e-12 2.230e-13 1.484e-04 1.23e-04 2.14e+01 4.39e-13 4.720e-13 6.614e-13 2.000e-13 1.488e-05 1.61e-05 2.42e+01 1.87e-13 2.110e-13 3.880e-13 1.770e-13 4.581e-06 5.06e-06 2.57e+01 1.47e-13 1.860e-13 3.590e-13 1.730e-13 3.560e-06 4.29e-06 3.12e+01 8.62e-14 7.860e-14 2.000e-13 1.220e-13 2.049e-06 1.92e-06 3.67e+01 6.30e-14 7.060e-14 1.460e-13 7.550e-14 1.450e-06 1.58e-06 4.22e+01 5.14e-14 5.073e-14 1.100e-13 5.900e-14 1.140e-06 1.13e-06 4.77e+01 4.57e-14 4.780e-14 9.230e-14 4.450e-14 9.860e-07 1.02e-06 5.32e+01 4.54e-14 5.060e-14 8.540e-14 3.480e-14 9.570e-07 1.05e-06 5.57e+01 4.84e-14 5.240e-14 8.610e-14 3.370e-14 1.017e-06 1.10e-06 5.82e+01 5.89e-14 8.830e-14 1.800e-13 2.961e-14 1.270e-06 1.84e-06 5.97e+01 1.49e-13 1.807e-13 2.105e-13 2.980e-14 7.537e-06 7.67e-06 Table 1.7 Experimental and calculational data for Be(10)-Li(40)-C(10) system. R.S.D of TLDD (Difference between UD136N and UD137N) and correlation matrix. Correlated part results from neutron strength estimation, uncorrelated part is originated from random error of TLD readings. r.s.d [%] Correlation (upper part of a symmetric matrix) 4.92 1.0 .20 .16 .13 .10 .12 .12 .13 .15 .16 .19 .21 7.31 1.0 .16 .14 .11 .13 .13 .14 .16 .16 .20 .22 9.42 1.0 .12 .09 .11 .11 .12 .13 .13 .16 .18 8.61 1.0 .09 .10 .10 .11 .12 .12 .14 .16 12.0 1.0 .08 .08 .09 .10 .10 .11 .12 9.36 1.0 .09 .10 .11 .11 .13 .15 9.88 1.0 .10 .11 .11 .13 .14 8.61 1.0 .12 .12 .14 .16 7.32 1.0 .13 .16 .17 7.10 1.0 .16 .18 5.59 1.0 .21 4.85 1.0 Table 1.8 Experimental and calculational data for Be(10)-Li(40)-C(10) system. R.S.D of TPR (derived from TLDD) and correlation matrix. Increased correlations result from response function and TPR cross section uncertainty. r.s.d [%] Correlation (upper part of a symmetric matrix) 13.7 1.0 .56 .15 .13 .09 .10 .09 .11 .14 .16 .21 .10 16.2 1.0 .40 .36 .25 .20 .16 .15 .15 .16 .19 .09 15.8 1.0 .75 .51 .38 .28 .22 .19 .18 .19 .06 15.7 1.0 .57 .41 .30 .23 .19 .18 .18 .05 21.2 1.0 .57 .39 .28 .21 .19 .17 .04 17.0 1.0 .56 .39 .28 .25 .21 .05 16.7 1.0 .53 .37 .32 .26 .05 13.7 1.0 .50 .42 .34 .07 10.7 1.0 .57 .45 .09 9.77 1.0 .52 .09 7.24 1.0 .07 20.6 1.0 Table 1.9 Experimental and calculational data for Be(10)-Li(40) system. Position TLDD calc. TLDD exp. UD136N exp. UD137N exp. TPR calc. TPR exp. [cm] --------------------------------------------------------------------------------------------------------- 2.03e+01 1.940e-12 1.620e-12 1.850e-12 2.230e-13 1.44e-04 1.200e-04 2.14e+01 4.110e-13 4.370e-13 6.300e-13 1.980e-13 1.43e-05 1.514e-05 2.42e+01 1.660e-13 1.813e-13 3.570e-13 1.750e-13 4.48e-06 4.550e-06 2.67e+01 1.100e-13 9.940e-14 2.400e-13 1.404e-13 2.76e-06 2.484e-06 2.78e+01 9.610e-14 8.690e-14 1.870e-13 9.956e-14 2.41e-06 2.180e-06 3.02e+01 7.425e-14 6.410e-14 1.740e-13 1.096e-13 1.86e-06 1.603e-06 3.56e+01 4.705e-14 4.320e-14 1.217e-13 7.850e-14 1.16e-06 1.068e-06 4.11e+01 3.220e-14 2.870e-14 7.884e-14 5.018e-14 7.80e-07 6.395e-07 4.66e+01 2.270e-14 1.615e-14 5.390e-14 3.760e-14 5.43e-07 3.860e-07 5.20e+01 1.630e-14 1.451e-14 4.030e-14 2.580e-14 3.86e-07 3.440e-07 5.75e+01 1.140e-14 9.044e-15 2.730e-14 1.827e-14 2.70e-07 2.149e-07 Table 1.10 Experimental and calculational data for Be(10)-Li(40) system. R.S.D of TLDD (Difference between UD136N and UD137N) and correlation matrix. Correlated part results from neutron strength estimation, uncorrelated part is originated from random error of TLD readings. r.s.d [%] Correlation (upper part of a symmetric matrix) 7.12 1.0 .19 .15 .12 .13 .11 .10 .11 .09 .10 .10 7.52 1.0 .15 .12 .14 .11 .11 .11 .09 .11 .10 10.2 1.0 .10 .11 .09 .09 .09 .08 .09 .08 13.1 1.0 .09 .08 .07 .08 .07 .07 .07 11.3 1.0 .08 .08 .08 .07 .08 .08 15.1 1.0 .07 .07 .06 .07 .06 15.8 1.0 .07 .06 .07 .06 15.3 1.0 .06 .07 .06 19.3 1.0 .06 .06 15.5 1.0 .06 17.2 1.0 Table 1.11 Experimental and calculational data for Be(10)-Li(40) system. R.S.D of TPR (derived from TLDD) and correlation matrix. Increased correlations result from response function and TPR cross section uncertainty. r.s.d [%] Correlation (upper part of a symmetric matrix) 13.8 1.0 .55 .11 .09 .09 .07 .06 .06 .05 .05 .04 15.8 1.0 .39 .33 .31 .26 .19 .14 .11 .09 .07 17.5 1.0 .70 .66 .54 .38 .28 .20 .16 .12 22.8 1.0 .82 .66 .46 .33 .23 .18 .13 23.3 1.0 .74 .50 .36 .25 .19 .14 26.0 1.0 .58 .40 .28 .21 .15 26.2 1.0 .57 .39 .28 .20 26.5 1.0 .57 .40 .28 30.5 1.0 .57 .39 26.1 1.0 .56 27.7 1.0 Table 1.12 Experimental and calculational data for Li(50)-C(20) system. Position [cm] TLDD cals. TLDD exp. UD136N exp. UD137N exp. TPR calc. TPR exp. 2.02e+01 8.76e-14 1.620e-12 6.08e-13 5.20e-13 3.110e-06 3.62e-06 2.57e+01 9.13e-14 4.370e-13 3.57e-13 2.65e-13 2.000e-06 2.58e-06 3.12e+01 3.51e-14 1.813e-13 2.19e-13 1.84e-13 1.433e-06 1.35e-06 3.67e+01 3.06e-14 9.940e-14 1.61e-13 1.30e-13 1.102e-06 9.79e-07 4.22e+01 3.69e-14 8.690e-14 1.30e-13 9.11e-14 9.000e-07 9.40e-07 4.77e+01 3.60e-14 6.410e-14 9.40e-14 5.75e-14 7.830e-07 8.49e-07 5.32e+01 2.45e-14 4.320e-14 7.67e-14 5.20e-14 7.480e-07 6.25e-07 5.87e+01 7.21e-14 2.870e-14 1.12e-13 4.18e-14 1.096e-06 1.63e-06 Table 1.13 Experimental and calculational data for Li(50)-C(20) system. R.S.D of TLDD (Difference between UD136N and UD137N) and correlation matrix. Correlated part results from neutron strength estimation, uncorrelated part is originated from random error of TLD readings. r.s.d [%] Correlation (upper part of a symmetric matrix) 35.4 1.0 .05 .04 .04 .05 .06 .05 .07 18.5 1.0 .05 .05 .06 .07 .06 .09 31.6 1.0 .05 .05 .06 .05 .07 25.9 1.0 .05 .06 .06 .08 16.3 1.0 .07 .07 .10 11.3 1.0 .08 .12 14.2 1.0 .11 5.94 1.0 Table 1.14 Experimental and calculational data for Li(50)-C(20) system. R.S.D of TPR (derived from TLDD) and correlation matrix. Increased correlations result from response function and TPR cross section uncertainty. r.s.d [%] Correlation (upper part of a symmetric matrix) 35.4 1.0 .59 .38 .26 .19 .15 .11 .08 18.5 1.0 .59 .39 .28 .21 .15 .11 31.6 1.0 .58 .39 .28 .20 .13 25.9 1.0 .57 .39 .27 .17 16.3 1.0 .56 .37 .23 11.3 1.0 .54 .31 14.2 1.0 .40 5.94 1.0 Table 1.15 Measured reaction rates (R.R.) in Li(50 cm t) sphere. Units are [x10-24 reactions/ source neutron/ atom] for R.R and [%] for error. Radius 6Li(n,a)T error 7Li(n,n'a)T error 93Nb(n,2n)92mNb error 27Al(n,a)24Na error 115In(n,n')115mIn [cm] 10.0 2.942e-04 5.4 2.343e-04 5.3 3.672e-04 6.2 9.356e-05 6.0 1.789e-04 6.4 20.3 1.751e-04 5.4 5.492e-05 6.0 7.002e-05 6.2 1.947e-05 6.1 5.254e-05 6.2 30.8 1.058e-04 5.5 2.060e-05 6.0 2.352e-05 6.3 6.777e-06 6.3 2.370e-05 6.2 41.4 6.788e-05 5.4 9.866e-06 10.5 9.645e-06 6.2 2.926e-06 6.4 1.248e-05 6.3 52.1 4.488e-05 5.5 5.218e-06 10.4 4.558e-06 6.3 1.469e-06 6.4 6.633e-06 6.3 57.7 4.151e-05 5.7 3.425e-06 10.4 3.180e-06 6.3 1.023e-06 6.4 4.290e-06 6.3 63.3 2.144e-06 15.6 Table 1.16 Measured reaction rates (R.R.) in Pb(10 cm t)+Li(40cm t) sphere. Units are [x10-24 reactions/ source neutron/ atom] for R.R and [%] for error. Radius 6Li(n,a)T error 7Li(n,n'a)T error 93Nb(n,2n)92mNb error 27Al(n,a)24Na error 115In(n,n')115mIn 10.0 1.155e-03 5.3 2.635e-04 5.4 4.081e-04 6.2 1.013e-04 6.1 3.337e-04 6.4 [cm] 20.3 4.517e-04 5.4 3.260e-05 6.1 4.124e-05 6.3 1.122e-05 6.2 7.687e-05 6.2 30.8 2.128e-04 5.4 1.158e-05 9.3 1.360e-05 6.3 3.952e-06 6.3 2.422e-05 6.2 41.4 1.234e-04 5.8 5.335e-06 16.4 5.598e-06 6.3 1.630e-06 6.4 1.021e-05 6.3 52.1 7.726e-05 5.8 2.815e-06 30.7 2.642e-06 6.3 8.302e-07 6.4 4.867e-06 6.3 57.7 6.704e-05 5.8 1.846e-06 43.6 1.939e-06 6.3 5.852e-07 6.4 3.115e-06 6.4 Fig.1.1 Pb(Be)-Li-C combined spherical system.