Appendix

Table 1. Fundamental constantt'

Quantity Symbol Value

Acceleration due to gravity g 9.80665m/s 3.21741 x 101 ftls

Atomic mass unit amu 1.660565 x 10-27 kg Alpha particle rest mass ma 6.644763 x 10-27 kg Avogadro constant NA 6.022045 x 1()23 (g.mole)-l Boltzmann constant k= (RINA) 1.380662 x 10-23 JIK Electron rest mass IDe 9.109534 x 10-31 kg Electronic charge e 1.6021892 x 10-19 coul Gas constant R 8.31441 J/mole.K Planck constant h 6.626176 x 10-34 J.s Proton rest mass mp 1.6726485 x 10-27 kg Neutron rest mass mn 1.6749544 x 10-27 kg Speed of light c 2.99792458 x 108 m/s Stefan-Boltzmann constant u 5.67032 x 10-8 watts/m2.K4

a Ref: Journal of Physics and Chemistry Reference Data, Vol. 2 (4), p. 663, 1973, E.R. Cohen and BN. Taylor

Table 2. Prefixes for decimal multiples

Factor Prefix Symbol Factor Prefix Symbol

10-18 atto a 1012 tera T 10-15 femto f 109 giga G 10-12 pico p 1()6 mega M 10-9 DanO n UP kilo k 10-6 micro J.t 102 hecto h 10-3 milli m 101 deca da 10-2 centi c 10-1 deci d

Appendix 549

Table 3. Some fundamental units

Quantity SI CGS British

Unit Symbol Unit Symbol Unit Symbol

Length [L] meter m centimeter em inch in Mass [M] kilogram kg gram g pound mass lb TIlDe [T] second s second s second s Temperature kelvin K degree Kelvin OK degree Fahrenheit OF

degree Celsius °C Force newton N dyne dyne pound lbr Energy joule J erg erg foot pound ftlb Pressure pascal Pa dyne/em'- dyne/em'- pound/in'- psi Power watt W erg/s erg/s foot pound/s ftlb/s Heat joule J calorie calorie British thennal unit Btu

550 Appenctix

Table 4. 0.0253 e V or 2200 mls Cross sections for elements and certain molecules (from Reactor Physics ConsllJnts, ANL-5SOO 1963)

Atomic ffiement Atomic Density Nuclei Microscopic Macroscopic No. or or g/em3 per Cross Section Cross Section

Com- MoL Unit b em- l

pound WL VoL xlO-24 1- ilo e u. u. Ut E. E. Et

H 1.008 8.9" 5.34 0.3386 1.000 0.33 38 38 1.7" 0.002 0.002 H2O 18.016 1 0.0335 0.676 0.948 0.66 103 103 0.022 3.45 3.45 ~O 20.030 1.10 0.03314 0.884 0.570 0.001 13.6 13.6 3.34 0.449 0.449

2 He 4.003 17.8" 2.6" 0.8334 0.425 0.007 0.8 0.807 0.02" 2.14 2.14 3 Li 6.940 0.534 0.0463 0.9047 0.268 71 1.4 72.4 3.29 0.065 3.35 4 Be 9.013 1.85 0.1236 0.9259 0.209 0.010 7.0 7.01 124h 0.865 0.865

BeO 25.02 3.025 O.0728h 0.939 0.173 0.010 6.8 6.8 734 0.501 0.501 5 B 10.82 2.45 0.1364 0.9394 0.171 755 4 759 103 0.346 104 6 C 12.0ll 1.60 0.0800 0.9444 0.158 0.004 4.8 4.80 32" 0.385 0.385 7 N 14.008 0.0013 5.34 0.9524 0.136 1.88 10 1l.9 9.9" 50" 60" 8 0 16.000 0.00145.34 0.9583 0.120 20" 4.2 4.2 0.000 214 214 9 F 19.00 0.0017 5.34 0.9649 0.102 0.001 3.9 3.90 0.014 20" 20"

10 Ne 20.183 0.0009 2.6" 0.9667 0.0968 <2.8 2.4 5.2 7.34 6.2" 13.54 II Na 22.991 0.971 0.0254 0.9710 0.0845 0.525 4 4.53 0.013 0.102 0.1l5 12 Mg 24.32 1.74 0.0431 0.9722 0.08ll 0.069 3.6 3.67 0.003 0.155 0.158 13 AI 26.98 2.699 0.0602 0.9754 0.0723 0.241 1.4 1.64 0.015 0.084 0.099 14 Si 28.09 2.42 0.0522 0.9762 0.0698 0.16 1.7 1.86 0.008 0.089 0.097 15 P 30.975 1.82 0.0354 0.9785 0.0632 0.20 5 5.20 0.007 0.177 0.184 16 S 32.066 2.07 0.0389 0.9792 0.0612 0.52 1.1 1.62 0.020 0.043 0.063 17 Cl 35.457 0.00325.34 0.9810 0.0561 33.8 16 49.8 0.002 80" 0.003 18 A 39.944 0.00 18 2.6" 0.9833 0.0492 0.66 1.5 2.16 1.7" 3.9 5.6" 19 K 39.100 0.87 0.0134 0.9829 0.0504 2.07 1.5 3.57 0.028 0.020 0.048 20 Ca 40.08 1.55 0.0233 0.9833 0.0492 0.44 3.0 3.44 0.010 0.070 0.080 21 Sc 44.96 2.5 0.0335 0.9852 0.0438 24 24 48 0.804 0.804 1.61 22 Ti 47.90 4.5 0.0566 0.9861 O.04ll 5.8 4 9.8 0.328 0.226 0.555 23 V 50.95 5.96 0.0704 0.9869 0.0387 5 5 10.0 0.352 0.352 0.704 24 Cr 52.01 7.1 0.0822 0.9872 0.0385 3.1 3 6.1 0.255 0.247 0.501 25 Mn 54.94 7.2 0.0789 0.9878 0.0359 13.2 2.3 15.5 1.04 0.181 1.22 26 Fe 55.85 7.86 0.0848 0.9881 0.0353 2.62 II 13.6 0.222 0.933 1.15 27 Co 58.94 8.9 0.0910 0.9887 0.0335 38 7 45 3.46 0.637 4.10 28 Ni 58.71 8.90 0.0913 0.9887 0.0335 4.6 17.5 22.1 0.420 1.60 2.02 29 Cu 63.54 8.94 0.0848 0.9896 0.0309 3.85 7.2 11.05 0.0326 0.6ll 0.937 30 Zn 65.38 7.14 0.0658 0.9897 0.0304 1.10 3.6 4.70 0.072 0.237 0.309 31 Ga 69.72 5.91 0.05ll 0.9925 0.0283 2.80 4 6.80 0.143 0.204 0.347 32 Ge 72.60 5.36 0.0445 0.9909 0.0271 2.45 3 5.45 0.109 0.134 0.243 33 As 74.91 5.73 0.0461 0.99ll 0.0264 4.3 6 10.3 0.198 0.277 0.475 34 Se 78.96 4.8 0.0366 0.9916 0.0251 12.3 II 23.3 0.450 0.403 0.853 35 Br 79.916 3.12 0.0235 0.9917 0.0247 6.7 6 12.7 0.157 0.141 0.298 36 Kr 83.80 0.0037 2.6" 0.9921 0.0236 31 7.2 38.2 814 19" 99" 37 Rb 85.48 1.53 0.01a! 0.9922 0.0233 0.73 12 12.7 0.008 0.130 0.138 38 Sr 87.63 2.54 0.0175 0.9925 0.0226 1.21 10 1l.2 0.021 0.175 0.195 39 Yt 88.92 5.51 0.0373 0.9925 0.0223 1.313 4.3 4.3 0.049 0.1l2 0.160 40 Zr 91.22 6.4 0.0423 0.9927 0.0218 0.185 8 8.2 0.008 0.338 0.347

Appendix 551

Table 4. (Contimud)

Z Blement A p N I-jloe 0'1 0'. O't EI E. Et

41 Nb 92.91 8.4 0.0545 0.9928 0.0214 1.16 5 6.16 0.063 0.273 0.336 42 Mo 95.95 10.2 0.0640 0.9931 0.0207 2.70 7 9.70 0.173 0.448 0.621 43 Tc 98.0 - 0.9932 0.0203 22 44 Ru 101.1 12.2 O.07n 0.9934 0.0197 2.56 6 8.56 0.186 0.436 0.622 45 Rh 102.91 12.5 0.0732 0.9935 0.0193 149 5 154 10.9 0.366 11.3 46 Pd 106.4 12.16 0.0689 0.9937 0.0187 8 3.6 11.6 0.551 0.248 0.799 47 Ag 107.88 10.5 0.0586 0.9938 0.0184 63 6 69 3.69 0.352 4.04 48 Cd 112.41 8.65 0.0464 0.9940 0.0178 2450 7 2457 114 0.325 114 49 In 114.82 7.28 0.0382 0.9942 0.0173 191 2.2 193 7.30 0.084 7.37 50 Sn 118.70 6.5 0.0330 0.9944 0.0167 0.625 4 4.6 0.021 0.132 0.152 51 Sb 121.76 6.69 0.0331 0.9945 0.0163 5.7 4.3 10.0 0.189 0.142 0.331 52 Te 127.61 6.24 0.0295 0.9948 0.0155 4.7 5 9.7 0.139 0.148 0.286 53 I 126.91 4.93 0.0234 0.9948 0.0157 7.0 3.6 10.6 0.164 0.084 0.248 54 Xe 131.30 0.00592.7" 0.9949 0.0152 35 4.3 39.3 95" 12" 0.001 55 Cs 13291 1.873 O.OOSS 0.9950 0.0150 28 20 48 0.238 0.170 0.408 56 Ba 137.36 3.5 0.0154 0.9951 0.0145 1.2 8 9.2 0.018 0.123 0.142 57 La 138.92 6.19 0.0268 0.9952 0.0143 8.9 15 24 0.239 0.403 0.642 58 Ce 140.13 6.78 0.0292 0.9952 0.0142 0.73 9 9.7 0.021 0.263 0.283 59 Pr 140.92 6.78 0.0290 0.9953 0.0141 11.3 4 15.3 0.328 0.116 0.444 60 Nd 144.27 6.95 0.0290 0.9954 0.0138 46 16 62 1.33 0.464 1.79 61 Pm 145.0 - 0.9954 0.0137 60 62 8m 150.35 7.7 0.0309 0.9956 0.0133 5600 5 560S 173 0.155 173 63 Eu 1520 5.22 0.0207 0.9956 0.0131 4300 8 4308 89.0 0.166 89.2 64 Gel 167.26 7.95 0.0305 0.9958 0.0127 46.000 - 1403 -65 Th 158.93 8.33 0.0316 0.9958 0.0125 46 1.45 66 Dy 16251 8.56 0.0317 0.9959 0.0122 950 100 1050 30.1 3.17 33.3 67 Ho 164.94 8.76 0.0320 0.9960 0.0121 65 2.08 68 Er 167.27 9.16 0.0330 0.9960 0.0119 173 15 188 5.71 0.495 6.20 69 Tm 168.94 9.35 0.0333 0.9961 0.0118 127 7 134 4.23 0.233 4.46 70 Yb 173.04 7.01 0.0244 0.9961 0.0115 37 12 49 0.0.3 0.293 1.20 71 Lu 174.99 9.74 0.0335 0.9962 0.0114 112 3.75 72 Hf 178.5 13.3 0.0449 0.9963 0.0112 105 8 113 4.71 0.03595.07 73 Ta 180.95 16.6 0.0553 0.9963 0.0110 21 5 26 1.16 0.277 1.44 74 W 183.86 19.3 0.0632 0.9964 0.0108 19.2 5 24.2 1.21 0.316 1.53 75 Re 186.22 20.53 0.0664 0.9964 0.0107 86 14 100 5.71 0.930 6.64 76 OS 190.2 22.48 0.0712 0.9965 0.0105 15.3 11 26.3 1.09 0.783 1.87 77 Ir 1922 22.42 0.0703 0.9965 0.0104 440 30.9 78 Pt 195.09 21.37 0.0660 0.9966 0.0102 8.8 10 18.8 0.581 0.660 1.24 79 Au 197.0 19.32 0.0591 0.9966 0.0101 98.8 9.3 107.3 5.79 0.550 6.34 80 Hg 200.61 13.55 0.0407 0.9967 0.0099 380 20 400 15.5 0.814 16.3 81 Ti 204.39 11.85 0.0349 0.9967 0.0098 3.4 14 17.4 0.119 0.489 0.607 82 Pb 207.21 11.35 0.0330 0.9968 0.0096 0.170 11 11.2 0.006 0.363 0.369 83 Bi 209.0 9.747 0.0281 0.9968 0.0095 0.034 9 9 0.001 0.253 0.256 84 Po 2ID.0 9.24 0.026S 0.9968 0.0095 -85 At 211.0 - 0.9968 0.0094 -86 Rn 2220 0.0097 2.(1' 0.9970 0.0090 0.7 87 Fr 223.0 - 0.9980 0.0089 -88 Ra 226.05 5 0.0133 0.9971 0.0088 20 0.266 -89 Ac 227.0 - 0.9971 0.0088 510

552 Appendix

Table 4. (Continrwl)

Z Element A p

90 Th 23205 11.3 91 Pa 231.0 15.4 92 U 238.07 18.9

UCh 270.07 10 93 Np 237.0 -94 Pu 239.0 19.74 95 Am 2420 -a Value has been multiplied by 1 as " Molealles/cm3

N 1-iloe CTa CT. CTt E.

0.0293 0.9971 0.0086 7.56 12.620.2 0.222 0.040Z 0.9971 0.0086 200 8.04 0.04783 0.9972 0.0084 7.68 8.3 16.0 0.367 0.0223" 0.9887 0.036 7.6 16.724.3 0.169

0.9972 0.0084 170 0.0498 0.9972 0.0083 1026 9.6 1036 51.1

0.9973 0.0082 8.000 -

Table 5. 0.0253 eV or 2200 m/s Cross sections of special interest

lOB llB 12C

13C

160 170 180 135Xe 149Pm

233U 235U 238U

239Pu

2~ 241Pu 242Pu

ITa = 3837b ITa = 0.005 ITa = 0.0034 (98.89% abundance) ITa = 0.0009 (1.1 % abundance) ITa = 0.178 X 10-3 (99.759% abundance) ITa = 0.235 (0.037% abundance) ITa = 0.16 X 10-3 (0.204% abundance) ITa = 2.7 X 106

ITa =4.1 X 104

IT-y =49 ITf=524 IT-y = 101 ITf = 577 IT-y =2.73 IT-y =274 IT-y =286 IT-y =425 IT-y =30

ITf = 741 ITf = 0.03 ITf =950 ITf < 0.2

E. Et

0.369 0.592 -0.397 0.765 0.372 0.542

0.478 51.6

Appenctix 553

Table 6. Representation of Laplacian V2 in various coordinate systems

(a) Cartesian:

(b) Cylindrical:

2 laa lal al V =--T-+--+­T aT aT r2 a(J2 ail

(c) Spherical:

554 Appmctix

Table 7. Heald funcsioos

% Jo(;c) Jl(;c) Yo(;c) Yl(;c) 10(%) It (;c) Ko(;c) Kl(%)

0 1.0000 0.0000 -00 -00 1.000 0.0000 00 00

O.OS 0.9994 0.0250 -1.979 -12.79 1.001 0.02S0 3.114 19.91 0.10 0.9975 0.0499 -1.534 -6.459 1.003 0.0501 2.427 9.854 0.15 0.9944 0.0748 -1.271 -4.364 1.006 0.0752 2.030 6.477 0.20 0.9900 0.995 -1.081 -3.324 1.010 0.1005 1.753 4.776

0.25 0.9844 0.1240 -0.9316 -2.704 1.016 0.1260 1.542 3.747 0.30 0.9776 0.1483 -0.8073 -2.293 1.023 0.1517 1.372 3.056 0.35 0.9696 0.1723 -0.7003 -2.000 1.031 0.1777 1.233 2.559 0.40 0.9604 0.1960 -0.6060 -1.781' 1.040 0.2040 1.115 2.184 0.45 0.9500 0.2194 -0.5214 -1.610 LOS 1 0.2307 1.013 1.892

0.50 0.9385 0.2423 -0.4445 -1.471 1.063 0.2579 0.9244 1.656 0.55 0.9258 0.2647 -0.3739 -1.357 1.077 0.2855 0.8466 1.464 0.60 0.9120 0.2867 -0.3085 -1.260 1.092 0.3137 0.7775 1.303 0.65 0.8971 0.3081 -0.2476 -1.177 1.108 0.3425 0.7159 1.167 0.70 0.8812 0.3290 -0.1907 -1.103 1.126 0.3719 0.6605 1.OS0

0.75 0.8642 0.3492 -0.1372 -1.038 1.146 0.4020 0.6106 0.9496 0.80 0.8463 0.3688 -0.0868 -0.9781 1.167 0.4329 0.5653 0.8618 0.85 0.8274 0.3878 -0.0393 -0.9236 1.189 0.4646 0.5242 0.7847 0.90 0.8075 0.4059 -0.0056 -0.8731 1.213 0.4971 0.4867 0.7165 0.95 0.7868 0.4234 0.0481 -0.8258 1.239 0.5306 0.4524 0.6560

1.0 0.7652 0.4401 0.0883 -0.7812 1.266 0.5652 0.4210 0.6019 1.1 0.6957 0.4850 0.1622 -0.6981 1.326 0.6375 0.3656 0.5098 1.2 0.6711 0.4983 0.2281 -0.6211 1.394 0.7147 0.3185 0.4346 1.3 0.5973 0.5325 0.2865 -0.5485 1.469 0.7973 0.2782 0.3725 1.4 0.5669 0.5419 0.3379 -0.4791 1.553 0.8861 0.2437 0.3lm 1.5 0.4838 0.5644 0.3824 -0.4123 1.647 0.9817 0.2138 0.2774 1.6 0.4554 0.5699 0.4204 -0.3476 1.750 1.085 0.1880 0.2406 1.7 0.3690 0.5802 0.4520 -0.2847 1.864 1.196 0.1655 0.2094 1.8 0.3400 0.5815 0.4774 -0.2237 1.990 1.317 0.1459 0.1826 1.9 0.2528 0.5794 0.4968 -0.1644 2.128 1.448 0.1288 0.1597

2.0 0.2239 0.5767 0.5104 -0.1070 2.280 1.591 0.1139 0.1399 2.1 0.1383 0.5626 0.5183 -0.0517 2.446 1.745 0.1008 0.1227 2.2 0.1104 0.5560 0.5lm -0.0015 2.629 1.914 0.0893 0.1079 2.3 0.0288 0.531l'5 0.5181 O.OS23 2.830 2.098 0.0791 0.0950 2.4 0.002S 0.52m 0.5104 0.1005 3.049 2.298 0.0702 0.0837

2.5 0.0729 0.4843 0.4981 0.1459 3.290 2.517 0.0623 0.0739 2.6 -0.0968 0.47(11 0.4813 0.1884 3.553 2.755 O.OS54 0.0653 2.7 -0.1641 0.4260 0.46Il'5 0.2276 3.842 3.016 0.0493 0.0571 2.8 -0.1850 0.4097 0.4359 0.2635 4.157 3.301 0.0438 0.0511 2.9 -0.2426 0.3575 0.4079 0.2959 4.503 3.613 0.0390 0.0453 3.0 -0.2601 0.3391 0.3769 0.3247 4.881 3.953 0.0347 0.0402 3.2 -0.3202 0.2613 0.3071 0.3707 5.747 4·734 0.0276 0.0316 3.4 -0.3643 0.1792 0.2296 0.4010 6.785 5.670 0.0220 0.0250 3.6 -0.3918 0.0955 0.1477 0.4154 8.028 6.793 0.6175 0.0198 3.8 -0.4026 0.0128 0.0645 0.4141 9.517 8.140 0.0140 0.0157

4.0 -0.3971 -0.0660 -0.0169 0.3979 11.302 9.759 0.0112 0.0125

Conversion factors

Length [1..]

meter

1 0.0254 0.3048 1609

inches

39.37 1 12 6.34 x 104

feet

3.28 0.08333 1 5280

mile (international)

6.21 x 10-4

1.58 x lO-s 1.89 x 10-4

1

Others: 1 (U.S. nautical) = 1.852 x 103 m 1 (U.S. statute) = 1.609 x 103 m 1 (international nautical) = 1.852 x 103 m 1 angstrom = 1.0 x 10-10 m

Mass [M]

Appenctix SSS

kilogram pounds tons (short, 2000 lb) tons (long, 2240 lb)

1 2.205 1.102 x 10-3 10-3 0.4536 1 5.0 x 10-4 4.536 x 10-4

907.2 2000 1 0.9072 1000 2205 1.102 1

Others: 1 ton (metric) = 1.0 x 103 kg 1 ounce (avoirdupois) = 2.835 x 10-2 kg

Time [T]

seconds minutes hours days years

1 1.667 x 10-2 2.778 x 10-4 1.157 x lO-s 3.169 x 10-8

60 1 1.667 x 10-2 6.944 x 10-4 1.901 x 10-6

3600 60 1 0.0417 1.141 x 10-4

8.64 x 104 1440 24 1 2.738 x 10-3 3.156 x 107 5.260 x lOS 8776 365.24 1

556 Appmdix

watt Btu/hr MeVIs

1 3.412 6.242 x 1012

0.2931 1 1.829 x 1012

1.602 x 10-13 5.466 x 10-13 1

Power density [MT-3L]

watt/m3 cal/scm3 Btu/hrft3 MeV/scm3

1 2.388 x 10-7 0.09662 6.242 x 106

4.187 x 106 1 4.045 x loS 2.613 x 1013

10.35 2.472 x 10-6 1 6.461 x 107

1.602 x 10-7 3.826 x 10-14 1.548 x 10-8 1

Heat flux ~3]

watt/m2 cal/scm2 Btu/hrftl MeV/scm2

1 2.388 x 10-5 0.3170 6.242 x lOS 4.187 x 104 1 1.327 x 104 2.613 x 1013

3.155 7.535 x 10-5 1 1.969 x 109 1.602 x 10-9 3.826 x 10-14 5.078 X 10-10 1

Thermal conductivity

watt/mK cal/scmoC

1 2.388 x 10-3 0.5778 418.7 x 104 1 241.9 1.731 4.134 x 10-3 1

VISCOSity

kg/ms poise = g/crn s Ibm/hrft

1 10 2419 0.1 1 241.9 4.134 x 10-4 4.134 x 10-3 1

Pressure [ML -IT-2]

Pa dyne/cm2 Bar

1 10 10-5

0.1 1 10-6

loS 106 1 6895 6.895 x 104 0.06895 1.013 x loS 1.013 x 106 1.013

Radiation units: 1 curie = 3.700 x 1010 Becquerel (Bq) 1 rad = 1.000 x 10-2 Gray (Gy) 1 rem = 1.000 x 10-2 Sievert (Sv)

psi

1.450 x 10-4

1.450 x 10-5

14.50 1 14.7

1 roentgen = 2.58 x 10-4 Coulomb/kg (C/kg)

Appendix 557

atm

9.869 x 10-6

9.869 x 10-7

0.9872 0.06805 1

Subject Index

I-DX code 201

Accident risk analysis 539 Activation of coolants 416 Activity - radioactive 306 Advisory Committee on Reactor Safeguards (ACRS) 490 As low as reasonably achievable (ALARA) 347 Atom percent 35 Atomic Energy Act 487 Atomic Energy Commission 487 Atomic Safety and Licensing Appeal Panel (ASLAP) 490 Atomic Safety and Licensing Board Panel (ASLBP) 490 Avogadro's number 34

Bam 55 Becquerel 39, 306 Bessel functions 174 Binding energy 13, 15 - average 15 - total 15 Bolumann constant 143 Boral 81 Buckling - geanetric 168 - material 166, 168 Bucklings 180 Buildup factors 368 - Berger form 378 - Taylor form 377 Buildup flux 374 - from line soun:e 386 - from plane source 380 Bumable poisoo 240 Boiling Water Reactor (BWR) 439 BWR (Boiling Water Reactor) 52

C-14 52 CALIB 225 Center-of-Mass 121, 123 Clemical shim 253 CHF (Critical Heat Flux) 473 Class 9 Accident 531, 533 Code of Federal Regulations (CFR) 494 COUIDE 127, 128, 146 Collision parameter 127 Compoond nucleus 23 CONTAIN 537 Containment 507, 510 -dry 507 - Mark I 512 - Mark n 512 - Mark ill 512 - pressure suppression 510 Conuol rods 239 - BWR (cruciform) 242 - central 244 - PWR pin 240 - rod worth 247 Core heat removal 433 Criticality 159 - condition 162 - delayed 215 - eigenvalues 161 - prompt 215 Cross section 53 - absorption 60 - capture 60 - charged particle capture 60 - coupled neutron-gamma 426 - energy dependence 63 - elastic scattering 60 - fission 60 - inelastic scattering 60 - macroscopic 53,55, 61 - microscopic 53,55 - one-group thermal 76 - radiative capture 60 - removal 404

-JeIClIIIIIlc:e 6S - sc:auerin& 60 Quie 39,306

Decay COIIItaIlt 43 Decay heal 447 Density 34 .Department of EneJBY (DOE) 488 Design-basis accicImts 49S Diffusion c:oefticient 89, 91 Diffusion equaIion 102 - boundary c:onditjons 104 - fiDit.e di1fmmc:e form 99 - inteJfac:e boundary c:oodiJions 104 - ru1e-of-thumb 108 - solution for a plane source 110 - solution for a point source 113 - symmetry bolUldary condition 109 - vacuum boundary lOS Diuus-Boelter corre1ation 464 DNB (Departure from Nucleate Boiling) 473

BCCS (EmelieDC)' Core Coolant Systems) SOO Effective muhipli.cati.oo factor 72, 79 EueJBY levels 19 EneJBY ReoJganization Act 488 EueJgy Research and Deve1quent Adminisua­tion (ERDA) 488 Euviromnental Protectiao Agency (EPA) 347 '1 (eta) 71 Excited states 19 BXOOSB 3S1 Extrapolation 1ength 106

Fast reactor 78 Fertile 31 Pick's Law 83, 92, 9S - Pick's Law analogues 94 FiDiIe di1fmmc:e methods 188 - iteration 194 Fissile 31,33 Fission 12, 26, 49, 271 - c:riJical eDeJBY 27 - delayed fission products 29 - eDeIJY re1eue 30 - prochc:t buildup 282 - product, Sm-149 279 - product, Xe-13S 273

Subject Index SS9

- produc:t, Xe-13S and Sm-149 271 - product, Xe transients 277 - product distribution 49 - product effects 271 - prompt fission products 28 - recoverable 31 - n:leued eDeJBY 27 Fission products 47, S14 - invenrory S16 - source term S14 Fissionable 31 Fourier's Heat ConduClioo Law 9S FUBLROD 466 Fusion 16

Gamma radiation 290 - attenuation 29S - Compton effect 293, 295 - delayed 290 - dose calculations 337 - internal source ca1cula1ion 3S2 - linear absorption c:oefticient 303 - linear attenuation c:oefticient 296 - mass attenuation c:oefticient 297 - pair procbclion 293, 295 - photoelectric effect 293, 294 - prompt 290 Gray 312

Half-life 43, 44 Heat flux 446 - CHF ratio 479 - c:riJical 476 - DNB ratio 479 Heat uansfer - bulk boiling 474 - c:oefticient 461 - nucleate boiling 474

ICRU (Jntemalional Commission on Radiation Units and Measurements) 304 InfiDit.e muldplWalioa factor 72 Intemational Commission on RadioJogical Protectiao 346 Isotropic directioaaI. distribution fi1

k.Ir 162 koo 75,165

560 Subject Index

Kinetic energy 25 - avai1aie 25

Lab coordinate system 122 Lab system 123 Laplacion operator 102 Lattice pitch 74 LEOPARD 73 Licensing Process 491 Loss-of-coolant accident (LOCA) - double-ended guillotine break 497 - small break 496

Manhattan Project 140 MARCH 537 Maximum Pennissible Dose (MPD) 347 Maxwellian distribution 141, 154 - average neutron velocity 147 - average thennal cross-section 149 - average velocity 143 - effective neutron temperature 150 - effective temperature 145 - mathematical properties of 154 - most probable velocity 143 - non-1/V factors 150, 152 Mean life 43 Moderators 139 Molea:ilar density 35 Monte Carlo method 428 MULTIDIF 99, 183, 194, 200

National Commission on Radiological Protec­tion 347 Neutron 12, 57 - meter per second Bux 148 - beam 57 - cum:D1 57,58 - delayed 209, 212 - delayed fraction 212 - dose calculation 341 - fast neutron dose 344 - Bux 57, 180 - interaction rate 54 - leakage 168 - maxwellian distribution 141 -prom~209 - thermal 141 - thennalBux 147 - thermal neutron dose 343

- transport theory 420 - transverse leakage 180 Neutron diffusion 83 - equation 96 Neutron lifetime 103 Neutron moderation 119 - liE region 135 - average gain in lethargy per eL collision

137 - energy distribution 134 -lethargy 136 - maximmn eneIBY loss 131 - moderating effectiveness 140 - minimum energy loss 131 Neutron population balance 7 Non-leakage probability 70 - fast neutron 186 - thennal 185 Nuclear - fuel depletion 280 Nuclear force 15 Nuclear reactor - cylindrical 172 - slab 162 - spherical 177 Nuclear Regulatory Commission (NRC) 487 Number 34 - atomic 34 - molecular 34

Ohm's Law 95 Ovennoderated 75, 266

Pasquil conditions 529 PERIOD 225, 229 POlNTK code 377 Precursor - delayed neutron 211 Pressurized Water Reactor (PWR) 436 Probabilistic Risk Analysis (PRA) 541 - event tree analysis 543 - fault tree analysis 544 Prompt critical 222 Prompt neutron 33 - spectJUm 33 Property balance law 3

Quality factor 325

Rad (radiation absorbed dose) 312 Radiation - abscxbed dose 312 - biological effects 323 - dose 313 - dose equiva1ent 313 - enmgy fluence 310 - exposure 309 - fluence 309 - linear eneJBY transfer (LET) 324 - man-made sources 314 - natural sources 314 - relative biological effectiveness (RBE) 325 Radiation effects - acute 331 - genelic: 331, 334 - latent 331, 332 Radiation Protection Guidelines (RPG) 348 Radiation protection standards 346 Radioactive decay 34 Radioactivity 36 - activity 39 - lIIDlospheric dispenim 521 - decay constant 38 - radioactive isotope balance 40 Radm 319 Radon-222 42 Reactivity 216 - $p 218 - dollar 218 - feedback 256 - fuel temperalure (doppler) coefficient 259 - moderator coefficient 26S - pcm 217 - pen:a1t of 217 - power coefficient 256, 269 - temperalure coefficient 256. 258 - void coefficient 268 Reactor 239 - control methods 239 - period 222 - shields 291 Reactor kinetics 209 - asymp.otic: period 227 - promJll jump 232 - single neutron group 220 - solutim 218 Reactor licensing 487 - Constructim Pennit (CP) 491

Subject Index 561

-licensing process 491 - Operating license (OP) 491 RegulalOly guides 494 Resmance 20 Resonance absorption probability 69 Resmance escape probabilil.y 69,263 Resonance integral 262 Rest mass 14 RODROP 22S Roentgen 310

SCATEREL 127, 132 Scattering 90 - angle, average cosine of 90, 132 - elastic 120 - inelastic 120 Self -shielding 261 Shiakbng 291, 362 - buildup factors 368 - line source 365 - plane source 367 - point keme1 365, 393 - point source 363 - transport theoIy 424 Sievert 313 SIXFAC 68, 72, 267 SIXFACl' 267,270 "Six Factor" formula 67 Slowing down parameters 140 Soluble poisoo (see also Cllemical shim) 240, 253 - Boric acid (113803) 240 - H3BO, 253 Spherical co-ordinate system 113

Thermal diffusion area 153 Thermal flux 147 Thermal utilization factor 71 'l1uee Mile Island accident 502 Transport cross section 89 lRIGA reactor 157

Undermoderated 75, 266

Wave1eugth 21

Software Description

The included diskette contains 12 programs that were developed primarily as a teaching tool to accompany the text "Nuclear Engineering, an introduction" by Almenas and Lee. The programs were developed during a time when the capabilities of the PC, especially its graphic output capability, was expanding and they reflect this development history. Thus some of the pograms combine both graphics and text, others provide only simple numerical output. Except for MUL TIDIF which is written in FORTRAN, all programs are written in QBASIC.

One note should be made at this point: the programs should serve primarily as an aid in learning. This goal can at times conflict with one of the common goals of software development, namely "user friendliness". Taken to its extreme,"user friendliness" implies that almost no thought is required to operate a program, that is, of course, the exact opposite of what would be expected of a learning experience. For this reason, the input of some of the programs (for example the POINTK code) might seem to be too detailed and require too much thought at each step. That is not a development shortcoming, but the desired effect.

Nuclear Engineering PC Programs

The included PC programs have the following purposes: a) To illustrate important physical principles. Thus the COLIDE program illustrates

neutron-nuclei interactions, the CALIB and ROD DROP programs illustrate control rod calibration procedures, the SIXFAC program illustrates the neutron life-cycle.

b) To serve as computational aids. For example, the EXDOSE and POINTK programs provide an automated means of performing routine shielding calculations; the A V ANGLE program performs mUltiple scattering calculations.

c) To serve as engineering design tools. In general, specialized engineering design tools (e.g. shielding, diffusion theory codes) require a higher level of complexity than is present in the educational programs provided in this package. Thus this purpose is secondary. Nevertheless, some of the programs use techniques and information which is employed in programs used for design purposes. This is true for the MULTIDIF, SIXFACT, POINTK and FUELROD programs. These programs can therefore serve as an introduction to the more complex design programs and also provide useful answers for estimation purposes.

564 Software Description

AVANGLE: An extension of the COLIDE program. Given a set of initial conditions describing two colliding particles. A V ANGLE perfonns a specified number of repeated calculations. each time choosing a random Center of Mass System scattering angle. For each event. the program prints out the C. M. angle. the Lab System angle. the energy loss of the flfSt particle and finally. the average of these parameters.

The program is suitable for illustrating the statistical nature of scattering events and the relationship between average scattering angles and average events increases. the average scattering angle in the C. M. system approaches 90 degrees.

CALm: Simulation of control rod calibration using the asymptotic period method. Uses the PERIOD program. Uses built in and for the student unknown rod value curves.

Suitable for illustrating the calibration method and emphasizes distinction between "differential" and "integral" control rod value. Illustrates the variation of control rod value with axial position.

COLIDE: A program for calculating the consequences of an elastic collision between two particles. The program has a general structure and thus requires a full specification of input conditions. This includes masses of the colliding particles and (x. y) components of initial velocities for both particles. The Center of Mass scattering angle is supplied by a random number.

Provides an animated graphic illustration of the scattering events. The program is suitable for illustrating general aspects of elastic scattering.

EXDOSE: Calculates the "Exposure" and "Dose" produced by gammara)J>eam or point source in air. Uses a data file which includes a library of attenuation coefficients in air. Multi-energy gamma sources can be considered.

Suitable for illustrating the basic principles in dose and exposure computations. The results can be checked by hand calculations. thus the code is useful for illustrating the concept that computer calculations can be erroneous if some of the input data is supplied incorrectly. Some attenuation coefficients in the included file can be altered in order to provide a suitable illustration.

FUELROD: Finite difference heat conduction code in cylindrical geometry. especially designed to detennine the temperature distribution in power reactor fuel rods. Considers the pellet. gap and clad as separate regions. Material properties for the main structural components are built into the code.

Software Description 565

Suitable for illustrating the dependence of the temperature profile on power density and geometric characteristics of the rod.

MULTIDIF: Finite difference, multi-energy group, multi-region diffusion theory code. Critically evaluates parameters and flux distributions for all standard one- dimensional geometries: slab, infinite cylinder and sphere. Input is divided into an "interactive" and "file" based part. This makes the code suitable for interactive "search" and "iterative" calculations. Includes a graphic output of the calculated fluxes.

Suitable for illustrating the principle of neutron balance computations. Extensively applicable in homework. Illustrates among others: effect of multikenergy neutron groups, effect of reflectors, use of reflective and vacuum boundary conditions, effect of reactor geometry.

PERIOD: Simulates the establishment of an asymptotic rate of power variation after a reactivity change. The program uses a three-delayed-group kinetics equation formulation to simulate the transition and the asymptotic periods.Includes a "speed­up" feature.

Can be used to illustrate the characteristics of the "transition" and "asymptotic" periods. The program uses an absolute timer, thus "real time" power rate changes can be simulated. With a speed-up; of 1, it gives an illustration of actual delay times that pass until the asymptotic period is established.

POINTK: A shield design code using the "Point-Kernel" method. Determines the gamma- ray fluency and the resulting dose rate behind a mixed-composition slab shield for gamma sources of various geometries. Mass attenuation coefficients and build-up factors (Berger form) are obtained from a supplied data library. User inputs the source geometry and intensity interactively using a graphed representation of the source-shield-dose point geometry.

Suitable for illustrating the "Point-Kernel" technique and the concept of build­up factors. Layered shields and odd-shaped source geometries can be employed. The geometric input is supplied interactively providing an immediate illustration of effects of distance, path of the ray through shields and shield composition.

RODDROP: Simulates the short term power change which follows a "step" insertion of a control rod. Required input is the prompt neutron life time and the effective delayed neutron fraction. The student chooses rod number to be "dropped" or "jerked". Output is presented numerically and graphically

Program can be used to simulate "rod-drop" and "rod-jerk" experiments. Since the student does not know the magnitude of the reactivity which produces the calculated power change rate, the program can be used in homework assignments.

566 Software Description

SCATEREL: A program for calculating neutron-nuclei elastic scattering parameters. As input, SCA TEREL requires only the mass of the scatterer and the initial energy of the neutron (in e V). It provides a table of post-collision values (Lab angle, final velocity, final energy and energy loss) for each lO-degree increment in the C. M. system scattering angle.

The program has the simplest input of all three routines demonstrating 2 body scattering characteristics. It is suitable for illustrating the dependence of scattering parameters on the atomic weight of the scatterer.

SIXFAC: Simulation of the neutron life cycle using the "six-factor" formula as a basis. This is a menu-driven, simple-to-use program with some tutorial features. It evaluates the basic neutronic parameters using only minimal input (rod diameter, lattice pitch, enrichment and rod number). The neutron life cycle is presented graphically in a sequential step-by-step manner.

Suitable as a tutorial for learning the main features of the neutron life cycle in a thermal reactor. Provides a graphic illustration of how the components of the six­factor formula enter into the calculation ofthe muliplication factor. Can be used for evaluating the dependence of the six-factor components on rod diameter and the fuel-to-moderator atomic ratio.

SIXFACT: SIX-FACtor-Temperature dependent. An extension of the SIXFAC program. In addition to parameters considered by SIXF AC, it evaluates the effect of temperature and soluble poison (H3B03). The effect of temperature can be evaluated parameterically. That is, all other parameters can be kept constant while the temperature is changed. The calculated results can then be reviewed in a graphic

form. Suitable for illustrating the effect of temperature on reactivity. Can be used to

demonstrate temperature effects of "overmoderated" and "undermoderated" cores. The graphic display feature can be used to illustrate the physical mechanisms which are producing temperature-caused reactivity changes.