Table 4. Fluence rate from unscattered photons of energy £ at | m in air for the U and
Pu spheres.

a. 5U (93.5 %) 1 kg sphere; fluence rates greater than 107 cm? st. Except for changes
less than 0.1 % in the fluence rates of the U characteristic x rays, these results hold for
sphere ages of 10 y, 25 y, and 50 y, and the total fluence rates of all 1182 lines
calculated are about 8.5 cm” s'! for these ages.

E/MeV @/em” s' | Nuclide
1.857E-01 | 3.899E+00 | U235
9.844E-02 |_1.084E+00 | U Kal
1.113E-01 TASIE-01 | UKB1
9.466E-02 |__6.097E-01 | U Ka2
2.053E-01 4.346E-01 | U235
1.438E-01 3.973E-01 | U235
1.633E-01 2.528E-01 | U235
9.335E-02 1.671E-01 | U235
1.092E-01 1.234E-01 | U235
1.056E-01 9.947E-02 | U235
2.021E-01 9.025E-02 | U235
8.996E-02 | 6.486E-02 | U235
8.421E-02 5.142E-02 | TH231
1.048E-01 5.109E-02 | U235
1.949E-01 4.828E-02 | U235
1.086E-01 4.028E-02 | U235
1.023E-01 2.910E-02 | TH231
9.586E-02 2.413E-02 | TH231
1.826E-01 2.225E-02 | U235
1.209E-01 2.024E-02 | U234
8.995E-02 1.867E-02 | TH231
3.878E-01 1.389E-02 | U235
2.214E-01 1.244E-02 | U235
1.084E-01 1.136E-02 | TH231
3.459E-01 1.109E-02 | U235
1.001E+00 1.032E-02 | PA234m

17


1.707000E-01
1.783000E-01
1.798000E-01
1.861000E-01
1.863000E-01
1.872000E-01
1.880000E-01
1.958000E-01
1.974000E-01
1.979000E-01
1.984000E-01
2.047000E-01
2.169000E-01
2.247000E-01
2.282000E-01
2.360000E-01
2.407000E-01
2.432000E-01
2.496000E-01
2.535000E-01
2.560000E-01
2.793000E-01
2.848000E-01
2.986000E-01
3.174000E-01
3.218000E-01
3.549000E-01
3.566000E-01
3.622000E-01
3.683000E-01
3.750000E-01
4.034000E-01
4.062000E-01
4.179000E-01
4.350000E-01
4.501000E-01
4.524000E-01
4.588000E-01
4.624000E-01
4.695000E-01
4.811000E-01
4.926000E-01
5.125000E-01
5.153000E-01
5.179000E-01
5.221000E-01
5.261000E-01
5.297000E-01
5.312001E-01
5.458000E-01
5.520000E-01
5.656000E-01
5.683000E-01
5.710000E-01
5.914000E-01
5.946000E-01
6.010000E-01
6.035000E-01
6.299000E-01
6.371000E-01
6.495000E-01
6.804001E-01
7.806000E-01

1.700000E-04
1.400000E-04
9.400000E-05
1.100000E-04
3.600000E-05
8.899999E-05
4.500000E-03
1.230000E-03
2.300000E-04
3.300000E-04
1.700000E-04
1.100000E-05
2.710000E-03
9.799999E-04
4.000000E-05
1.500000E-05
1.000000E-04
3.000000E-05
1.200000E-04
1.160000E-03
6.000000E-06
2.500000E-04
6.300000E-05
1.800000E-05
1.100000E-06
3.000000E-05
2.300000E-05
2.290000E-06
4.200000E-05
6.000000E-06
1.700000E-05
1.600000E-06
6.699999E-05
4.800000E-05
2.400000E-05
3.200000E-05
8.900000E-04
5.800000E-06
8.000000E-06
2.800000E-05
2.900000E-04
2.200000E-06
5.000000E-06
1.900000E-04
1.500000E-04
1.800000E-05
3.300000E-04
7.100000E-05
4.000000E-05
4.600000E-06
5.600000E-05
1.900000E-06
1.300000E-05
3.200000E-05
7.000000E-06
2.800000E-05
3.700000E-05
1.600000E-05
2.600000E-06
1.000000E-06
1.200000E-05
6.100000E-06
5.000000E-07

AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225

8.242000E-01 4.000000E-07

2
1.270000E-02 1.380000E-01
4.000000E-02 3.000000E-01
3
6.280000E-03 1.410000E-08
6.670000E-03 3.100000E-07
1.275000E-02 3.100000E-03
1.352000E-02 1.550000E-02
2.640000E-02 1.400000E-04

83

1.000000E-02 1.390000E-04
1.170000E-02 2.290000E-01
1.440000E-02 1.670000E-04
3.198000E-02 9.700000E-07
6.950001E-02 7.000000E-05
7.090001E-02 3.500000!
8.106901E-02 1.500000E-01
8.378701E-02 2.470000E-01
9.424701E-02 2.980000E-02
9.486800E-02 5.690000E-02
9.753000E-02 2.140000E-02
1.022000E-01 8.000000E-06
1.032000E-01 6.000000E-05
1.042300E-01 1.900000E-04
1,067800E-01 2.360000E-04
1.085000E-01 6.000000E-05
1.108560E-01 5.800000E-04
1.147000E-01 1.000000E-04
1.223190E-01 1.209000E-02
1.316000E-01 6.000000E-05
1.383000E-01 1.700000E-05
1.442350E-01 3.270000E-02
1.472000E-01 6.000000E-05
1.542080E-01 5.700000E-02
1.586350E-01 6.950000E-03
1.658000E-01 6.000000E-05
1.756500E-01 1.900000E-04
1.773000E-01 4.700000E-04
1.795400E-01 1.530000E-03
1.993000E-01 2.800000E-05
2.213200E-01 3.600000E-04
2.472000E-01 1.000000E-04
2.493000E-01 3.900000E-04
2.516000E-01 4.200000E-04
2.552000E-01 5.300000E-04
2.557000E-01 6.000000E-05
2.604000E-01 7.000000E-05
2.694630E-01 1.390000E-01
2.703000E-01 7.000000E-06
2.860000E-01 1.100000E-05
2.881800E-01 1.600000E-03
3.238710E-01 3.990000E-02
3.283800E-01 2.090000E-03
3.340100E-01 1.010000E-03
3.382820E-01 2.840000E-02
3.428700E-01 2.220000E-03
4.200000E-05
3.557000E-01 2.800000E-05
3.620520E-01 4.600000E-04

38

AC225

RA225
RA225

RA224
RA224
RA224
RA224
RA224

RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223


6.515101E-01
6.601000E-01
6.638200E-01
6.664500E-01
6.720001E-01
6.741600E-01
6.747500E-01
6.771100E-01
6.840000E-01
6.881000E-01
6.925001E-01
6.990800E-01
7.017471E-01
7.074100E-01
7.184800E-01
7.268630E-01
7.377200E-01
7.553151E-01
7.700400E-01
7.72291 1E-01
7.741000E-01
7.765600E-01
7.782300E-01
7.821420E-01
7.914900E-01
7.928000E-01
7.949471E-01
8.137701E-01
8.167101E-01
8.249341E-01
8.304861E-01
8.357100E-01
8.403770E-01
8.531700E-01
8.704601E-01
8.731700E-01
8.744400E-01
8.774601E-01
8.807601E-01
8.873301E-01
9.012300E-01
9.042001E-01
9.112040E-01
9.189700E-01
9.219800E-01
9.240301E-01
9.309300E-01
9.398701E-01
9.441960E-01
9.479820E-01
9.586101E-01
9.647660E-01
9.68971 1E-01
9.759601 E-01
9.794800E-01
9.877 101E-01
9.886301E-01
1.000690E+00
1.013580E+00
1.016440E+00
1.017920E+00
1.019860E+00
1.033248E+00

9.000000E-04
5.000000E-05
2.800000E-04
6.199999E-04
2.600000E-04
5.000000E-04.
5.000000E-04
6.199999E-04
1.900000E-04
1.340000E-03
5.600000E-05
3.700000E-04
1.730000E-03
1.550000E-03
1.900000E-04
6.200000E-03
3.700000E-04
1.000000E-02
6.300000E-05
1.490000E-02
6.000000E-04
1.900000E-04
2.200000E-04
4.850000E-03
2.300000E-04
8.000000E-04
4.250000E-02
7.000000E-05
3.000000E-04
5.000000E-04
5.400000E-03
1.610000E-02
9.100000E-03
3.100000E-05
4.400000E-04
3.100000E-04
4.700000E-04
1.400000E-04
6.200000E-05
2.700000E-04
1.600000E-04
7.699999E-03
2.580000E-01
2.700000E-04
2.940000E-04
7.500000E-05
2.480000E-04
8.999999E-05
9.500000E-04
1.060000E-03
2.800000E-03
4.990000E-02
1.580000E-01
5.000000E-04
2.600000E-04
7.700000E-04
7.700000E-04
5.000000E-05
4,600000E-05
3.800000E-04
5.700000E-05
2.100000E-04
2.010000E-03

AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228

34

1.039650E+00
1.040920E+00
1.053090E+00
1.0541 10E+00
1.062550E+00
1.065180E+00
1.0747 10E+00
1.088180E+00
1.095679E+00
-103410E+00
-110610E+00
117630E+00
135240E+00
142850E+00
-148120E+00
153520E+00
.157140E+00
164500E+00
175310E+00
-190810E+00
1.217030E+00
1.229400E+00
1.245050E+00
1.247080E+00
1.250040E+00
1.276690E+00
1.286270E+00
1.287680E+00
1.3097 10E+00
1.315340E+00
1.344590E+00
1.347500E+00
1.357780E+00
1.365700E+00
1.374190E+00
1.401490E+00
1.415660E+00
1.430950E+00
1.451400E+00
1.459138E+00
1.4697 10E+00
1.495910E+00
1.501570E+00
1.537890E+00
1.548650E+00
1.5571 10E+00
1.559850E+00
1.571520E+00
1.573260E+00
1.580530E+00
1.588200E+00
1.609410E+00
1.625060E+00
1.630627E+00
1.638281E+00
1.666523E+00
1.677670E+00
1.686090E+00
1.700590E+00
1.702430E+00
1.706190E+00
1.713470E+00
1.724210E+00

4.400000E-04
4.400000E-04
1.300000E-04
1.800000E-04
1.000000E-04
1.320000E-03
1.000000E-04
5.900000E-05
1.290000E-03
1.500000E-04
3.040000E-03
5.400000E-04
9.800000E-05
1.030000E-04
5.900000E-05
1.390000E-03
7.000000E-05
6.499999E-04
2.400000E-04
6.200000E-05
2.100000E-04
7.500000E-05
9.500000E-04
5.000000E-03
6.199999E-04
1.400000E-04
5.000000E-04
8.000000E-04
1.900000E-04
1.500000E-04
8.999999E-05
1.500000E-04
2.000000E-04
1.400000E-04
1.400000E-04
1.200000E-04
2.100000E-04
3.500000E-04
1.060000E-04
8.300000E-03
2.000000E-04
8.600000E-03
4.600000E-03
4.700000E-04
3.800000E-04
1.780000E-03
2.000000E-04
5.700000E-05
3.300000E-04
6.000000E-03
3.220000E-02
7.700000E-05
2.550000E-03
1.510000E-02
4.700000E-03
1.780000E-03
5.400000E-04
9.500000E-04
1.010000E-04
4.800000E-04
8.500000E-05
5.400000E-05
2.900000E-04

AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228


8.683001E-02
8.734901E-02
8.978400E-02
1.181600E-01
1.962000E-01
2.056800E-01
2.384000E-01
2.419970E-01
2.588700E-01
2.748000E-01
2.952240E-01
2.987600E-01
3.052600E-01
3.143200E-01
3.238300E-01
3.519320E-01
4.620000E-01
4.804300E-01
4.870900E-01
5.110000E-01
5.336600E-01
5.384100E-01
5.438100E-01
5.801300E-01
7.859601E-01
8.390400E-01

1
7.788000E-01

3
3.238100E-01
5.449001E-01
8.680000E-01

24
1.110000E-02
7.686301E-02
7.929000E-02
8.925600E-02
8.980700E-02
9.231701 E-02
1.476600E-01
2.928000E-01
4.028000E-01
4.404500E-01
5.749000E-01
6.009001E-01
6.049401E-01
6.597500E-01
7.108100E-01
8.073601E-01
8.265201E-01
8.679800E-01
8.866600E-01
1.003550E+00
1,045700E+00
1.100130E+00
1.119290E+00
1.328200E+00

1.280000E-02
2.440000E-02
9.000000E-03
9.399999E-04
6.900000E-04
1.150000E-04
8.000001E-05
7.430000E-02
5.240000E-03
4.740000E-03
1.930000E-01
1.000000E-04
3.100000E-04
7.800000E-04
2.800000E-04
3.760000E-01
2.210000E-03
3.200000E-03
4.220000E-03
3.200000E-04
1.860000E-03
2.000000E-04
6.900000E-04
3.520000E-03
1.070000E-02
5.870000E-03

4.800000E-05

1.650000E-03
1.650000E-04
1.270000E-04

1.540000E-02
1.080000E-02
1.790000E-02
2.170000E-03
4.160000E-03
1.540000E-03
1.500000E-04
4.290000E-03
1.000000E-06
2.594000E-01
2.500000E-05
4.200000E-05
2.300000E-05
3.610000E-04
1.110000E-04
2.920000E-03
7.100000E-05
1.110000E-04
1.020000E-05
5.300000E-04
1.800000E-04
2.590000E-03
5.200000E-04
4.000000E-06

PB214
PB214
PB214
PB214
PB214
PB214
PB214
PB214
PB214
PB214
PB214
PB214
PB214
PB214
PB214
PB214
PB214
PB214
PB214
PB214
PB214
PB214
PB214
PB214
PB214
PB214

PO213

BI213A
BI213A
BI213A

BI213B
BI213B
BI213B
BI213B
BI213B
BI213B
BI213B
BI213B
BI213B
BI213B
BI213B
BI213B
BI213B
BI213B
BI213B
BI213B
BI213B
BI213B
BI213B
BI213B
BI213B
BI213B
BI213B
BI213B

43

15
1.030000E-02
3.985700E-02
7.083201E-02
7.287300E-02
8.21 1500E-02
8.257400E-02
8.486500E-02
2.882000E-01
3.280300E-01
4.337000E-01
4.529800E-01
4.730000E-01
4.933000E-01
5.760000E-01
6.200000E-01

18
1.110000E-02
7.686301E-02
7.929000E-02
8.925600E-02
8.980700E-02
9.231701E-02
1.802000E-01
7.273300E-01
7.853701E-01
8.934081E-01
9.521201E-01
1.073600E+00
1.078620E+00
1.512700E+00
1.620500E+00
1.679700E+00
1.800200E+00
1.806000E+00

11
1.080000E-02
7.481501E-02
7.710700E-02
8.683001E-02
8.734901E-02
8.978400E-02
1.151830E-01
1.766800E-01
2.386320E-01
3.000870E-01
4.152000E-01

9
1.060000E-02
7.280500E-02
7.496901 E-02
8.445000E-02
8.493800E-02
8.730001E-02
3.282000E-01
5.696501 E-01
8.978000E-01

7.000000E-02
1.060000E-02
5.400000E-04
9.050000E-04
1.090000E-04
2.090000E-04
7.620000E-05
3.370000E-03
1.250000E-03
1.700000E-04
3.630000E-03
5.000000E-04
1.800000E-05
1.800000E-06
5.000000E-06

5.750000E-04
3.930000E-04
6.550000E-04
7.910000E-05
1.520000E-04
5.610000E-05
3.200000E-05
6.670000E-02
1.102000E-02
3.780000E-03
1.700000E-03
1.600000E-04
5.640000E-03
2.900000E-03
1.470000E-02
5.800000E-04
4.100000E-05
9.000000E-04

1.430000E-01
1.028000E-01
1.710000E-01
2.070000E-02
3.970000E-02
1.460000E-02
5.960000E-03
5.200000E-04
4.360000E-01
3.300000E-02
1.310000E-04

8.100000E-05
5.780000E-05
9.600000E-05
1.170000E-05
2.230000E-05
8.200000E-06
3.300000E-05
5.450000E-03
5.610000E-03

BI212A
BI212A
BI212A
BI212A
BI212A
BI212A
BI212A
BI212A
BI212A
BI212A
BI212A
BI212A
BI212A
BI212A
BI212A

BI212B
BI212B
BI212B
BI212B
BI212B
BI212B
BI212B
BI212B
BI212B
BI212B
BI212B
BI212B
BI212B
BI212B
BI212B
BI212B
BI212B
BI212B

PB212
PB212
PB212
PB212
PB212
PB212
PB212
PB212
PB212
PB212
PB212

PO211
PO211
PO211
PO211
PO211
PO211
PO211
PO211
PO211


Table 3. Fluence from photons of energy £ at 1 m in air for the U and Pu spheres. Given are
the fluence of the unscattered emergent source photons, ®,(£), the associated fluence of
emergent annihilation quanta, ®p.2(0.511 MeV), and the fluences of emergent K-shell
characteristic x rays, ®xgi(Expi), Pxa(Ekai), and Pxa2(Eka2). The fluences are given in units of
cm”, normalized to one source photon emitted uniformly and isotropically in the sphere.

a. U sphere. The energies of the x-ray lines are: Exgi=0.11130 MeV,
Exai=0.09844 MeV, and Ex.2=0.09466 MeV.

E/MeV PDJ/omTM | Pmeo/emTM | Pxgi/emTM | Pxa/emTM | Pxe2/emTM
3.5 2.71E-06 2.87E-07 5.11E-09 8.02E-09 4.34E-09
3.0 2.69E-06 2.35E-07 4.92E-09 7.62E-09 4.19E-09
2.5 2.64E-06 1.75E-07 4.79E-09 TATE-09 4.02E-09
2.0 2.52E-06 1.05E-07 4.67E-09 7.03E-09 3.89E-09
1.5 2.27E-06 3.18E-08 4.76E-09 7.26E-09 4.02E-09
1.0 1.70E-06 0 5.60E-09 8.69E-09 4.81E-09
0.8 1.36E-06 0 6.30E-09 9.67E-09 5.25E-09
0.6 9.50E-07 0 7T.A0E-09 1.09E-08 6.12E-09
0.5 7.20E-07 0 7.88E-09 1.19E-08 6.69E-09
0.4 4.92E-07 0 8.33E-09 1.28E-08 7.25E-09
0.3 2.75E-07 0 9.55E-09 1.44E-08 8.17E-09
0.2 1.09E-07 0 1.12E-08 1.69E-08 9,.51E-09
0.15 5.39E-08 0 1.21E-08 1.85E-08 1.04E-08
0.116 2.83E-08 0 1.22E-08 1.95E-08 1.10E-08
0.115 1.10E-07 0 0 0 0
0.1 7.81E-08 0 0 0 0
0.08 5.70E-09 0 0 0 0
0.06 1.35E-09 0 0 0 0
0.05 5.25E-10 0 0 0 0
0.04 1.68E-10 0 0 0 0
0.03 3.78E-11 0 0 0 0

11


Acknowledgements

The author is grateful to Michael Unterweger and Ronald Collé for frequent guidance
on the radioactive decay calculations, and to Craig Heimbach who pointed out significant errors
in the previous version of this report. This work was supported in part by an Interagency
Agreement with the Domestic Nuclear Detection Office of the Department of Homeland
Security, IAA HSHQDC-08-X-00277.

References

Bateman, H. (1910). “The solution of a system of differential equations occurring in the theory
of radioactive transformations,” Proc. Cambridge Phil. Soc., 15, 423-427.

Berger, M.J., and Hubbell, J.H. (1987). XCOM: Photon Cross Sections on a Personal
Computer, Report NBSIR 87-3597, National Bureau of Standards, Gaithersburg, MD.

Coursey, J.S., Schwab, D.J., and Dragoset, R.A. (2005). Atomic Weights and Isotopic
Compositions (version 2.4.1). [Online] Available: http://physics.nist.gov/Comp [2008,
April]. National Institute of Standards and Technology, Gaithersburg, MD.

Fetter S., Frolov, V.A., Prilutsky, O.F., and Sagdeev, R.Z. (1990). “Fissile Materials and
Weapon Design,” Appendix A in Science & Global Security, Vol. 1, pp. 225-302,
Gordon and Breach Science Publishers.

Halbleib, J.A., Kensek, R.P., Mehlhorn, T.A., Valdez, G.D., Seltzer, S.M., and Berger, M.J.
(1992). ITS Version 3.0: The Integrated TIGER Series of Coupled Electron/Photon
Monte Carlo Transport Codes, Report SAND91-1634, Sandia National Laboratories,
Albuquerque, NM.

Hollas, C.L., Goulding, C., and Myers, W. (2005). “Determination of neutron multiplication of
subcritical HEU systems using delayed neutrons,” Nucl. Inst. and Meth. A, 543, 559-
569.

Larsson, C.L., and Haslip, D.S. (2004). Consolidated Canadian Results to the HEU Roaund
Robin Exercise, Technical Memorandum 2004-192, Defence Research and
Development Canada, Ottawa, Canada.

Nguyen, C.T., and Zsigrai, J. (2006). « Basic characterization of highly enriched unranium by
gamma spectrometry,” Nucl. Inst. and Meth. B, 246, 417-424.

Phillips, G.W., Nagel, D.J., and Coffey, T. (2005). A Primer on the Detection of Nuclear and
Radiological Weapons, Defense & Technology Paper, National Defense University
Center for Technology and National Security Policy, Fort Lesley J. McNair,
Washington, DC.

Sapr, J.L., Kidman, R, and Brewer, R.W., ?U(94 %) Spheres Surrounded bu Natural-Uranium
Reflectors, Report LA-UR-98-1664 of the Los Alamos National Laboratory, Los

21


3.629000E-01
3.685600E-01
3.716760E-01
3.729000E-01
3.761000E-01
3.828000E-01
3.877000E-01
3.901000E-01
4.306000E-01
4.321200E-01
4.450330E-01
4.875000E-01
5.000000E-01
5.100001 E-01
5.27611 1E-01
5.376000E-01
5.420001E-01
5.458000E-01
5.741000E-01
5.796000E-01
5.843000E-01
5.940000E-01
5.9872 10E-01
6.093100E-01
6.191000E-01
6.235000E-01
6.317000E-01
6.417000E-01
6.461000E-01
6.969001 E-01
7.113000E-01
7.184001 E-01
7.284001E-01
7.328000E-01

129
1.230000E-02
2.027000E-02
2.960000E-02
2.978000E-02
3.169000E-02
4.350000E-02
4.400000E-02
4.980000E-02
5.009400E-02
6.143000E-02
6.231000E-02
7.350000E-02
7.965101E-02
8.543100E-02
8.847100E-02
8.908001E-02
9.388001E-02
9.943201 E-02
1.001300E-01
1.024980E-01
1.110500E-01
1.345900E-01
1.555000E-01
1.733800E-01
1.846800E-01
2.007000E-01
2.049000E-01

1.500000E-04
8.000001E-05
4.870000E-03
5.000000E-04
1.300000E-04
1.400000E-04
1.500000E-04
7.000000E-05
1.900000E-04
3.500000E-04
1.290000E-02
1.110000E-04
1.400000E-05
4.000000E-06
7.100000E-04
2.090000E-05
1.400000E-05
1.100000E-05
1.100000E-05
1.400000E-05
1.400000E-05
1.400000E-05
9.500000E-04
5.700000E-04
3.500000E-05
8.000001E-05
4.000000E-06
1.700000E-05
4.000000E-06
7.000000E-06
3.600000E-05
1.400000E-05
2.800000E-06
2.800000E-06

2.700000E-01
1.600000E-02
2.400000E-04
5.400000E-04
1.500000E-05
2.400000E-05
1.500000E-05
2.800000E-02
3.400000E-01
3.900000E-05
1.800000E-04
1.500000E-05
8.700000E-02
1.630000E-02
2.700000E-02
6.000000E-04
6.600000E-04
3.200000E-03
6.200000E-03
2.300000E-03
5.400000E-05
5.299999E-03
3.000000E-05
1.200000E-03
2.500000E-03
3.000000E-05
9.800000E-03

RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223
RA223

FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223

39

2.056000E-01
2.106000E-01
2.188000E-01
2.347500E-01
2.360500E-01
2.456000E-01
2.502400E-01
2.546000E-01
2.561700E-01
2.629000E-01
2.728000E-01
2.807000E-01
2.860000E-01
2.896800E-01
2.965000E-01
2.999500E-01
3.044000E-01
3.077800E-01
3.126500E-01
3.146000E-01
3.192600E-01
3.298000E-01
3.343000E-01
3.395000E-01
3.425000E-01
3.505000E-01
3.693800E-01
4.344000E-01
4.396000E-01
4.445000E-01
4.529000E-01
4.575000E-01
4.693000E-01
4.754000E-01
4.809000E-01
4.934000E-01
5.069000E-01
5.167000E-01
5.248000E-01
5.331000E-01
5.372000E-01
5.398000E-01
5.454000E-01
5.523000E-01
5.563000E-01
5.689400E-01
5.761000E-01
5.813000E-01
5.923000E-01
5.969000E-01
6.007000E-01
6.076000E-01
6.136000E-01
6.327000E-01
6.637000E-01
6.719000E-01
7.083000E-01
7.231000E-01
7.241501E-01
7.374001E-01
7.424001E-01
7.463000E-01
7.536501E-01

6.600000E-05
1.080000E-04
9.600000E-05
3.000000E-02
3.000000E-04
2.900000E-04
2.030000E-04
6.300000E-05
3.000000E-04
3.900000E-05
4.500000E-05
1.200000E-05
1.000000E-04
3.000000E-04
1.500000E-05
2.100000E-04
1.500000E-04
1.480000E-04
1.700000E-04
2.400000E-05
4.900000E-03
2.700000E-04
1.100000E-04
6.700000E-04
2.000000E-04
3.000000E-05
9.900000E-04
2.400000E-05
3.300000E-06
1.200000E-05
1.800000E-05
8.999999E-06
2.400000E-05
6.300000E-05
1.500000E-05
2.700000E-05
2.400000E-05
3.600000E-05
4.800000E-05
2.100000E-05
5.700000E-05
6.600000E-05
3.300000E-06
3.000000E-05
1.200000E-05
5.500000E-04
1.200000E-05
1.500000E-05
3.600000E-05
8.999999E-06
6.000000E-06
2.400000E-05
1.200000E-05
2.400000E-05
1.200000E-05
6.000000E-06
1.500000E-05
4.400000E-04
1.600000E-04
1.000000E-05
1.200000E-05
2.200000E-04
1.000000E-04

FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223


Table 1. Assumed initial parameters for the spheres.

U sphere Pu sphere
Mass density 18.95 g/em* 19.84 g/em®
Radius 2.327 cm 1.819 cm
Composition (mass fraction): 0.7% *U 0.05 % “"Pu

93.5% U_| 93.57% Pu
5.8 % *U 6.00 % Pu
0.29 % "Pu
0.02 % "Pu
0.11% *TAm

The compositions given in Table 1 were adopted based on best estimates suggested by a
number of unclassified documents (see, e.g., Stefaka et al., 2008; Valkovic, 2006; Nguyen and
Zsigrai, 2006; Hollas et al., 2005; Phillips et al., 2005; Larsson and Haslip, 2004; Fetter et al.,
1990).

The calculations were carried out in stages. First, decay data for the radionuclides
involved were assembled from the on-line databases of the Brookhaven National Nuclear Data
Center (NuDat 2.4, http://www.nnde.bni.gov/nudat2/indx_dec.jsp, accessed March-April,
2008). Ina very few cases of questionable, very minor, gamma-ray line energies and
intensities, the Lawrence Berkeley National Laboratory on-line Table of Isotopes
(http://ie. Ib]. gov/education/isotopes.htm, accessed April 2008) was consulted to help make a
decision.

The relevant assumed decay-chain data, including the symbol of the radionuclide, its
half-life, and its branching fractions, are depicted in Figs. 1a to 1d. For decay calculations it
was decided to ignore any branching whose fraction was less than 1 %, mainly to simplify the
decay-chain activity calculations. We assume that little important relevant information has
been sacrificed by this simplification; the neglected radionuclides are indicated with a dashed
box in Fig. 1. Shown in the cutout in Fig. 1a is the branching decay of *“"Pa (half life of 1.159
min), which decays by beta emission (99.84 %) to *“U and by isomeric transition (0.16 %) to
°4a (half life 6.70 h) that then decays by beta emission (100 %) to *“U. According to the
adopted procedure, the decay of "Pa to>“U through the isomeric transition to 234) has been
ignored.

The data used in the calculations for the emission spectra of photons with energies
above | keV for the radionuclides of interest are listed in Appendix A.


8.995000E-02
9.228200E-02
9.302000E-02
9.586301 E-02
9.927800E-02
1.022700E-01
1.058100E-01
1.066100E-01
1.075950E-01
1.084220E-01
1.114860E-01
1.156300E-01
1.168200E-01
1.249140E-01
1.340300E-01
1.356640E-01
1.367500E-01
1.405400E-01
1.450600E-01
1.459400E-01
1.631010E-01
1.650000E-01
1.696600E-01
1.741500E-01
1.835000E-01
1.887600E-01
2.179400E-01
2.360100E-01
2.402700E-01
2.425000E-01
2.496000E-01
2.504500E-01
2.676200E-01
2.741000E-01
3.087800E-01
3.110000E-01
3.178700E-01
3.201500E-01
3.518000E-01

18
1.230000E-02
6.767200E-02
8.543100E-02
8.847100E-02
9.943201 E-02
1.001300E-01
1.024980E-01
1.100000E-01
1.248000E-01
1.438720E-01
1.860530E-01
2.051000E-01
2.350000E-01
2.537290E-01
2.538000E-01
5.518000E-01
5.705000E-01
6.200000E-01

82
1.230000E-02
1.736000E-02

1.000000E-02
3.700000E-03
4.700000E-04
6.000000E-03
1.310000E-03
4.360000E-03
7.800000E-05
1.760000E-04
7.500000E-04
1.430000E-03
5.500000E-04
1.060000E-05
2.220000E-04
5.800000E-04
2.500000E-04
7.900000E-04
4.400000E-05
7.300000E-06
5.700000E-05
3.170000E-04
1.540000E-03
3.430000E-05
1.320000E-05
1.780000E-04
3.300000E-04
3.300000E-05
3.960000E-04
9.200000E-05
2.900000E-06
8.300000E-06
7.900000E-06
6.600000E-06
1.250000E-05
3.400000E-07
3.600000E-06
3.100000E-05
9.600000E-07
1.500000E-06
6.600000E-07

7.700000E-02
3.800000E-03
4.200000E-05
6.800000E-05
8.300000E-06
1.590000E-05
6.000000E-06
6.000000E-07
2.800000E-09
4.899999E-04
8.800000E-05
5.200000E-08
8.400000E-08
1.110000E-04
8.500000E-06
5.500000E-09
3.300000E-08
8.000000E-09

7.300000E-01
1.800000E-03

TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231

TH230
TH230
TH230
TH230
TH230
TH230
TH230
TH230
TH230
TH230
TH230
TH230
TH230
TH230
TH230
TH230
TH230
TH230

TH229
TH229

32

2.360000E-02
2.539000E-02
3.030000E-02
3.110000E-02
3.150000E-02
3.157000E-02
3.780000E-02
4.230000E-02
4.282000E-02
4.399000E-02
4.975000E-02
5.099000E-02
5.375000E-02
5.511000E-02
5.651800E-02
6.370001 E-02
6.809000E-02
6.883001 E-02
7.509000E-02
7.763000E-02
7.830001E-02
8.543100E-02
8.625001E-02
8.640000E-02
8.847100E-02
9.473000E-02
9.492000E-02
9.943201E-02
1.001300E-01
1.011000E-01
1.024980E-01
1.046000E-01
1.071080E-01
1.092000E-01
1.103320E-01
1.153000E-01
1.159800E-01
1.179900E-01
1.199800E-01
1.231930E-01
1.245500E-01
1.246500E-01
1.264000E-01
1.265000E-01
1.319260E-01
1.342000E-01
1.369900E-01
1.420000E-01
1.429620E-01
1.476400E-01
1.481500E-01
1.500400E-01
1.516000E-01
1.543360E-01
1.564090E-01
1.584200E-01
1.633400E-01
1.669760E-01
1.674500E-01
1.717500E-01
1.729260E-01
1.742200E-01
1.748200E-01

1.230000E-05
8.000001E-05
2.100000E-04
8.400000E-03
1.190000E-02
6.800000E-04
3.300000E-05
8.200000E-04
1.640000E-03
6.600000E-03
2.150000E-04
1.700000E-04
1, 100000E-04
2.700000E-05
2.870000E-03
5.100000E-05
6.900000E-04
1,360000E-03
6.100000E-03
4,500000E-04
8.200000E-05
1.470000E-01
1.330000E-02
2.570000E-02
2.400000E-01
2.670000E-03
1,300000E-04
2.930000E-02
5.610000E-02
1.800000E-04
2.120000E-02
8.999999E-05
8.100000E-03
4,400000E-04
1.240000E-03
2.800000E-04
1.700000E-04
1.300000E-04
5.100000E-04
1.510000E-03
6.900000E-03
7.400000E-03
2.100000E-04
1.100000E-04
3.360000E-03
1.050000E-04
1.180000E-02
1.100000E-04
4.040000E-03
2.050000E-03
8.800000E-03
3.000000E-04
2.600000E-04
7.699999E-03
1.190000E-02
4.800000E-04
2.100000E-04
2.050000E-03
5.100000E-04
2.100000E-04
1.130000E-03
1.800000E-04
1.500000E-04

TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229


Table 4. Fluence rate from unscattered photons of energy £ at | m in air for the U and
Pu spheres.

b. “Pu (6.0 %) 0.5 kg sphere of age 50 y; fluence rates greater than 107 cm? s!. Total
fluence rate for all 2490 lines calculated is 211 em? s".

E/MeV. @ Icm” s' | Nuclide E/MeV_| @/cm?s" | Nuclide
5.954E-02 | _1.311E+02 | AM241 3.354E-01 | 4.388E-01 | AM241
4.137E-01 | 9.378E+00 | PU239 LOLIE-01 | 3.792E-01 | AM241
3.751E-01 | 8.272E+00 | PU239 3.119E-01 | _3.767E-O1 | PA233
9.843E-02 | 4.765E+00 | PU239 1.253E-01 | 3.589E-01 | AM241
1.030E-01 |_4.576E+00 | AM241 3.415E-01 | 2.921E-01 | PU239
1.037E-01 |_3.736E+00 | Pu Kal 1.031E-01 | 2.446E-01 | PU239
9.897E-02 | 3.634E+00 | AM241 2.080E-01 | 2.403E-01 | AM241
1.293E-01 | _2.882E+00 | PU239 3.687E-01 | 2.324E-01 | AM241
3.450E-01 | 2.505E+00 | PU239 5.162E-02 | 2.293E-01 | PU239
1.172E-01 | 2.423E+00 | Pu KB1 3.238E-01 | 2.130E-01 | PU239
9.953E-02 | _2.102E+00 | Pu Ka2 3.209E-01 | 2.100E-01 | PU239
3.328E-01 | 2.067E+00 | PU239 6.459E-01 1.970E-01 | PU239
3.931E-01 | 2.038E+00 | PU239 9.843E-02 | _1.883E-01 | PU241A
9.465E-02 | _2.007E+00 | PU239 2.554E-01 1.880E-01 | PU239
1.042E-01 | 1.999E+00 | PU240 9.707E-02 |_1.715E-01 | AM241
1.113E-01 | 1.980E+00 | PU239 1.442E-01 | _1.693E-01 | PU239
3.802E-01 1.667E+00 | PU239 2.975E-01 1.641E-01 | PU239
3.828E-01 | 1.434E+00 | PU239 4.267E-01 |__1.575E-01 | PU239
4.515E-01 1.412E+00 | PU239 3.767E-01 1.541E-01 | AM241
9.878E-02 | 1.244E+00 | PU239 6.190E-01 | 1.510E-01 | AM241
3.925E-01 | _1.190E+00 | PU239 3.450E-01 | 1.352E-01 | PU239
1,104E-01 | 1.028E+00 | PU239 1.957E-01 1.350E-01 | PU239
6.624E-01 | 1.015E+00 | AM241 9.985E-02 |__1.340E-01 | PU238
1.163E-01 8.483E-01 | PU239 1.142E-01 1.328E-01 | AM241
4.226E-01 8.107E-01 | PU239 3.324E-01 | 1.294E-01 | AM241
2.036E-01 7.889E-01 | PU239 6.589E-01 | 1.291E-O1 | PU239
1.144E-01 7.873E-01 | PU239 3,.225E-01 1.239E-01 | AM241
1.154E-01 6.863E-01 | PU239 6.400E-01 | 1.113E-01 | PU239
7.220E-01 6.100E-01 | AM241 7.694E-01 | _1.096E-01 | PU239
3.361E-01 4.783E-01 | PU239 6.530E-01 | 1.032E-01 | AM241
3.671E-01 4.542E-01 | PU239 1.714E-01 | 1.007E-01 | PU239
3.686E-01 4.527E-01 | PU239

18


6.887200E-01 3.250000E-07
6.966000E-01 5.340000E-08
7.220100E-01 1.960000E-06
7.297200E-01 1,330000E-08
7.373400E-01 8.000000E-08
7.559001E-01 7.600000E-08
7.670000E-01 5.000000E-08
7.705700E-01 4.740000E-08
7.724001E-01 2.660000E-08
7.860000E-01 6.200000E-09
8.019400E-01 1.360000E-08
8.062600E-01 3.100000E-09
8.285000E-01 2.400000E-09
8.607001E-01 8.000000E-10
8.627000E-01 5.300000E-09
8.873000E-01 2.200000E-09
9.215000E-01 1.900000E-09

19

1.360000E-02 1.250000E-05
2.670000E-02 1.000000E-06
4.420000E-02 4.165000E-08
4.486000E-02 8.330000E-09
5.632000E-02 2.499000E-08
5.676000E-02 9.800000E-09
7.160001E-02 2.870000E-08
7.710000E-02 2.060000E-07
9.465400E-02 3.120000E-06
9.843400E-02 4.990000E-06
1.010000E-01 7.100000E-10
1.036800E-01 1.012000E-06
1.104210E-01 6.250000E-07
1.112980E-01 1.180000E-06
1.140000E-01 8.100000E-07
1.144450E-01 4.590000E-07
1.212000E-01 6,860000E-09
1.485670E-01 1.860000E-06
1.599550E-01 6.539999E-08

18

1.360000E-02 9.600000E-02
4.524400E-02 4.470000E-04
9.465400E-02 2.540000E-07
9.843400E-02 4.050000E-07
1.042340E-01 7.140000E-05
1.104210E-01 5.080000E-08
1.112980E-01 9.600000E-08
1.144450E-01 3.730000E-08
1.603080E-01 4.020000E-06
2.124600E-01 2.900000E-07
5.380901E-01 1.470000E-09
6.423500E-01 1.300000E-07
6.875700E-01 3.500000E-08
6.990001E-01 1.300000E-10
8.739200E-01 5.800000E-09
9.580001E-01 5.000000E-10
9.600000E-01 3.000000E-10
9.670001E-01 3.000000E-10

174

1.297500E-02 3.410000E-04
1.360000E-02 4.380000E-02
3.004000E-02 2.170000E-06

AM241
AM241
AM241
AM241
AM241
AM241
AM241
AM241
AM241
AM241
AM241
AM241
AM241
AM241
AM241
AM241
AM241

PU241A
PU241A
PU241A
PU241A
PU241A
PU241A
PU241A
PU241A
PU241A
PU241A
PU241A
PU241A
PU241A
PU241A
PU241A
PU241A
PU241A
PU241A
PU241A

PU240
PU240
PU240
PU240
PU240
PU240
PU240
PU240
PU240
PU240
PU240
PU240
PU240
PU240
PU240
PU240
PU240
PU240

PU239
PU239
PU239

24

3.866100E-02
4.193000E-02
4.621000E-02
4.668000E-02
4.760000E-02
5.162400E-02
5.403901 E-02
5.682800E-02
6.570800E-02
6.767400E-02
6.869600E-02
6.874000E-02
7.759201E-02
7.843000E-02
8.964001E-02
9.465400E-02
9.614000E-02
9.760001E-02
9.843400E-02
9.878001 E-02
1.030600E-01
1.104210E-01
1.112980E-01
1.144450E-01
1.153800E-01
1.162600E-01
1.197000E-01
1.223500E-01
1.232280E-01
1.236200E-01
1.245100E-01
1.252100E-01
1.292960E-01
1.416570E-01
1.433500E-01
1.442010E-01
1.460940E-01
1.581000E-01
1.601900E-01
1.614500E-01
1.678100E-01
1.713930E-01
1.725600E-01
1.737000E-01
1.792200E-01
1.882300E-01
1.893600E-01
1.956790E-01
2.035500E-01
2.180000E-01
2.254200E-01

-420800E-01
2.433800E-01
2.449200E-01
2.489500E-01
2.553840E-01
2.639500E-01

2.657000E-01
2.812000E-01
2.853000E-01
2.974600E-01
3.028700E-01

1.044000E-04
1.460000E-06
7.210000E-07
4.650000E-07
6.250000E-07
2.722000E-04
1.944000E-06
1.152000E-05
5.200000E-07
1.517000E-06
3.600000E-06
1.300000E-06
3.800000E-06
1.542000E-06
2.700000E-07
3.600000E-05
3.790000E-07
8.000000E-07
5.800000E-05
1.470000E-05
2.160000E-06
7.200000E-06
1.370000E-05
5.300000E-06
4.600000E-06
5.670000E-06
2.100000E-07
9.500000E-09
1.600000E-11
2.370000E-07
6.810000E-07
5.630000E-07
6.310000E-05
3.200000E-07
1.730000E-07
2.830000E-06
1.190000E-06
1.000000E-08
6.200000E-08
1.230000E-06
2.900000E-08
1.100000E-06
3.000000E-11
3.100000E-08
6.600000E-07
1.090000E-07
8.300000E-07
1.070000E-06
5.690000E-06
1.200000E-08
1.510000E-07
1.440000E-07
7.300000E-08
2.530000E-07
5.100000E-08
7.200000E-08
8.000000E-07
2.650000E-07
1.600000E-08
2.100000E-08
1.900000E-08
4.980000E-07
5.100000E-08

PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239
PU239


Table 4. Fluence rate from uscattered photons of energy E at | m in air for the U and Pu
spheres.

d. Pu (6.0 %) 0.5 kg sphere of age 10 y; fluence rates greater than 107 cm? s!. Total
fluence rate for all 2490 lines calculated is 159 em? s".

E/MeV__| @/cm?s" | Nuclide E/MeV_| @/cm?s" | Nuclide
5.954E-02 8.151E+01 | AM241 3.671E-01 4.547E-01 | PU239
4.137E-01 | _9.389E+00 | PU239 3.686E-01 | 4.532E-01 | PU239
3.751E-01 | 8.281E+00 | PU239 1.140E-01 | 3.837E-O1 | PU241A
9.843E-02 | _4.770E+00 | PU239 1.486E-01 3.829E-01 | PU241A
1.037E-01 | 3.684E+00 | Pu Kal 7.220E-01 | 3.793E-01 | AM241
1.293E-01 2.886E+00 | PU239 1.037E-01 3.778E-01 | PU241A
1.030E-01 | 2.845E+00 | AM241 3.415E-01 | 2.925E-01 | PU239
3.450E-01 | 2.508E+00 | PU239 1.104E-01 | 2.852E-01 | PU241A
1.172E-01 2.389E+00 | Pu KB1 3.354E-01 2.728E-01 | AM241
9.897E-02 | 2.260E+00 | AM241 1.031E-01 | 2.449E-01 | PU239
9.953E-02 | 2.073E+00 | Pu Ka2 1.011E-01 2.357E-01 | AM241
3.328E-01 | 2.070E+00 | PU239 5.162E-02 | _2.295E-01 | PU239
3.931E-01 | 2.041E+00 | PU239 1.253E-01 | 2.231E-01 | AM241
9.465E-02 | _2.009E+00 | PU239 1.144E-01 2.180E-01 | PU241A
1.042E-01 | 2.008E+00 | PU240 3.238E-01 | 2.132E-01 | PU239
1.113E-01 1.982E+00 | PU239 3.209E-01 | 2.103E-01 | PU239
3.802E-01 1.669E+00 | PU239 6.459E-01 1.972E-01 | PU239
3.828E-01 1.435E+00 | PU239 2.554E-01 1.882E-01 | PU239
4.515E-01 1.413E+00 | PU239 9.985E-02 1.838E-01 | PU238
9.843E-02 | 1.311E+00 | PU241A 1.442E-01 1.695E-01 | PU239
9.878E-02 | 1.246E+00 | PU239 2.975E-01 1.643E-01 | PU239
3.925E-01 1.192E+00 | PU239 4.267E-01 1.577E-01 | PU239
1.104E-01 1.029E+00 | PU239 2.080E-01 1.494E-01 | AM241
1.163E-01 8.493E-01 | PU239 3.687E-01 1.445E-01 | AM241
4.226E-01 8.116E-01 | PU239 3.450E-01 1.353E-01 | PU239
2.036E-01 7.898E-01 | PU239 1.957E-01 1.352E-01 | PU239
1.144E-01 7.882E-01 | PU239 6.589E-01 1.292E-01 | PU239
1.154E-01 6.871E-01 | PU239 6.400E-01 L.LIS5E-01 | PU239
6.624E-01 6.313E-01 | AM241 7.694E-01 1.097E-01 | PU239
9. A65E-02 5.561E-01 | PU241A 9.707E-02 1.066E-01 | AM241
1.113E-01 S5.A51E-01 | PU241A 1.714E-01 1.008E-01 | PU239
3.361E-01 4.788E-01 | PU239

20


1.797570E-01
1.839280E-01
1.935090E-01
1.943000E-01
2.008070E-01
2.046900E-01
2.101500E-01
2.108530E-01
2.151000E-01
2.181540E-01
2. '200E-01
2.251490E-01
2.362490E-01
2.424000E-01
2.524300E-01
2.590800E-01
2.962000E-01

20
1.230000E-02
7.440001E-02
8.437300E-02
8.543100E-02
8.847100E-02
9.943201 E-02
1.001300E-01
1.024980E-01
1.316130E-01
1.420000E-01
1.664100E-01
1.822000E-01
2.059300E-01
2.159830E-01
2.285000E-01
7.005000E-01
7.422001E-01
8.320000E-01
9.081000E-01
9.929001E-01

239

1.300000E-02
1.840000E-02
4.246000E-02
5.776600E-02
7.734000E-02
8.995701E-02
9.335000E-02
9.950901 E-02
1.0041 00E-01
1.048190E-01
1.056040E-01
1.085820E-01
1.145600E-01
1.290650E-01
1.355400E-01
1.410200E-01
1.458490E-01
1.539770E-01
1.686500E-01
1.739640E-01
1.845400E-01
1.913530E-01

1.970000E-03
1.420000E-03
4.410000E-02
3.100000E-04
6.900000E-04
6.000000E-03
1.900000E-03
2.800000E-02
1.370000E-03
1.850000E-03
2.300000E-04
7.200000E-04
1.740000E-03
9.399999E-04
9.500000E-04
3.400000E-04
1.200000E-04

8.800000E-02
4.000000E-06
1.220000E-02
1.850000E-04
3.020000E-04
3.690000E-05
7.060000E-05
2.670000E-05
1.305000E-03
1.300000E-08
1.036000E-03
5.200000E-08
1.960000E-04
2.540000E-03
1.800000E-07
3.100000E-08
1.500000E-08
1.460000E-07
1.710000E-08
1.460000E-08

3.370000E-01
1.400000E-04
8.999999E-05
4.700000E-03
2.600000E-04
1.900000E-02
3.100000E-02
1.260000E-02
9.300000E-04
3.800000E-03
7.200000E-03
2.800000E-03
9.800000E-05
2.420000E-02
1.800000E-04
5.000000E-04
1.580000E-03
7.220000E-03
1.300000E-04
3.500000E-04
7.000000E-04
1.230000E-03

TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229
TH229

TH228
TH228
TH228
TH228
TH228
TH228
TH228
TH228
TH228
TH228
TH228
TH228
TH228
TH228
TH228
TH228
TH228
TH228
TH228
TH228

AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228

33

1.994070E-01
2.040260E-01
2.092530E-01
2.148500E-01
2.238500E-01
2.314200E-01
2.575200E-01
2.635800E-01
2.702450E-01
2.789500E-01
2.820000E-01
3.216460E-01
3.260400E-01
3.274400E-01
3.280000E-01
3.323700E-01
3.383200E-01
3.409600E-01
3.569400E-01
3.725700E-01
3.779900E-01
3.846300E-01
3.891200E-01
3.979400E-01
3.996200E-01
4.094620E-01
4.163000E-01
4.194200E-01
4.404400E-01
4.491500E-01
4.524700E-01
4.571 700E-01
4.630040E-01
4.702500E-01
4.717600E-01
4.747500E-01
4.783300E-01
4.809400E-01
4.903300E-01
4.923700E-01
4.974900E-01
5.038230E-01
5.089591E-01
5.150600E-01
5.201510E-01
5.231310E-01
5.407600E-01
5.464700E-01
5.487300E-01
5.551201E-01
5.625000E-01
5.709100E-01
5.721400E-01
5.834100E-01
5.904000E-01
6.106400E-01
6.162200E-01
6.203800E-01
6.232700E-01
6.272300E-01
6.294001E-01
6.403400E-01
6.488401E-01

3.150000E-03
1.120000E-03
3.890000E-02
2.900000E-04
5.400000E-04
2.500000E-04
3.000000E-04
4.000000E-04
3.460000E-02
1.910000E-03
7.200000E-04
2.260000E-03
3.300000E-04
1.200000E-03
2.950000E-02
4.000000E-03
1.127000E-01
3.690000E-03
1.700000E-04
6.699999E-05
2.500000E-04
6.699999E-05
1.030000E-04
2.700000E-04
2.900000E-04
1.920000E-02
1.320000E-04
2.100000E-04
1.210000E-03
4.800000E-04
1.500000E-04
1.500000E-04
4.400000E-02
1.300000E-04
3.300000E-04
2.200000E-04
2.090000E-03
2.300000E-04
1.110000E-04
2.350000E-04
5.900000E-05
1.820000E-03
4.500000E-03
4.899999E-04
6.700000E-04
1.030000E-03
2.600000E-04
2.010000E-03
2.300000E-04
4.600000E-04
8.700000E-03
1.820000E-03
1.500000E-03
1.110000E-03
1.700000E-04
2.300000E-04
8.000000E-04
8.000000E-04
1.100000E-04
1.400000E-04
4.500000E-04
5.400000E-04
8.000000E-04

AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228


1.E+01
*U sphere, 50 y
4.£+00
“M °
o 1E01b 4
ga!
S he ay Zinpa
s = Lg *%
& 1602 gots ot
3 oe ;
S 16-03 |S HF .
ira a, £ oe 8
oe ay wo ee
seo4 | 8 ¢S ase et aes
: “hey es a nan o
. at! 3h, weet? %e
° * ° of * oF
16-05 ERT PSE tei Sa, octet gee oad tt wf.i¢
1

00 02 04 O06 O8 10 12 14
Photon Energy, MeV

Fig. 3. Unscattered fluence rate at 1 m in air of photon lines emergent from the 7*°U
(93.5 %) sphere, age 50 y, of Table 1.

15


Calculations of the activities of the radionuclides as a function of time were done by
means of the usual Bateman equation (Bateman, 1910) for each original constituent
radionuclide, assuming the concentrations of all progeny are initially zero. Thus the number of
atoms 7 at time ¢ from an initial number of the parent atoms 7 is

1 0) = Ady Am a)

“TTA -4,)

hay
where J; is the decay constant for the pertinent radionuclide. The relative atomic weights of the
pertinent radionuclides were taken from Coursey ef a/. (2005). Note that the possible
production of radionuclides through emission and absorption of neutrons is not included, and is
assumed to be negligible for this problem. Complex decay (i.e., multiple branching) occurs in
all four decay series, but at most only once with our procedures. The associated branching
fractions were inserted to multiply the J terms in Eq. | just to the right of the equal sign that
multiply 7(0). In the cases of complex decay, the chain was calculated for both branches, and
the results for radionuclides below the split were then summed.

The activities at time ¢ are given by 2,n((t), and can be evaluated for any ¢. The results
for our spheres at t= 10 y, 25 y, and 50 y are given in Table 2.


8.080000E-02
8.180001E-02
8.250000E-02
8.480000E-02
8.520000E-02
8.659501E-02
8.900000E-02
8.930001E-02
9.000000E-02
9.100001E-02
9.150001E-02
9.220000E-02
9.270000E-02
9.300000E-02
9.350000E-02
9.465400E-02
9.670001E-02
9.700000E-02
9.843400E-02
1.006000E-01
1.021000E-01
1.025000E-01
1.038600E-01
1.057000E-01
1.063000E-01
1.081000E-01
1.104210E-01
1.112980E-01
1.130000E-01
1.144450E-01
1.165000E-01
1.169000E-01
1.196000E-01
1.220000E-01
1.251000E-01
1.283000E-01
1.300000E-01
1.310000E-01
1.329000E-01
1.352000E-01
1.358000E-01
1.365000E-01
1.393000E-01
1.427000E-01
1.431000E-01
1.444000E-01
1.485000E-01
1.505000E-01
1.537000E-01
1.547000E-01
1.561000E-01
1.570000E-01
1.579000E-01
1.591000E-01
1.600000E-01
1.612000E-01
1.624000E-01
1.633000E-01
1.666000E-01
1.680000E-01
1.706000E-01
1.728000E-01
1.737000E-01

1.500000E-05
4,500000E-05
1.500000E-05
7.000000E-05
1.400000E-04
1.950000E-02
7.000000E-05
7.000000E-05
1.200000E-05
1.200000E-05
1.200000E-05
7.000000E-05
1.200000E-05
8.000000E-06
8.000000E-06
1.056000E-01
4.000000E-05
5.000000E-05
1.690000E-01
3.100000E-05
1.900000E-05
4.600000E-05
8.540000E-03
8.000000E-06
1.600000E-05
1.200000E-05
2.120000E-02
4.010000E-02
3.500000E-05
1.550000E-02
5.800000E-05
5.800000E-05
8.000000E-06
1.500000E-05
3.000000E-05
1.200000E-05
1.200000E-05
3.000000E-05
1.200000E-05
4.600000E-05
1.500000E-05
1.900000E-05
4.600000E-05
2.300000E-05
1.500000E-05
7.000000E-05
2.700000E-05
2.300000E-05
3.900000E-05
4.600000E-05
2.300000E-05
2.700000E-05
2.300000E-05
3.900000E-05
3.100000E-05
2.700000E-05
2.300000E-05
2.300000E-05
1.200000E-05
3.100000E-05
5.000000E-05
2.700000E-05
8.399999E-05

PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233

30

1.747000E-01
1.752000E-01
1.780000E-01
1.801000E-01
1.827000E-01
1.833000E-01
1.848000E-01
1.857000E-01
1.985000E-01
2.021000E-01

2.158000E-01
2.178000E-01
2.244000E-01
2.252000E-01
2.261000E-01
2.268000E-01
2.285700E-01
2.321000E-01
2.350000E-01
2.360000E-01
2.385000E-01

398000E-01
2.423000E-01
2.434000E-01
2.446000E-01
2.483800E-01
2.496000E-01
2.504000E-01
2.523000E-01
2.584500E-01
2.614000E-01
2.644000E-01
2.681000E-01
2.693000E-01
2.715550E-01
2.728000E-01
2.806100E-01
2.884200E-01
2.901000E-01
2.988100E-01
3.001290E-01
3.019900E-01
3.040000E-01
3.054000E-01
3.119040E-01
3.135000E-01
3.176000E-01
3.207300E-01

-359000E-01
3.404760E-01
3.445000E-01
3.518000E-01
3.639000E-01
3.740000E-01
3.754040E-01
3.802800E-01
3.868000E-01
3.933000E-01
3.984920E-01

4.200000E-05
1.200000E-05
5.400000E-05
2.700000E-05
2.700000E-05
1.200000E-05
3.100000E-05
3.500000E-05
3.100000E-05
6.200000E-05
3.100000E-05
2.700000E-05
2.300000E-05
2.700000E-05
3.100000E-05
2.300000E-05
9.200000E-05
5.400000E-05
3.100000E-05
4.200000E-05
2.700000E-05
1.200000E-05
2.300000E-05
5.400000E-05
3.100000E-05
5.400000E-05
2.300000E-05
2.700000E-05
6.090000E-04
3.100000E-05
3.100000E-05
3.900000E-05
2.740000E-04
7.800000E-05
3.500000E-05
3.100000E-05
3.100000E-05
3.230000E-03
3.900000E-05
1.100000E-04
1.600000E-04
3.500000E-05
8.799999E-04.
6.630000E-02
1,000000E-04
4.600000E-05
5.000000E-05
3.850000E-01
1.390000E-04
2.300000E-05
5.100000E-05
2.300000E-05
2.700000E-05
4.450000E-02
1.500000E-05
4.600000E-05
3.500000E-05
7.300000E-05
6.790000E-03
3.700000E-05
3.100000E-05
5.000000E-05
1.391000E-02

PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233


1.085820E-01
1.127900E-01
1.711500E-01

37
1.300000E-02
1.959000E-02
3.160000E-02
3.470000E-02
4.140000E-02
4.196000E-02
5.122000E-02
5.410000E-02
5.425000E-02
6.435000E-02
7.270000E-02
7.502000E-02
7.619800E-02
8.995701E-02
9.335000E-02
9.609000E-02
1.048190E-01
1.056040E-01
1.085820E-01
1.091600E-01
1.154500E-01
1.203500E-01
1.365500E-01
1.407600E-01
1.424000E-01
1.437600E-01
1.509300E-01
1.633300E-01
1.733000E-01
1.826100E-01
1.857150E-01
1.949400E-01
1.989000E-01
2.021100E-01
2.053110E-01
2.152800E-01
2.213800E-01
2.287800E-01
2.335000E-01
2.408700E-01
2.468400E-01
2.664500E-01
2.751290E-01
2.754300E-01
2.814200E-01
2.829200E-01
2.895600E-01
2.916500E-01
3.017000E-01
3.171000E-01
3.435000E-01
3.459000E-01
3.560300E-01
3.878200E-01
4.102900E-01
4.287100E-01
4.484000E-01

1.800000E-06
1.900000E-04
6.200000E-07

2.800000E-01
6.000000E-05
1.700000E-04
3.700000E-04
3.000000E-04
6.000000E-04
3.400000E-04
8.999999E-06
1.500000E-04
1.300000E-04
1.100000E-03
6.000000E-04
8.000001E-05
3.470000E-02
5.600000E-02
9.099999E-04
6.930000E-03
1.320000E-02
5.060000E-03
1.540000E-02
3.000000E-04
2.600000E-04
1.200000E-04
2.200000E-03
5.000000E-05
1.096000E-01
8.000000E-04
5.080000E-02
6.000000E-05
3.400000E-03
5.720000E-01
6.300000E-03
4.200000E-04
1.080000E-02
5.010000E-02
2.900000E-04
1.200000E-03
7.000000E-05
2.900000E-04
7.500000E-04
5.300000E-04
6.000000E-05
5.200000E-04
7.000000E-05
6.000000E-05
6.000000E-05
7.000000E-05
4.000000E-04
5.000000E-05
1.000000E-05
3.000000E-05
4.000000E-04
5.000000E-05
4.000000E-04
3.000000E-05
1.000000E-05
1.000000E-05

U236
U236
U236

U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235
U235

27

15
1.300000E-02
5.320000E-02
8.995701 E-02
9.335000E-02
1.048190E-01
1.056040E-01
1.085820E-01
1.209000E-01
4.549500E-01
5.035000E-01
5.082000E-01
5.817000E-01
6.244001E-01
6.349000E-01
6.776000E-01

124
1.360000E-02
6.270000E-02
9.465400E-02
9.843400E-02
1.104210E-01
1.112980E-01
1.144450E-01
1.353200E-01
1.372300E-01
1.401000E-01
1.665000E-01
1.847000E-01
1.934000E-01
1.979100E-01
1.999000E-01
2.033000E-01
2.099000E-01
2.359000E-01
2.477000E-01
2.582270E-01
2.755000E-01
2.990000E-01
3.110000E-01
3.167000E-01
3.381000E-01
3.402000E-01
3.575000E-01
3.628000E-01
3.876000E-01
4.274000E-01
4.459100E-01
4.509700E-01
4.535800E-01
4.567000E-01
4.684300E-01
4.75T400E-01
4.854400E-01
5.075001E-01
5.092000E-01
5.166000E-01
5.260201E-01
5.439800E-01
5.572400E-01
5.720000E-01
5.811900E-01

9.999999E-02
1.230000E-03
2.510000E-05
4.050000E-05
5.010000E-06
9.550000E-06
3.660000E-06
4.000000E-04
2.500000E-07
9.599999E-09
1.500000E-07
1.200000E-07
8.000000E-09
1.400000E-07
9.800000E-09

1.340000E-04
1.200000E-05
6.600000E-05
1.060000E-04
1.330000E-05
2.500000E-05
9.699999E-06
4.300000E-08
4.700000E-07
1.280000E-05
2.400000E-09
1.680000E-05
1.440000E-05
2.700000E-07
5.700000E-06
1.700000E-05
1.350000E-05
8.000000E-07
2.440000E-06
7.639999E-04
3.100000E-06
6.500000E-06
8.400000E-07
1.900000E-06
1.100000E-05
7.000000E-07
8.000000E-06
6.800000E-06
1.398000E-05
2.000000E-07
3.000000E-07
3.110000E-05
2.130000E-05
7.200000E-06
2.290000E-05
2.390000E-05
1.900000E-07
1.570000E-05
2.100000E-05
1.300000E-07
9.300000E-08
3.670000E-05
8.400000E-08
8.670000E-06
8.200000E-07

U234
U234
U234
U234
U234
U234
U234
U234
U234
U234
U234
U234
U234
U234
U234

PA234M
PA234M
PA234M
PA234M
PA234M.
PA234M
PA234M.
PA234M
PA234M
PA234M
PA234M
PA234M.
PA234M
PA234M.
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M.
PA234M
PA234M.
PA234M
PA234M
PA234M
PA234M
PA234M.
PA234M
PA234M.
PA234M
PA234M.
PA234M
PA234M
PA234M
PA234M
PA234M.
PA234M
PA234M.
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M


Neptunium Series

DITAt
32.3ms

4(0.99993)

2198
45.49 min
40.0220) AT aoareo)
2071 219R0
2.20 min 42us

29pp
3.253h

Y 5040)

2098
1.9E+19 y

410)

208)

BOOT Ha1.0)

Fig. 1b. Neptunium series.

22F
4.90 min

‘a(1.0)

2uPy
14.290 y

a(0.0000245),
o yO

Y 810.999975)

2am
432.6 y

29Pa
26.875 d
yom
2m
1.592645 y|
%(1.0)
zeth
7340 y
ai)
25Ra
149d
i)
20540
10.04
(1.0)



Uranium Series

(0.00021)

ze) 1
43min ¢

Toxo

210p5
22.209

yam

2108
50126

Y

2109
198.376 4

(1.0)

209p5

2epy
3.7356+5 y

aD)

aay
4.4686+9 y|
‘a(1.0)
24TH
24.104
YR)
/ mpg, Neo r zinpa || copy
/ 4.159 min f |atsomin |) e77y

, Paw
Leasse+s y
WO
20TH
7-s38e+4
(10)
aire
1600 y
Gi0)
in
382354

ae

218R9
3.10 min

70,9980)

26 pp
26.8 min

Tm)

2M Bi
19.9 min

YF10.99979)

2upo
164.3 ps

BIO. 9964) ] Zac10)

Fig. 1. Decay data giving assumed half-lives and branching fractions. The dotted squares
indicate a branch that was ignored in the calculations.

a. Uranium series


1.E+03

Pu sphere, 50 y
1.E+02

1,.E+01

cm? s*

1.E+00

Fluence Rate,
m
Ss

1.E-02

00 01 02 03 04 05 06 07 08 09 1.0 14 12 13 1.4
Photon Energy, MeV

1.E+02

« Pu sphere, 50
1.E+01 P ¥

1.E+00

1.E-01

1.E-02

Fluence Rate, cm? s*

1,.E-03 —

ra mm we,
0.0 01 02 03 04 05 06 0.7 08 09 1.0 1.1 12 13 1.4
Photon Energy, MeV

1.E-04

Fig. 4. Unscattered fluence rate at 1 m in air of photon lines emergent from the 40Dy

(6.0 %) sphere, age 50 y, of Table 1. Both plots are of the same data but with different
ordinate scales.

16


Actinium Series 209Pu
28110 y
1.0)
zy
7.038E+8
A00)
2th
25.52h
i)
2Pa
3.276E+4 |
‘a(1.0)
RAG
2772y
10.0138, 810-9862)
nsf arth
22.00min} | 18.684
B(0.99994), a(1.0)
Ra
11.434
(1.9)
200Rn
3.96 s
a(1.0)
2150
4.781 ms
“A ‘a(0.9980)
2B
36.1 min
yet
angi
2.14 min
(0.99724), B(0.00276)
0.0972 B00

2orT
4.773 min

207P

Fig. 1d. Actinium series.


Alamos, NM.

Stefaka, Z, Katoma, R., and Varga, Z. (2008). “Laser ablationb assisted ICP-MS as a tool for
rapid categorization od seized unranium oxide materials based on isotopic composition
determination,” J. Anal. At. Spectrom., 23, 1030-1033.

Valkovié, V. (2006). “Applications of nuclear techniques relevant for civil security,” J. Phys.:
Conf. Series, 41, 81-100.

22


NISTIR 7557

CALCULATIONS OF FLUENCE RATES OF
UNSCATTERED X- AND GAMMA-RAY PHOTONS
EMERGING FROM MODEL SPHERES OF
SPECIAL NUCLEAR MATERIAL

Stephen Seltzer

NUsT

National Institute of Standards and Technology
Technology Administration, U.S. Department of Commerce



3.708400E+00 2.000000E-05 TL208
3.960900E+00 1.500000E-05 TL208

9
1.060000E-02 2.090000E-05 TL207
7.280500E-02 1.570000E-05 TL207
7.496901E-02 2.610000E-05 TL207
8.445000E-02 3.150000E-06 TL207
8.493800E-02 6.050000E-06 TL207
8.730001E-02 2.210000E-06 TL207
3.281000E-01 1.400000E-05 TL207
5.696200E-01 1.590000E-05 TL207
8.977700E-01 2.600000E-03 TL207

45


Table 2. Activities of radionuclides in spheres at a function of age, from initial isotopic
compositions given in Table 1.

b. Plutonium
Activity Activity
Anil s inl s!

Nuclide 10 y 25y 50 y Nuclide 10 y 25y 50 y
Pu-242 1.463E+07 | 1.463E+07 |_1.463E+07 | Fr-223 1,.514E-03 | 2.120E-02 1.435E-01
Pu-241 3.428E+12 | 1.656E+12 | 4.925E+11 | Ra-223 1.060E-01 | 1.516E+00 | 1.034E+01
Am-241 1.387E+11 | 1.932E+11 | 2.231E+11 | Rn-222 5.790E-02 | 8.798E-01 | 6.700E+00
Pu-240 2.517E+I1 | 2.513E+11 | 2.506E+11 | Fr-221 1.861E-03 | 3.814E-02 | 3.839E-01
Pu-239 1.073E+12 | _1.073E+12 | 1.072E+12 | Rn-220 2.922E-06 | _4.786E-05 |_2.923E-04
U-238 2.270E-02 | 5.674E-02 | _1.135E-01 | Rn-219 1.060E-01 | 1.516E+00 | 1.034E+01
Pu-238 2.927E+10 | 2.600E+10 | 2.134E+10 | Po-218 5.789E-02 | 8.796E-01 | 6.699E+00
Np-237 3.465E+05 |_1.169E+06 | 2.883E+06 | At-217 1.861E-03 | 3.814E-02 | 3.839E-01
U-236 7.A53E+04 | 1.862E+05 | 3.719E+05 | Po-216 2.922E-06 | _4.786E-05 |_2.923E-04
U-235 1.057E+04 |_2.643E+04 | 5.284E+04 | Po-215 1.060E-01 | 1.516E+00 | 1.034E+01
Th-234 2.248E-02 | 5.653E-02 1.133E-01 | Pb-214 5.789E-02 | 8.796E-01 | 6.699E+00
Pa-234m 2.245E-02 | 5.644E-02 | 1.131E-01 | Bi-214 5.788E-02 | 8.794E-01 | 6.697E+00
U-234 8.600E+05 | 2.029E+06 | 3.694E+06 | Po-214 5.788E-02 | 8.794E-01 | 6.697E+00
Pa-233 3.418E+05 | 1.162E+06 | 2.875E+06 | Bi-213 1.861E-03 | 3.814E-02 | 3.839E-01
U-233 6.580E+00 | 5.426E+01 | 2.718E+02 | Po-213 1.820E-03 | 3.730E-02 | _3.754E-01
Th-232 1.839E-05 1.149E-04 | 4.590E-04 | Pb-212 2.921E-06 | 4.785E-05 | 2.923E-04
Th-231 1.057E+04 | 2.642E+04 | 5.283E+04 | Bi-212 2.920E-06 | _4.785E-05 |_2.923E-04
Pa-231 1.118E+00 | _6.987E+00 | 2.794E+01 | Po-212 1.871E-06 | 3.065E-05 1.872E-04
Th-230 4.006E+01 | 2.409E+02 | 9.049E+02 | Pb-211 1.060E-01 | 1.516E+00 | 1.034E+01
Th-229 1.921E-03 | 3.864E-02 | 3.864E-01 | Bi-211 1.057E-01 | 1.512E+00 | 1.031E+01
Ra-228 5.607E-06 | _6.270E-05 | _3.320E-04 | Pb-210 4.261E-03 | 1.492E-01 | 2.003E+00
Ac-228 5.606E-06 | 6.269E-05 | _3.320E-04 | Bi-210 4.228E-03 |_1.488E-01 | _2.000E+00
Th-228 2.936E-06 | 4.793E-05 | _2.925E-04 | Po-210 3.449E-03 | 1.371E-01 | 1.922E+00
Ac-227 1.097E-01 | 1.536E+00 | _1.040E+01 | TI-209 4.094E-05 | 8.390E-04 | 8.445E-03
Th-227 1.059E-01 | 1.503E+00 | 1.022E+01 | Pb-209 1.861E-03 | 3.814E-02 | 3.838E-01
Ra-226 5.817E-02 | 8.813E-01 | 6.706E+00 | Bi-209 1.390E-21 | 9.161E-21 1.629E-19
Ra-225 1.885E-03 | 3.834E-02 | 3.849E-01 | TI-208 1.050E-06 | _1.720E-05 | _1.050E-04
Ac-225 1.861E-03 | 3.814E-02 | 3.839E-01 | Tl-207 1.057E-01 | 1.512E+00 | 1.031E+01
Ra-224 2.922E-06 | 4.786E-05 | 2.923E-04



Table 2. Activities of radionuclides in spheres at a function of age, from initial isotopic
compositions given in Table 1.

a. Uranium

Activity

Anil s!

Nuclide 10 y 25y 50 y
U-238 7.213E+05 |_7.213E+05 | 7.213E+05
U-235 7.47T6E+07 | _7.476E+07 | _7.476E+07
Th-234 7.213E+05 |_7.213E+05 | _7.213E+05
Pa-234m_|_7.202E+05 | 7.202E+05 | 7.202E+05
U-234 1.611E+09 | 1.611E+09 | 1.611E+09
Th-231 7.AT6E+07 | _7.476E+07 | 7.476E+07
Pa-231 1.581E+04 | 3.953E+04 | 7.905E+04
Th-230 1.482E+05 | _3.704E+05 | 7.407E+05
Ac-227 2.269E+03 | _1.227E+04 | 3.950E+04
Th-227 2.206E+03 | _1.204E+04 | 3.886E+04
Ra-226 3.205E+02 |_1.999E+03 | _7.965E+03
Fr-223 3.131E+01 | 1.693E+02 | 5.451E+02
Ra-223 2.218E+03 | _1.217E+04 | 3.935E+04
Rn-222 3.195E+02 | 1.996E+03 | 7.961E+03
Rn-219 2.218E+03 | _1.217E+04 | 3.935E+04
Po-218 3.195E+02 |_1.996E+03 | 7.959E+03
Po-215 2.218E+03 | 1.217E+04 | 3.935E+04
Pb-214 3.195E+02 |_1.996E+03 | 7.959E+03
Bi-214 3.194E+02 | 1.995E+03 | 7.957E+03
Po-214 3.194E+02 | 1.995E+03 | 7.957E+03
Pb-211 2.218E+03 | _1.217E+04 | _3.935E+04
Bi-211 2.212E+03 | 1.214E+04 | 3.924E+04
Pb-210 3.077E+01 | 4.320E+02 | 2.926E+03
Bi-210 3.059E+01 | 4.310E+02 | 2.923E+03
Po-210 2.617E+01 | 4.054E+02 | 2.839E+03
TI-207 2.212E+03 | 1.214E+04 | 3.924E+04



1
8.049001E-01

2

2.980000E-01
7.997000E-01

238

1.1 10000E-02
7.686301E-02
7.929000E-02
8.925600E-02
8.980700E-02
9.231701 E-02
2.210000E-01
2.300000E-01
2.528000E-01
2.688000E-01
2.738000E-01
2.809500E-01
3.042000E-01
3.333100E-01
3.347800E-01
3.489200E-01
3.519000E-01
3.560000E-01
3.867700E-01
3.888800E-01
3.940500E-01
3.960100E-01
4.057400E-01
4.280000E-01
4.529200E-01
4.547700E-01
4.610000E-01
4.697600E-01
4.744100E-01
4.859200E-01
4.867000E-01
4.879500E-01
4.942000E-01
4.969000E-01
5.019600E-01
5.199000E-01
5.246000E-01
5.280000E-01
5.367700E-01
5.430000E-01
5.476000E-01
5.727600E-01
5.952300E-01
6.000000E-01
6.093121E-01
6.157300E-01
6.170000E-01
6.264001E-01
6.307900E-01
6.331400E-01
6.347200E-01
6.396700E-01
6.491800E-01
6.515000E-01
6.587000E-01

1.900000E-05

5.200000E-07
1.040000E-04

6.000000E-03
3.970000E-03
6.610000E-03
8.000000E-04
1.530000E-03
5.660000E-04
3.000000E-05
4.000000E-05
3.000000E-05
2.000000E-04.
1.500000E-03
6.000000E-04
4.200000E-04
8.000000E-04
3.400000E-04
1.200000E-03
7.000000E-04
7.000000E-05
3.100000E-03
3.700000E-03
1.480000E-04
2.900000E-04
1.700000E-03
1.100000E-05
3.100000E-04
3.000000E-03
5.300000E-04
1.290000E-03
1.100000E-03
2.200000E-04
3.000000E-05
2.800000E-04
1.200000E-04
6.899999E-05
1.800000E-04
1.600000E-04
1.700000E-04
4.000000E-05
6.800000E-04
8.400000E-04
2.000000E-05
7.400000E-04
1.700000E-04
8.000001E-05
4.610000E-01
6.000000E-04
3.400000E-04
5.000000E-05
1.800000E-04
5.500000E-04
6.500000E-05
3.000000E-04
6.000000E-04
1.000000E-05
1.500000E-04

PO216

PO214
PO214

BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B

Al

6.611000E-01
6.654530E-01
6.774100E-01
6.832200E-01
6.876000E-01
6.933000E-01
6.979001 E-01
6.998200E-01
7.031 100E-01
7.049001E-01
7.088000E-01
7.106700E-01
7.198600E-01
7.229800E-01
7.338000E-01
7.407300E-01
7.528400E-01
7.683560E-01
7.697001E-01
7.861000E-01
7.886000E-01
8.061740E-01
8.150001 E-01
8.211800E-01
8.263000E-01
8.323901E-01
8.404000E-01
8.471600E-01
8.730701E-01
8.780301E-01
9.042900E-01
9.157400E-01
9.178000E-01
9.302000E-01
9.340610E-01
9.341000E-01
9.345000E-01
9.386501E-01
9.396000E-01
9.433401E-01
9.498000E-01
9.522001E-01
9.616100E-01
9.640800E-01
9.650000E-01
9.761800E-01
9.914901E-01
1.013800E+00
1.021000E+00
1.032370E+00
1.033300E+00
1.038000E+00
1.045600E+00
1.051960E+00
1.067200E+00
1.069960E+00
1.103640E+00
-104790E+00
-118900E+00
-120287E+00
-130290E+00
-133660E+00

1
1
1
1
1
1.155190E+00

4.700000E-04
1.460000E-02
6.000000E-05
8.100000E-04
6.899999E-05,
6.000000E-05
5.100000E-04
1.600000E-04
4.720000E-03
4.700000E-04
1.700000E-04
7.500000E-04
3.790000E-03
3.500000E-04
4.300000E-04
4.000000E-04
1.300000E-03
4.940000E-02
3.000000E-04
3.100000E-03
1.500000E-04
1.220000E-02
3.800000E-04
1.580000E-03
1.100000E-03
2.800000E-04
8.999999E-05
2.600000E-04
1.800000E-04
1.200000E-04
8.500000E-04
2.600000E-04
5.000000E-05
3.300000E-04
3.030000E-02
5.000000E-04
1.000000E-04
1.300000E-04
1.800000E-04
1.700000E-04
5.500000E-05
6.000000E-05
1.200000E-04
3.620000E-03
1,000000E-04
1.900000E-04
1.000000E-04
8.300000E-05
1.400000E-04
7.800000E-04
2.400000E-04
8.300000E-05
2.600000E-04
3.150000E-03
2.700000E-04
2.750000E-03
1,000000E-03
7.700000E-04
4.000000E-04
1.510000E-01
4.000000E-04
2.480000E-03
1.630000E-02

BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B


9.103000E-02
9.335000E-02
9.624401E-02
9.713401 E-02
1.000300E-01
1.017700E-01
1.036000E-01
1.048190E-01
1.056040E-01
1.085820E-01
1.120000E-01
1.144000E-01
1.1641 00E-01
1.171590E-01
1.189680E-01
1.208160E-01
1.238930E-01
1.254100E-01
1.292500E-01
1.312000E-01
1.353600E-01
1.397600E-01
1.444000E-01
1.453370E-01
1.463450E-01
1.481560E-01
1.531000E-01
1.547700E-01
1.561400E-01
1.624000E-01
1.645220E-01
1.657000E-01
1.690100E-01
1.708400E-01
1.723600E-01
1.741900E-01
1.843000E-01
1.879690E-01
1.921300E-01
2.060000E-01
2.0817 10E-01
2.123400E-01
2.160800E-01
2.171590E-01
2.177000E-01
2.193800E-01
2.233000E-01
2.267000E-01
2.281000E-01
2.301100E-01
2.403900E-01
2.453450E-01
2.487260E-01
2.559400E-01
2.593300E-01
2.606500E-01
2.619200E-01
2.686600E-01
2.723400E-01
2.747280E-01
2.7811 10E-01
2.880330E-01
2.913540E-01

3.000000E-06
1.310000E-04
1.270000E-05
2.000000E-04
5.000000E-07
8.200000E-07
9.200000E-07
1.620000E-05
3.100000E-05
1.190000E-05
4.500000E-06
2.300000E-06
1.900000E-06
2.300000E-05
4.060000E-05
3.320000E-05
5.900000E-06
6.000000E-07
6.400000E-07
3.000000E-07
2.320000E-05
9.600000E-07
2.700000E-06
1.500000E-05
6.570000E-05
3.300000E-06
5.000000E-07
1.400000E-06
5.300000E-07
6.900000E-07
6.230000E-05
3.500000E-06
6.200000E-07
1.300000E-06
3.200000E-07
2.100000E-06
2.300000E-07
1.900000E-05
3.700000E-07
6.000000E-07
2.290000E-05
1.260000E-06
6.100000E-06
3.200000E-05
4.600000E-07
1.400000E-06
3.000000E-07
9.000000E-08
2.000000E-07
6.200000E-07
3.500000E-06
3.620000E-05
1.430000E-05
3.900000E-07
1.600000E-06
9.800000E-07
2.800000E-06
2.300000E-06
5.700000E-07
4.000000E-06
1.080000E-05
9.699999E-06
5.370000E-05

U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233

29

2.939100E-01
3.028900E-01
3.095000E-01
3.120000E-01
3.171600E-01
3.205410E-01
3.234200E-01
3.285370E-01
3.366100E-01
3.389000E-01

1
3.937000E-01
3.967000E-01
4.366000E-01
4.841000E-01

190
1.360000E-02
1.726000E-02
1.870000E-02
1.970000E-02
2.390000E-02
2.470000E-02
2.855900E-02
3.190000E-02
3.530000E-02
3.580000E-02
3.850000E-02
4.034900E-02
4.166300E-02
4.170000E-02
4.270000E-02
4.580000E-02
4.670000E-02
4.770000E-02
4.880000E-02
4.970000E-02
5.180000E-02
5.250000E-02
5.320000E-02
5.500000E-02
5.800000E-02
5.920000E-02
5.960000E-02
6.060000E-02
6.160000E-02
6.320000E-02
6.360000E-02
6.550001E-02
6.640001E-02
6.750000E-02
6.850000E-02
6.960000E-02
7.030001E-02
7.130001E-02
7.400000E-02
7.526900E-02
7.700001E-02
7.790001 E-02
7.840001E-02
7.910001E-02

1.300000E-06
6.400000E-07
6.600000E-07
2.500000E-07
7.159999E-05,
2.900000E-05
7.100000E-06
6.000000E-07
5.400000E-06
7.000000E-08
5.300000E-07
7.500000E-06
8.700000E-07
7.000000E-08
8.000000E-08
4.600000E-08
4.000000E-08

4.300000E-01
4.000000E-05
4.600000E-04
4.600000E-04
3.100000E-05
3.100000E-05
7.100000E-04
2.300000E-05
1.500000E-05
1.900000E-05
6.300000E-05
2.360000E-04
1.400000E-04
1.000000E-04
1.900000E-05
4.000000E-06
8.000000E-06
8.000000E-06
1.600000E-05
8.000000E-06
3.600000E-05
1.600000E-05
1.200000E-05
8.000000E-06
1.200000E-05
8.000000E-06
8.000000E-06
2.400000E-04
1.600000E-05
8.000000E-06
8.000000E-06
2.700000E-05
1.900000E-05
1.900000E-05
2.700000E-05
4.600000E-05
2.700000E-05
7.800000E-05
3.500000E-05
1.320000E-02
3.800000E-05
1.200000E-05
7.700000E-05
8.000000E-06

U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233

PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233


6.246000E-01 1.150000E-06
6.490000E-01 1.041000E-05
6.553000E-01 1.380000E-05
6.708000E-01 3.700000E-06
6.739001E-01 6.500000E-06
6.834000E-01 5.700000E-06
6.910000E-01 8.920000E-05
6.955000E-01 1.620000E-05
6.990200E-01 5.700000E-05
7.020000E-01 7.240000E-05
7.059400E-01 5.600000E-05
7.082000E-01 6.730000E-06
7.190101E-01 2.600000E-07
7.325000E-01 1.300000E-05
7.401000E-01 1.090000E-04
7.428131E-01 1.066000E-03
7.501200E-01 1.800000E-07
7.605301E-01 4.300000E-08
7.664200E-01 3.170000E-03
7.817500E-01 7.770000E-05
7.834001E-01 3.900000E-07
7.862801E-01 5.440000E-04
7.919400E-01 9,999999E-08
8.057500E-01 5.900000E-05
8.082001E-01 2.780000E-05
8.182001E-01 1.000000E-05
8.256000E-01 6.600000E-05
8.441000E-01 1.100000E-05
8.515801E-01 6.899999E-05
8.668000E-01 1.140000E-05
8.809001E-01 4.000000E-05
8.832200E-01 3.500000E-05
9.217200E-01 1.278000E-04
9.266101E-01 1.240000E-05
9.363000E-01 1.100000E-05
9.419601E-01 2.520000E-05
9.459400E-01 1.010000E-04
9.600000E-01 8.000000E-06
9.961000E-01 5.600000E-05
1.001030E+00 8.420000E-03
1.041700E+00 1.240000E-05
1.059400E+00 2.280000E-05
1.061860E+00 2.140000E-05
1.081900E+00 8.999999E-06
1.084250E+00 8.000000E-06
1.120600E+00 1.720000E-05
1.124930E+00 3.370000E-05
1.174200E+00 1.940000E-05
1.193730E+00 1.358000E-04
1.237260E+00 5.250000E-05
1.392700E+00 3.460000E-05
1.413880E+00 2.260000E-05
1.434140E+00 9.730000E-05
1.458500E+00 1.900000E-05
1.501000E+00 9.300000E-06
1.510210E+00 1.305000E-04
1.527270E+00 2.010000E-05
1.550000E+00 1.140000E-05
1.553750E+00 8.209999E-05
1.558400E+00 7.200000E-06
1.570670E+00_ 1.090000E-05
1.593870E+00 1.890000E-05
1.601800E+00 4.700000E-06

PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M
PA234M

28

1.667600E+00 1.150000E-05
1.694100E+00 4.500000E-06
1.737750E+00 2.130000E-04
1.765440E+00 8.750000E-05
1.796200E+00 4.200000E-06
1.809040E+00 3.740000E-05
1,.819690E+00 8.800000E-06
1.831360E+00 1.742000E-04
1.863090E+00 1.210000E-05
1.867690E+00 9.259999E-05
1.874880E+00 8.180000E-05
1.893510E+00 1.890000E-05
1.911190E+00 6.240000E-05
1,926500E+00 4.500000E-06
1.937040E+00 2.100000E-05
1,.970000E+00 4.100000E-06

16
1.330000E-02 6.900000E-02
2.002000E-02 5.000000E-05
2.949000E-02 1.200000E-05
6.286000E-02 1.600000E-04
6.329001E-02 3.700000E-02
7.392000E-02 1.300000E-04
8.330001E-02 6.000000E-04
9.228200E-02 1.710000E-04
9.238000E-02 2.130000E-02
9.280001E-02 2.100000E-02
9.586301E-02 2.800000E-04
1.033500E-01 3.200000E-05
1.075950E-01 3.400000E-05
1.084220E-01 6.500000E-05
1.114860E-01 2.500000E-05
1.128100E-01 2.100000E-03

107

1.300000E-02 5.500000E-02
2.531800E-02 1.110000E-05
2.919200E-02 1.200000E-04
3.152000E-02 2.500000E-06
3.240000E-02 9.100000E-06
3.798000E-02 3.300000E-06
4.244000E-02 8.620000E-04
5.262000E-02 2.300000E-06
5.360800E-02 4.100000E-05
5.469900E-02 1.820000E-04
6.388000E-02 3.000000E-07
6.612200E-02 7.700000E-06
6.794301E-02 2.900000E-06
6.887001E-02 9.800000E-07
7.028000E-02 5.500000E-06
7.181900E-02 2.400000E-05
7.288000E-02 5.400000E-06
7.457000E-02 1.500000E-05
7.639001E-02 3.600000E-06
7.713000E-02 6.600000E-06
7.815000E-02 5.500000E-07
8.295701E-02 1.600000E-06
8.543000E-02 1.700000E-06
8.677000E-02 1.200000E-06
8.727000E-02 1.700000E-06
8.846001E-02 4.000000E-06
8.995701E-02 8.130000E-05

PA234M.
PA234M,
PA234M.
PA234M,
PA234M
PA234M.
PA234M
PA234M.
PA234M,
PA234M.
PA234M,
PA234M.
PA234M,
PA234M
PA234M.
PA234M

TH234
TH234
TH234
TH234
TH234
TH234
TH234
TH234
TH234
TH234
TH234
TH234
TH234
TH234
TH234
TH234

U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233
U233


Thorium Series

(0.3594)

20871
3.053 min

22Th
1.40810 y|
a t1.0)
20Ra
575 y
i)
Ac
6.15h
i)
zh
1912y
(1.0)
20tRa
3.66 d
“a(1.0)
Rn
55.68
‘a(1.0)
216P9
0.1455
Za1.0)
2b
10.64h
yom
2
60.55 min
PAi0.5406)
2P9
0.299 us

Pp

BAT A190)

Fig. lc. Thorium series.

20Pu
6561 y
ea)
20
2.a4ze+7 y
44.0)


Table 4. Fluence rate from unscattered photons of energy £ at | m in air for the U and
Pu spheres.

c. Pu (6.0 %) 0.5 kg sphere of age 25 y; fluence rates greater than 10! cm” s". Total
fluence rate for all 2490 lines calculated is 192 em? s".

E/MeV__| @/cm?s" | Nuclide E/MeV_| @/cm?s" | Nuclide
5.954E-02 1.135E+02 | AM241 1.253E-01 3.107E-01 | AM241
4.137E-01 | _9.385E+00 | PU239 3.415E-01 | 2.923E-01 | PU239
3.751E-01 | 8.278E+00 | PU239 9.465E-02 | 2.686E-01 | PU241A
9.843E-02 | _4.768E+00 | PU239 1.113E-01 2.633E-01 | PU241A
1.030E-01 | 3.962E+00 | AM241 1.031E-01 | 2.448E-01 | PU239
1.037E-01 | 3.716E+00 | Pu Kal 5.162E-02 | _2.294E-01 | PU239
9.897E-02 | 3.147E+00 | AM241 3.238E-01 | 2.131E-01 | PU239
1.293E-01 | 2.885E+00 | PU239 3.209E-01 | 2.102E-01 | PU239
3.450E-01 2.507E+00 | PU239 2.080E-01 2.081E-01 | AM241
1.172E-01 |_2.410E+00 | Pu KB1 3.687E-01 | 2.012E-01 | AM241
9.953E-02 | 2.091E+00 | Pu Ka2 6.459E-01 1.971E-01 | PU239
3.328E-01 | 2.069E+00 | PU239 2.554E-01 1.881E-01 | PU239
3.931E-01 | 2.040E+00 | PU239 1.140E-01 1.854E-01 | PU241A
9. 465E-02 | 2.008E+00 | PU239 1.486E-01 1.850E-01 | PU241A
1.042E-01 | 2.004E+00 | PU240 1,037E-01 1.825E-01 | PU241A
1.113E-01 1.981E+00 | PU239 1.442E-01 1.694E-01 | PU239
3.802E-01 1.668E+00 | PU239 2.975E-01 1.642E-01 | PU239
3.828E-01 1.435E+00 | PU239 9.985E-02 | 1.633E-01 | PU238
4.515E-01 1.413E+00 | PU239 4.267E-01 1.576E-01 | PU239
9.878E-02 | 1.245E+00 | PU239 3.119E-01 1.523E-01 | PA233
3.925E-01 1.191E+00 | PU239 9.707E-02 1.485E-01 | AM241
1.104E-01 1.028E+00 | PU239 1.104E-01 1.378E-01 | PU241A
6.624E-01 8.791 E-01 | AM241 3.450E-01 1.353E-01 | PU239
1.163E-01 8.489E-01 | PU239 1.957E-01 1.351E-01 | PU239
4.226E-01 8.113E-01 | PU239 3.767E-01 1.334E-01 | AM241
2.036E-01 7.895E-01 | PU239 6.190E-01 1.308E-01 | AM241
1.144E-01 7.879E-01 | PU239 6.589E-01 1,292E-01 | PU239
1.154E-01 6.868E-01 | PU239 1.142E-01 1.150E-01 | AM241
9.843E-02 6.331E-01 | PU241A 3.324E-01 1.120E-01 | AM241
7.220E-01 5.282E-01 | AM241 6.400E-01 1.114E-01 | PU239
3.361E-01 4.786E-01 | PU239 7.694E-01 1.097E-01 | PU239
3.671E-01 4.545E-01 | PU239 3.225E-01 1.073E-01 | AM241
3.686E-01 4.530E-01 | PU239 1.144E-01 1.053E-01 | PU241A
3.354E-01 3.799E-01 | AM241 1.714E-01 1.007E-01 | PU239
1.011E-01 3.283E-01 | AM241

19


2.860900E-01
2.895900E-01
2.897700E-01
2.924100E-01
2.965000E-01
2.999800E-01
3.005000E-01
3.045000E-01
3.084000E-01
3.126900E-01
3.148500E-01
3.184600E-01
3.192400E-01
3.248800E-01
3.259900E-01
3.298500E-01
3.343700E-01
3.397600E-01
3.425500E-01
3.464500E-01
3.505400E-01
3.526100E-01
3.626300E-01
3.693500E-01
3.709300E-01
3.748000E-01
3.762700E-01
3.822000E-01
3.835100E-01
3.986000E-01
4.022000E-01
4.151100E-01
4.323300E-01
4.480000E-01
4.575000E-01
4.668000E-01
4.800000E-01
4.820000E-01
4.931000E-01
5.075001E-01
5.166000E-01
5.245000E-01
5.346000E-01
5.369000E-01
5.524001E-01
5.561000E-01
5.690000E-01
5.760000E-01
5.790001E-01
5.890000E-01
5.960000E-01
6.077000E-01
6.214001E-01
6.238000E-01
6.323000E-01
6.410000E-01
6.443000E-01
6.628000E-01
6.920000E-01
7.043000E-01
7.072001E-01
7.185000E-01
7.221000E-01

2.400000E-02
2.600000E-02
2.600000E-04
8.900000E-04
6.000000E-03
3.000000E-02
1.900000E-04
1.560000E-02
2.300000E-04
7.000000E-03
1.320000E-02
8.999999E-05
4.400000E-04
1.400000E-04
8.999999E-05
4.000000E-02
1.540000E-02
5.200000E-05
4.700000E-03
1.630000E-04
1.500000E-03
1.400000E-04
6.900000E-04
8.399999E-05
5.000000E-05
2.100000E-05
7.000000E-05
8.700000E-05
3.000000E-04
1.900000E-05
1.000000E-04
1.900000E-05
5.600000E-05
1.900000E-06
9.500000E-07
6.700000E-06
4.000000E-06
1.900000E-06
7.300000E-06
8.999999E-06
3.900000E-06
2.600000E-06
1.300000E-06
1.500000E-05
3.100000E-06
5.100000E-06
8.100000E-06
4.000000E-06
6.000000E-06
8.000000E-07
1.400000E-07
2.500000E-06
8.000000E-07
2.300000E-06
1.900000E-06
2.600000E-07
1.200000E-06
8.000000E-07
5.400000E-07
1.090000E-06
5.400000E-07
4.000000E-07
5.100000E-06

TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227

36

7.235000E-01
7.344000E-01
7.354001E-01
7.384000E-01
7.464001E-01
7.488000E-01
7.541000E-01
7.569001E-01
7.622001E-01
7.663000E-01
7.734001E-01
7.758000E-01
7.810000E-01
7.842001E-01
7.874001E-01
7.926000E-01
7.973000E-01
8.039001E-01
8.086000E-01
8.126000E-01
8.180000E-01
8.181000E-01
8.234001E-01
8.267000E-01
8.285000E-01
8.378000E-01
8.425000E-01
8.467001E-01
8.483000E-01
8.543000E-01
8.573000E-01
8.589001 E-01
8.630000E-01
8.673000E-01
8.763000E-01
8.782001E-01
8.910000E-01
8.930001E-01
8.961000E-01
9.086000E-01
9.100000E-01
9.200000E-01
9.270000E-01
9.380000E-01
9.416000E-01
9.587001 E-01
9.700000E-01
9.717001 E-01
9.900001E-01
9.950001 E-01
9.998000E-01
1.015200E+00
1.020000E+00
1.025000E+00

69
1.200000E-02
1.290000E-02
2.595000E-02
3.350000E-02
3.500000E-02
3.747000E-02
4.470000E-02

3.700000E-06
1.400000E-06
2.300000E-06
9.500000E-07
1.400000E-06
5.600000E-06
6.600000E-06
5.200000E-06
3.700000E-06
4.000000E-06
2.100000E-06
2.100000E-05
4.400000E-06
1.300000E-06
1.000000E-06
5.400000E-07
1.240000E-05
8.999999E-06
1.000000E-06
2.300000E-05
2.300000E-06
2.300000E-06
3.500000E-05
2.300000E-06
2.600000E-06
7.200000E-06
1.210000E-05
2.000000E-06
3.700000E-06
9.500000E-07
8.000000E-07
3.500000E-06
2.600000E-07
4,000000E-06
3.100000E-06
1,900000E-06
2.600000E-07
1.800000E-07
1.500000E-06
3.200000E-05
2.100000E-07
1.600000E-07
9.000000E-08
1.400000E-07
9.600000E-07
8.400000E-07
1.900000E-06
1.400000E-07
4.700000E-07
9.000000E-08
4.000000E-07
2.100000E-07
2.600000E-07
2.100000E-07

8.200000E-04
8.000000E-08
6.100000E-09
1.200000E-06
3.000000E-07
3.000000E-08
1.200000E-06

TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227

AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A


5.106000E-02
5.232000E-02
5.370000E-02
5.500000E-02
5.580000E-02
5.756000E-02
5.940000E-02
6.060000E-02
6.928000E-02
7.060000E-02
7.250001E-02
7.954001E-02
8.220000E-02
8.300000E-02
8.323101E-02
8.500000E-02
8.610000E-02
8.610500E-02
8.670000E-02
8.810000E-02
8.850000E-02
9.000000E-02
9.681500E-02
9.747400E-02
9.960000E-02
1.002140E-01
1.010000E-01
1.050000E-01
1.068500E-01
1.080000E-01
1.187000E-01
1.216000E-01
1.345000E-01
1.374000E-01
1.409000E-01
1.430000E-01
1.436500E-01
1.460000E-01
1.476100E-01
1.493000E-01
1.592000E-01
1.604900E-01
1.614000E-01
1.626000E-01
1.720000E-01
1.743000E-01
1.761000E-01
2.068000E-01
2.166000E-01
2.297000E-01
2.309000E-01
2.317900E-01
2.426000E-01
2.439000E-01
2.834000E-01
3.517000E-01
4.156000E-01
4.396000E-01
4.410000E-01
4.602000E-01
5.276000E-01
5.404000E-01

3.000000E-09
1.500000E-08
4.600000E-07
4.900000E-06
4.300000E-08
3.500000E-08
4.600000E-07
4.600000E-07
4.300000E-05
9.000000E-07
1.600000E-06
1.200000E-05
8.999999E-06
1.500000E-08
3.500000E-05
1.200000E-07
5.200000E-06
6.000000E-05
3.000000E-05
1.600000E-05
1.100000E-08
2.000000E-06
7.000000E-06
1.300000E-05
5.600000E-05
5.000000E-06
8.000000E-06
3.800000E-06
1.200000E-05
4.600000E-07
4.600000E-07
2.800000E-05
6.100000E-06
4.600000E-06
2.300000E-06
6.000000E-06
2.900000E-07
9.999999E-08
2.700000E-05
1.500000E-07
6.100000E-06
4.900000E-05
1.500000E-06
6.000000E-07
1.100000E-05
3.000000E-06
7.200000E-06
1.100000E-05
6.000000E-07
4.600000E-06
1.500000E-07
7.900000E-08
3.000000E-06
3.000000E-07
6.000000E-07
6.000000E-07
2.300000E-06
3.800000E-07
6.000000E-07
2.300000E-06
3.200000E-07
7.699999E-07

AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A
AC227A

37

11
1.170000E-02
8.106901E-02
8.378701E-02
9.424701 E-02
9.486800E-02
9.753000E-02
1.862110E-01
2.622700E-01
4.146000E-01
4.493700E-01
6.006600E-01

113
1.064200E-02
1.200000E-02
2.600000E-02
3.670000E-02
3.850000E-02
4.620000E-02
4.910000E-02
5.780000E-02
6.290001 E-02
6.430001E-02
6.987000E-02
7.140000E-02
7.350000E-02
7.390001E-02
7.460000E-02
7.880001 E-02
8.323101E-02
8.610500E-02
8.740000E-02
9.490000E-02
9.670001E-02
9.681 500E-02
9.747400E-02
9.960000E-02
9.980001 E-02
1.002140E-01
1.008000E-01
1.036000E-01
1.084000E-01
1.115000E-01
1.128000E-01
1.140000E-01
1.199000E-01
1.238000E-01
1.248000E-01
1.262000E-01
1.292000E-01
1.336000E-01
1.349000E-01
1.376000E-01
1.396000E-01
1.447000E-01
1.452000E-01
1.501000E-01
1.526000E-01
1.539000E-01
1.573000E-01
1.691000E-01
1.699000E-01

8.000000E-03
1.930000E-03
3.190000E-03
3.850000E-04
7.350000E-04
2.760000E-04
3.590000E-02
5.000000E-05
3.000000E-06
1.900000E-06
4.900000E-06

8.500000E-02
1.300000E-01
1.500000E-05
1.550000E-04
9.400000E-05
3.900000)
6.600000E-05
3.900000E-05
4.300000E-03
4.100000E-04
4.700000E-05
1.260000E-04
2.500000E-04
2.640000E-03
2.200000E-04
1.070000E-04
7.500000E-03
1.230000E-02
2.260000E-03
8.400000E-04
2.800000E-04
1.500000E-03
2.900000E-03
7.000000E-03
1.000000E-02
1.080000E-03
7.500000E-04
2.300000E-05
2.160000E-03
2.640000E-03
1.800000E-05
7.500000E-06
6.600000E-04
7.200000E-04
2.400000E-04
7.000000E-05
2.200000E-05
1.700000E-04
2.700000E-04
1.900000E-05
1.200000E-05
4.000000E-06
1.260000E-03
6.000000E-03
1.900000E-04
1.820000E-03
3.200000E-03
7.000000E-05
1.200000E-04

RA226
RA226
RA226
RA226
RA226
RA226
RA226
RA226
RA226
RA226
RA226

AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225
AC225


3.078500E-01 5.500000E-08 PU239 6.708000E-01 8.999999E-11 PU239

3.117800E-01 2.580000E-07 PU239 6.709900E-01 8.999999E-11 PU239
3.164100E-01 1.320000E-07 PU239 6.740500E-01 5.150000E-09 PU239
3.196800E-01 4.800000E-08 PU239 6.744000E-01 5.150000E-09 PU239
3.208620E-01 5.420000E-07 PU239 6.908100E-01 9.000000E-09 PU239
3.238400E-01 5.390000E-07 PU239 6.932001E-01 2.000000E-10 PU239
3.328450E-01 4.940000E-06 PU239 6.978000E-01 7.400000E-10 PU239
3.361130E-01 1.120000E-06 PU239 7.011000E-01 5.120000E-09 PU239
3.415060E-01 6.620000E-07 PU239 7.036800E-01 3.950000E-08 PU239
3.450130E-01 5.560000E-06 PU239 7.147101E-01 7.900000E-10 PU239
3.450140E-01 3.000000E-07 PU239 7.180001E-01 2.800000E-08 PU239
3.540000E-01 7.000000E-09 PU239 7.203000E-01 4.900000E-10 PU239
3.618900E-01 1.220000E-07 PU239 7.279001E-01 1.240000E-09 PU239
3.670730E-01 8.900000E-07 PU239 7.365000E-01 3.000000E-10 PU239
3.685540E-01 8.800000E-07 PU239 7.474000E-01 8.100000E-10 PU239
3.750540E-01 1.554000E-05 PU239 7.564000E-01 3.470000E-08 PU239
3.801910E-01 3.050000E-06 PU239 7.626000E-01 9.999999E-11 PU239
3.827500E-01 2.590000E-06 PU239 7.636000E-01 2.200000E-10 PU239
3.925300E-01 2.050000E-06 PU239 7.664700E-01 1.300000E-09 PU239
3.931400E-01 3.500000E-06 PU239 7.672900E-01 1.400000E-09 PU239
3.995300E-01 5.900000E-08 PU239 7.691501E-01 5.100000E-08 PU239
4.068000E-01 2.500000E-08 PU239 7.693700E-01 6.800000E-08 PU239
4.112000E-01 7.000000E-08 PU239 7.695400E-01 8.000000E-10 PU239
4.123000E-01 1.800000E-10 PU239 7.794001E-01 1.360000E-09 PU239
4.137130E-01 1.466000E-05 PU239 7.929001E-01 2.000000E-10 PU239
4.225980E-01 1.220000E-06 PU239 8.059000E-01 2.700000E-10 PU239
4.266800E-01 2.330000E-07 PU239 8.084000E-01 1.210000E-09 PU239
4.284000E-01 1.000000E-08 PU239 8.137001E-01 4.500000E-10 PU239
4.300800E-01 4.300000E-08 PU239 8.160000E-01 2.400000E-10 PU239
4.457200E-01 8.799999E-08 PU239 8.213000E-01 5.500000E-10 PU239
4.514810E-01 1.894000E-06 PU239 8.325000E-01 2.960000E-10 PU239
4.576100E-01 1.490000E-08 PU239 8.404000E-01 4.800000E-10 PU239
4.612500E-01 2.270000E-08 PU239 8.437800E-01 1.340000E-09 PU239
4.639000E-01 2.800000E-09 PU239 8.792000E-01 3.600000E-10 PU239
4.739000E-01 5.000000E-10 PU239 8.910000E-01 7.500000E-10 PU239
4.816600E-01 4.600000E-08 PU239 9.187000E-01 7.999999E-11 PU239
4.870600E-01 2.650000E-09 PU239 9.403000E-01 5.000000E-10 PU239
4.930800E-01 8.700000E-09 PU239 9.556000E-01 3.100000E-10 PU239
5.264000E-01 5.700000E-10 PU239 9.576000E-01 3.200000E-10 PU239
5.505000E-01 4.200000E-09 PU239 9.683700E-01 2.800000E-10 PU239
5.794001E-01 8.600000E-10 PU239 9.797001E-01 2.800000E-10 PU239
5.828900E-01 6.150000E-09 PU239 9.869001E-01 2.100000E-10 PU239
5.863000E-01 1.530000E-09 PU239 9.927000E-01 2.700000E-10 PU239
5.960000E-01 3.900000E-10 PU239 1.005700E+00 1.800000E-10 PU239
5.979900E-01 1.670000E-08 PU239 1.057300E+00 4.500000E-10 PU239
5.996000E-01 2.000000E-09 PU239

6.069000E-01 1.200000E-09 PU239 36

6.128300E-01 9.500000E-09 PU239 1.360000E-02 1.020000E-01 PU238
6.171000E-01 1.340000E-08 PU239 4.349800E-02 3.920000E-04 PU238
6.182801E-01 2.040000E-08 PU239 6.270000E-02 5.000000E-11 PU238
6.192101E-01 1.210000E-08 PU239 9.465400E-02 5.790000E-07 PU238
6.247801E-01 4.370000E-09 PU239 9.843400E-02 9.249999E-07 PU238
6.331500E-01 2.530000E-08 PU239 9.985300E-02 7.290000E-05 PU238
6.377000E-01 2.560000E-08 PU239 1,104210E-01 1.160000E-07 PU238
6.378000E-01 2.560000E-08 PU239 1.112980E-01 2.200000E-07 PU238
6.399900E-01 8.700000E-08 PU239 1.144450E-01 8.520000E-08 PU238
6.459400E-01 1.520000E-07 PU239 1.401500E-01 9.999999E-12 PU238
6.493201E-01 7.100000E-09 PU239 1.527200E-01 9.289999E-06 PU238
6.520500E-01 6.600000E-08 PU239 1.929100E-01 6.400000E-12 PU238
6.548800E-01 2.250000E-08 PU239 2.009700E-01 3.900000E-08 PU238
6.588600E-01 9.700000E-08 PU239 2.031200E-01 4.000000E-11 PU238
6.645800E-01 1.660000E-08 PU239 2.359000E-01 9.999999E-11 PU238
6.682000E-01 3.900000E-10 PU239 2.583000E-01 8.400000E-10 PU238

25


Calculations of Fluence Rates of Unscattered X- and Gamma-Ray Photons Emerging
From Model Spheres of Special Nuclear Material

Stephen M. Seltzer
Ionizing Radiation Division
National Institute of Standards and Technology
Gaithersburg, MD 20899

ABSTRACT

Calculations have been done to develop estimates of the fluence rate of unscattered x and
gamma rays emerging from two model spheres of special nuclear material: one of uranium
enriched to 93.5 % (mass fraction) of 7°U; one of plutonium enriched to 6.0 % (mass fraction)
of °Pu.

Key Words: fluence rate; photons; plutonium; radionuclides; spheres; uranium

Introduction

This report describes calculations to estimate the fluence rates of unscattered x and
gamma rays emerging from spheres of special nuclear material. The results reported here are
based on models with the following major parameters: (1) a 1 kg sphere of uranium originally
enriched to 93.5 % (mass fraction) of °U and assumed to be 50 y old; and (2) a 0.5 kg sphere
of plutonium originally enriched to 6 % (mass fraction) of “°Pu and assumed to be up to 50 y
old. The calculations focus on the fluence rate of the emergent unscattered x- and gamma-ray
lines at a distance of | m from the center of the spheres, assumed to be surrounded by air. Thus
the reported results pertain to the discrete line energies in the spectrum of emergent photons.

Method of Calculation

The assumed original compositions of the spheres are listed in Table 1. Note that the
mass densities of actual spheres could be slightly lower (see, e.g., Sapir et al. (1998)), perhaps
by about 1 % or more. However, such a difference will have a negligible effect on the results
calculated here, as the transport of the photons in such spheres to a point 1 m from the center is
essentially governed only by the mass of the sphere. That is, the absorption and scattering
depends on the product of attenuation coefficients and pathlengths, and this product (number of
mean-free paths) is independent of the density. For the assumed spherically symmetric
geometry, even a 3 % change in mass density results in a change of only 1 % in the radius of
the sphere, and such a change compared to the 1 m radius of the scoring surface is expected to
produce negligible effects.


7
1.030000E-02 9.600000E-03
7.083201E-02 7.340000E-03
7.287300E-02 1.230000E-02
8.211500E-02 1.490000E-03
8.257400E-02 2.850000E-03
8.486500E-02 1.038000E-03
3.510600E-01 1.292000E-01

29

1.080000E-02 5.100000E-03
6.542000E-02 7.700000E-04
7.481501E-02 2.260000E-03
7.710700E-02 3.760000E-03
8.683001E-02 4.550000E-04
8.734901E-02 8.699999E-04
8.978400E-02 3.200000E-04
9.500001E-02 1.800000E-04
3.135900E-01 3.100000E-04
3.429100E-01 3.500000E-04
3.620720E-01 4.300000E-04
4.048530E-01 3.780000E-02
4.270880E-01 1.760000E-02
4.300000E-01 6.000000E-05
5.041200E-01 5.800000E-05
6.093800E-01 4.300000E-04
6.766900E-01 1.300000E-04
7.046400E-01 4.620000E-03
7.665101E-01 6.169999E-03
8.320100E-01 3.520000E-02
8.659300E-01 5.900000E-05
9.510000E-01 2.200000E-04
1.014640E+00 1.730000E-04
1.080160E+00 1.230000E-04
1.103520E+00 4.600000E-05
1.109480E+00 1.150000E-03
1.196330E+00 1.020000E-04
1.234300E+00 1.300000E-05
1.270710E+00 6.800000E-05

7
1.060000E-02 3.820000E-08
7.280500E-02 2.710000E-08
7.496901E-02 4.520000E-08
8.445000E-02 5.460000E-09
8.493800E-02 1.050000E-08
8.730001E-02 3.830000E-09
8.031000E-01 1.210000E-05

2
1.080000E-02 2.360000E-01
4.653900E-02 4.250000E-02

22

1.060000E-02 1.900000E-01
7.280500E-02 2.300000E-02
7.496901E-02 3.800000E-02
8.300000E-02 2.000000E-02
8.445000E-02 4.600000E-03
8.493800E-02 8.800000E-03
8.730001E-02 3.200000E-03
9.700000E-02 4.000000E-02
2.960000E-01 7.900000E-01

BI211A
BI211A
BI211A
BI211A
BI211A
BI211A
BI211A

PB211
PB211
PB211
PB211
PB211
PB211
PB211
PB211
PB211
PB211
PB211
PB211
PB211
PB211
PB211
PB211
PB211
PB211
PB211
PB211
PB211
PB211
PB211
PB211
PB211
PB211
PB211
PB211
PB211

PO210
PO210
PO210
PO210
PO210
PO210
PO210

PB210
PB210

TL210
TL210
TL210
TL210
TL210
TL210
TL210
TL210
TL210

44

4.800000E-01 2.000000E-02
7.996000E-01 9.895999E-01
8.600000E-01 6.900000E-02
1,070000E+00 1.200000E-01
1.110000E+00 6.900000E-02
1.210000E+00 1.700000E-01
1.316000E+00 2.100000E-01
1.410000E+00 4.900000E-02
1.590000E+00 2.000000E-02
2.010000E+00 6.900000E-02
2.270000E+00 3.000000E-02
2.360000E+00 8.000000E-02
2.430000E+00 9.000000E-02

11
1.060000E-02 8.700000E-02
7.280500E-02 6.210000E-02
7.496901E-02 1.040000E-01
8.445000E-02 1.250000E-02
8.493800E-02 2.400000E-02
8.730001E-02 8.800000E-03
1.172110E-01 8.430000E-01
4.651300E-01 9.690000E-01
9.201301E-01 6.100000E-03
1.239160E+00 4.600000E-03
1.567090E+00 9.980000E-01

37

1,060000E-02 2.750000E-02
7.280500E-02 2.010000E-02
7.496901E-02 3.350000E-02
8.445000E-02 4.040000E-03
8.493800E-02 7.760000E-03
8.730001E-02 2.830000E-03
2.114000E-01 1.800000E-03
2.333600E-01 3.100000E-03
2.526100E-01 7.799999E-03
2.773710E-01 6.600000E-02
4.859500E-01 4.899999E-04
5.107700E-01 2.260000E-01
5.831870E-01 8.500000E-01
5.877001E-01 6.000000E-04
6.501000E-01 5.000000E-04
7.052000E-01 2.200000E-04
7.220400E-01 2.400000E-03
7.487000E-01 4.600000E-04
7.631301E-01 1.790000E-02
8.212001E-01 4.100000E-04
8.605570E-01 1.250000E-01
8.833000E-01 3.100000E-04
9.276000E-01 1.250000E-03
9.827000E-01 2.050000E-03
1.093900E+00 4.300000E-03
1,125700E+00 5.000000E-05
1,160800E+00 1.100000E-04
1.185200E+00 1.700000E-04
1.282800E+00 5.200000E-04
1.381100E+00 7.000000E-05
1,647500E+00 2.000000E-05
1.744000E+00 2.000000E-05
2.614511E+00 9.975399E-01
3.197700E+00 4.000000E-05
3.475100E+00 1.500000E-05

TL210

TL210

TL210

TL210
TL210
TL210
TL210
TL210
TL210
TL210
TL210
TL210
TL210

TL209
TL209
TL209
TL209
TL209
TL209
TL209
TL209
TL209
TL209
TL209

TL208
TL208
TL208
TL208
TL208
TL208
TL208
TL208
TL208
TL208
TL208
TL208
TL208
TL208
TL208
TL208
TL208
TL208
TL208
TL208
TL208
TL208
TL208
TL208
TL208
TL208
TL208
TL208
TL208
TL208
TL208
TL208
TL208
TL208
TL208


1.155600E+00
1.156000E+00
1.167300E+00
1.172980E+00
1.207680E+00
1.226700E+00
1.230600E+00
1.238110E+00
1.279000E+00
1.280960E+00
1.284000E+00
1.285100E+00
1.303760E+00
1.316960E+00
1.330000E+00
1.341490E+00
1.377669E+00
1.3853 10E+00
1.392500E+00
1.401500E+00
1.407980E+00
1.415800E+00
1.419700E+00
1.470900E+00
1.479150E+00
1.509228E+00
1.515500E+00
1.538500E+00
1.543320E+00
1.583220E+00
1.594730E+00
1.595000E+00
1.598000E+00
1.5993 10E+00
1.636300E+00
1.637000E+00
1.657000E+00
1.661280E+00
1.665800E+00
1.683990E+00
1.711000E+00
1.729595E+00
1.751400E+00
1.764494E+00
1.813730E+00
1.819200E+00
1.838360E+00
1.847420E+00
1.873160E+00
1.890300E+00
1.895920E+00
1.898700E+00
1.935500E+00
1.994600E+00
2.010780E+00
2.016700E+00
2.021600E+00
2.052940E+00
2.085100E+00
2.089700E+00
2.109920E+00
2.118550E+00
2.120000E+00

1.600000E-04
7.000000E-05
1.200000E-04
5.100000E-04
4.510000E-03
1.800000E-04
1.500000E-04
5.790000E-02
1.200000E-04
1.430000E-02
1.100000E-04
1.700000E-04
1.120000E-03
8.000000E-04
1.100000E-04
2.200000E-04
4.000000E-02
7.570000E-03
1.900000E-04
1.270000E-(
2.150000E-02
4.810000E-03
5.100000E-05
9.200000E-05
5.100000E-04
2.110000E-02
6.899999E-05,
3.760000E-03
2.000000E-03
6.900000E-03
2.500000E-03
5,000000E-05
6.000000E-05
2.300000E-03
1.200000E-04
6.000000E-05
4.600000E-04
1.150000E-02
8.300000E-05
2.160000E-03
1.800000E-05
2.920000E-02
8.999999E-06
1.540000E-01
1.100000E-04
7.000000E-06
3.600000E-03
2.110000E-02
2.190000E-03
8.000000E-04
1.600000E-03
5.700000E-04
4.100000E-04
5.000000E-05
4.700000E-04
6.000000E-05
2,000000E-04
6.900000E-04
9.100000E-05
5.000000E-04
8.799999E-04
1.140000E-02
7.000000E-05

BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B

42

2.147900E+00 1.400000E-04
2.160400E+00 1.800000E-05
2.176500E+00 3.200000E-05
2.192580E+00 3.400000E-04
2.204210E+00 5.080000E-02
2.251600E+00 5.500000E-05
2.260300E+00 8.700000E-05
2.266510E+00 1.800000E-04
2.270900E+00 1.300000E-05
2.284300E+00 5.100000E-05
7650E+00 4.600000E-05
.293400E+00 3.050000E-03
2.310200E+00 1.400000E-05
2.312400E+00 8.999999E-05
2.319300E+00 4.000000E-06
2.325000E+00 1.700000E-05
2.331300E+00 2.210000E-04
2.348000E+00 1.400000E-06
2.353500E+00 4.000000E-06
2.361000E+00 1.700000E-05
2.369000E+00 2.700000E-05
2.376900E+00 8.800000E-05
2.390800E+00 1.600000E-05
2.405100E+00 4.100000E-06
2.423270E+00 4.600000E-05
2.444700E+00 8.000001E-05
2.447860E+00 1.570000E-02
2.482800E+00 1.500000E-05
2.505400E+00 5.700000E-05
2.550700E+00 4.600000E-06
2.553000E+00 1.000000E-06
2.562000E+00 1.800000E-06
2.564000E+00 1.400000E-06
2.604500E+00 4.000000E-06
2.630900E+00 8.000000E-06
2.662400E+00 3.000000E-06
2.694700E+00 3.100000E-04
2.699400E+00 2.800000E-05
2.719300E+00 1.800000E-05
2.769900E+00 2.500000E-04
2.785900E+00 5.500000E-05
2.827000E+00 2.300000E-05
2.861100E+00 3.800000E-06
2.880300E+00 9.200000E-05
2.893500E+00 6.000000E-05
2.921900E+00 1.400000E-04
2.928600E+00 1.100000E-05
2.934600E+00 4.600000E-06
2.978900E+00 1.380000E-04
3.000000E+00 8.800000E-05
3.053900E+00 2.100000E-04
3.081700E+00 4.800000E-05
3.094000E+00 4.400000E-06
3.142600E+00 1.200000E-05
3.149000E+00 8.800000E-07
3.160600E+00 3.200000E-06
3.183600E+00 1.290000E-05

30

1.080000E-02 1.330000E-01
5.322750E-02 1.200000E-02
7.481501E-02 6.330000E-02
7.710700E-02 1.050000E-01

BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B
BI214B

PB214
PB214
PB214
PB214


Table 3. Fluence from photons of energy £ at 1 m in air for the U and Pu spheres. Given are
the fluence of the unscattered emergent source photons, ®,(£), the associated fluence of
emergent annihilation quanta, ®p.2(0.511 MeV), and the fluences of emergent K-shell
characteristic x rays, ®xgi(Expi), Pxa(Ekai), and Pxa2(Eka2). The fluences are given in units of
cm”, normalized to one source photon emitted uniformly and isotropically in the sphere.

b. Pu sphere. The energies of the x-ray lines are: Exgi=0.11723 MeV,
Exai=0.1037 MeV, and Ex2=0.09953 MeV.

E/MeV PDJ/omTM | Pmeo/emTM | Pxgi/emTM | Pxa/emTM | Pxe2/emTM
4.0 3.08E-06 3.60E-07 6.53E-09 9.79E-09 5.51E-09
3.5 3.08E-06 3.11E-07 6.25E-09 9.49E-09 5.20E-09
3.0 3.05E-06 2.56E-07 6.02E-09 8.84E-09 5.10E-09
2.5 3.00E-06 1.92E-07 5.76E-09 8.77E-09 4.80E-09
2.0 2.87E-06 1.16E-07 5.77E-09 8.36E-09 4.85E-09
1.5 2.59E-06 3.61E-08 5.84E-09 8.76E-09 4.94E-09
1.0 1.95E-06 0 6.95E-09 1,05E-08 5.94E-09
0.8 1.57E-06 0 8.00E-09 1.19E-08 6.76E-09
0.6 1.09E-06 0 9.03E-09 1.39E-08 7.16E-09
0.5 8.23E-07 0 9.99E-09 1.49E-08 8.49E-09
0.4 5.61E-07 0 1.08E-08 1.64E-08 9.23E-09
0.3 3.13E-07 0 1.24E-08 1.84E-08 1.04E-08
0.2 1.24E-07 0 1.44E-08 2.15E-08 1.21E-08
0.15 6.15E-08 0 1.54E-08 2.37E-08 1.33E-08
0.122 3.69E-08 0 1.55E-08 2.45E-08 1.38E-08
0.121 1.40E-07 0 0 0 0

0.1 8.71E-08 0 0 0 0

0.08 TA4E-09 0 0 0 0

0.06 1.69E-09 0 0 0 0

0.05 6.59E-10 0 0 0 0

0.04 2.13E-10 0 0 0 0

0.03 4.86E-11 0 0 0 0

12


Results

The final stage is to combine our results as the product of the calculated activities in
Table 2, the inherent emission probabilities in Appendix A, and interpolated values of the
unscattered emergent probabilites in Table 3. Because of the large number of photons emitted
by the radionuclides involved, even considering only those with energies above 30 keV leads to
1182 lines from the U sphere and 2490 lines from the Pu sphere. Complete results are available
from the author in the form of lists of energy-fluence-rate pairs for each assumed sphere and
age, ordered either in increasing photon energy or in decreasing fluence rate.

In an effort to communicate the scale of the results, Figs. 3 and 4 plot the unscattered
fluence rates for 50-year-old spheres, simply as points, over about 6 orders of magnitude. Note
that these plots are not estimates of detector pulse-height distributions, because the effects of
background, detector efficiency and resolution, and counting statistics are not included. Rather
the points simply represent the fluence rates of the discrete line energies. The plots indicate the
level of fluence rates obtained, and perhaps identify a few of the more-prominent lines.
However, any interpretation in terms of detectability should take into account the possible
overlap of lines close in energy, due to the inherent spreading of these lines by the detector
resolution and response function, and the influences of counting statistics, contributions from
source photons scattered in the spheres and from emergent bremsstrahlung, and contributions of
environmental sources.

The higher fluence rates are listed in Table 4, in order of descending fluence rate. There
are negligible differences in these fluence rates for the 235Uy (93.5 %) sphere of ages 10 y, 25 y,
and 50 y (Table 4a). However, the decay dynamics of the “Pu (6.0 %) sphere show a bit more
complexity, and separate tables are given for ages of 50 y (Table 4b), 25 y (Table 4c), and 10 y
(Table 4d).

14




1.738220E+00 1.800000E-04
1.740400E+00 1.100000E-04
1.742000E+00 8.000001E-05
1.750540E+00 8.000001E-05
1.758110E+00 3.500000E-04
1.772200E+00 1.800000E-05
1.795100E+00 2.100000E-05
1.797500E+00 2.100000E-05
1.800860E+00 4.400000E-05
1.823220E+00 4.400000E-04
1.826700E+00 2.100000E-05
1.835430E+00 3.800000E-04
1.842130E+00 4.200000E-04
1.850130E+00 4.400000E-05
1.870830E+00 2.430000E-04
1.879600E+00 1.300000E-05
1.887100E+00 9.000000E-04
1.900070E+00 2.800000E-05
1,907180E+00 1.190000E-04
1.929780E+00 1.990000E-04
1.936300E+00 2.100000E-05
1.952330E+00 5.900000E-04
1.955900E+00 8.000000E-06
1.958400E+00 1.500000E-05
1.965240E+00 2.040000E-04
1.971900E+00 3.600000E-05
1.979300E+00 1.800000E-05
2.029400E+00 1.800000E-05

5
6.280000E-03 1.410000E-08
6.670000E-03 3.100000E-07
1.275000E-02 3.100000E-03
1.352000E-02 1.550000E-02
2.640000E-02 1.400000E-04

206

6.500000E-03 1.200000E-03
8.150000E-03 1.000000E-04
2.025000E-02 3.200000E-03
2.960000E-02 7.000000E-05
2.986000E-02 1.030000E-03
3.158000E-02 9.300000E-04
3.339000E-02 1.000000E-04
4.020000E-02 2.100000E-04
4.193000E-02 3.900000E-04
4.377000E-02 2.900000E-03
4.380000E-02 8.000000E-04
4.422000E-02 7.200000E-04
4.440000E-02 2.200000E-04
4.830000E-02 1.900000E-04
4.982000E-02 5.800000E-03
5.013000E-02 1.140000E-01
5.085000E-02 2.100000E-04
5.419000E-02 9.570000E-05
5.600000E-02 6.699999E-05
5.642000E-02 1.200000E-04
6.144100E-02 1.220000E-03
6.245000E-02 5.400000E-03
6.268001E-02 1.000000E-04
6.435000E-02 3.500000E-04
6.874000E-02 1.580000E-03
6.980000E-02 1.400000E-04

AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228
AC228

RA228
RA228
RA228
RA228
RA228

TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227

35

7.285000E-02
7.363000E-02
7.501001E-02
7.969001 E-02
8.543 100E-02
8.847100E-02
8.960000E-02
9.388001E-02
9.497000E-02
9.603000E-02
9.943201E-02
9.958000E-02
9.960000E-02
1.001300E-01
1.002700E-01
1.024980E-01
1.025000E-01
1.077600E-01
1.092000E-01
1.106500E-01
1.131100E-01
1.172000E-01
1.235800E-01
1.244400E-01
1.346000E-01
1.414200E-01
1.501400E-01
1.621900E-01
1.683600E-01
1.699500E-01
1.734500E-01
1.758000E-01
1.846500E-01
1.975600E-01
2.005000E-01
2.016400E-01
2.041400E-01
2.049800E-01
2.060800E-01
2.106200E-01
2.127000E-01
2.189000E-01
2.255000E-01
2.299000E-01
2.347600E-01
2.359600E-01
2.461200E-01
2.496000E-01
2.501500E-01
2.502700E-01
2.525000E-01

2.670500E-01
2.678600E-01
2.705600E-01
2.729100E-01
2.798000E-01
2.807000E-01
2.814200E-01
2.842400E-01
2.855200E-01

3.000000E-04
1,900000E-04
3.700000E-04
2.640000E-02
1.810000E-02
2.960000E-02
5.200000E-05
2.050000E-02
6.600000E-04
9.500000E-04
3.620000E-03
3.500000E-04
1.750000E-04
6.900000E-03
1.140000E-03
2.620000E-03
1.570000E-05
2.000000E-04
7.200000E-05
4.000000!
9.500000E-03
2.700000E-03
1.900000E-04
6.000000E-05
4,600000E-04
3.200000E-03
1,500000E-04
1.000000E-04
2.000000E-04
8.000001E-05
2.400000E-04
2.800000E-04
4.899999E-04
1.700000E-04
1.700000E-04
3.200000E-04
3.100000E-03
2.200000E-03
3.400000E-03
1.700000E-02
1.330000E-03
2.980000E-03
1.200000E-04
5.200000E-05
6.100000E-03
1.750000E-01
1.660000E-04
1.000000E-04
1.210000E-04
6.100000E-03
1.510000E-03
9.600000E-03
9.500000E-02
1.450000E-03
1.400000E-04
1.000000E-04
3.900000E-04
6.900000E-03
7.400000E-04
3.500000E-05
4,820000E-03
5.400000E-04
6.000000E-04

TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227
TH227


Appendix A

The following lists the photon emission data assumed for the relevant radionuclide
decay. Photon energies below | keV are not shown nor were considered. Radionuclides not
listed have no photon emission. Each listing gives the number of lines, followed by a table: of
photon energy in MeV, emission probability per decay, and the radionuclide designator (an A

or B indicates o or B emission, respectively).
2.467300E-01 2.400000E-08 AM241

9 2.490000E-01 5.400000E-09 AM241
1.360000E-02 8.500000E-02 PU242 2.608000E-01 1.210000E-08 AM241
4.491500E-02 3.730000E-04 PU242 2.648900E-01 9.000000E-08 AM241
9.465400E-02 1.810000E-07 PU242 2.675800E-01 2.630000E-07 AM241
9.843400E-02 2.890000E-07 PU242 2.757700E-01 6.600000E-08 AM241
1.035000E-01 2.550000E-05 PU242 2.780400E-01 4.400000E-09 AM241
1,104210E-01 3.600000E-08 PU242 2.913000E-01 3.100000E-08 AM241
1.112980E-01 6.900000E-08 PU242 2.927700E-01 1.420000E-07 AM241
1.144450E-01 2.660000E-08 PU242 3.042100E-01 1.010000E-08 AM241
1.588000E-01 3.000000E-06 PU242 3.091000E-01 1.400000E-08 AM241
3.168000E-01 3.000000E-10 AM241

110 3.225200E-01 1.520000E-06 AM241
1.390000E-02 3.700000E-01 AM241 3.323500E-01 1.490000E-06 AM241
2.634460E-02 2.270000E-02 AM241 3.353700E-01 4.960000E-06 AM241
3.319600E-02 1.260000E-03 AM241 3.377000E-01 4.290000E-08 AM241
4.270400E-02. 5.500000E-05 AM241 3.582500E-01 1.200000E-08 AM241
4.342000E-02 7.300000E-04 AM241 3.686500E-01 2.170000E-06 AM241
5.101000E-02 2.600000E-07 AM241 3.709400E-01 5.230000E-07 AM241
56000E-02 1.810000E-04 AM241 3.766500E-01 1.380000E-06 AM241
5.954091E-02 3.590000E-01 AM241 3.838100E-01 2.820000E-07 AM241
6.483001E-02 1.450000E-06 AM241 3.986400E-01 2.000000E-08 AM241
6.745000E-02 4.200000E-06 AM241 4.013000E-01 4.900000E-09 AM241
6.976000E-02 2.900000E-05 AM241 4.063500E-01 1.450000E-08 AM241
7.580001E-02 5.900000E-06 AM241 4.193300E-01 2.870000E-07 AM241
9.706900E-02 1.140000E-05 AM241 4.264700E-01 2.460000E-07 AM241
9897000E-02 2.030000E-04 AM241 4.464300E-01 4.900000E-09 AM241
1.010590E-01 1.810000E-05 AM241 4.526000E-01 2.400000E-08 AM241
1029800E-01 1.950000E-04 AM241 4.546600E-01 9.700000E-08 AM241
1.097000E-01 4.900000E-08 AM241 4.596800E-01 3.600000E-08 AM241
1.133030E-01 2.270000E-06 AM241 4.632200E-01 1.000000E-08 AM241
1.142340E-01 4.300000E-06 AM241 4.681200E-01 2.880000E-08 AM241
1.174630E-01 1.680000E-06 AM241 4.873000E-01 4.400000E-09 AM241
1.203600E-01 4.500000E-08 AM241 5.125000E-01 1.150000E-08 AM241
1.230520E-01 1.000000E-05 AM241 5.140000E-01 2.600000E-08 AM241
1.253000E-01 4.080000E-05 AM241 5.220600E-01 1.000000E-08 AM241
1.394400E-01 5.300000E-08 AM241 5.291700E-01 4.600000E-09 AM241
1.465500E-01 4.610000E-06 AM241 5.454000E-01 7.400000E-09 AM241
1.500400E-01 7.400000E-07 AM241 5.630500E-01 7.400000E-09 AM241
1.542700E-01 5.400000E-09 AM241 5.739400E-01 1.250000E-08 AM241
1.592600E-01 1.400000E-08 AM241 5.865901E-01 1.310000E-08 AM241
1.615400E-01 1.500000E-08 AM241 5.902801E-01 2.860000E-08 AM241
1.646900E-01 6.670000E-07 AM241 5.974800E-01 7.400000E-08 AM241
1.658100E-01 2.320000E-07 AM241 6.190100E-01 5.940000E-07 AM241
1.695600E-01 1.730000E-06 AM241 6.271800E-01 5.600000E-09 AM241
1.750700E-01 1.820000E-07 AM241 6.329300E-01 1.260000E-08 AM241
1.919600E-01 2.160000E-07 AM241 6.414700E-01 7.100000E-08 AM241
1.970000E-01 4.900000E-09 AM241 6.530200E-01 3.770000E-07 AM241
2.040600E-01 2.900000E-08 AM241 6.624001E-01 3.640000E-06 AM241
2.080100E-01 7.910000E-06 AM241 6.665000E-01 4.900000E-09 AM241
14600E-01 4.240000E-07 AM241 6.698300E-01 3.800000E-09 AM241
2.328100E-01 4.600000E-08 AM241 6.760300E-01 6.400000E-09 AM241
2.343300E-01 7.000000E-09 AM241 6.801000E-01 3.130000E-08 AM241

23


NISTIR 7557

CALCULATIONS OF FLUENCE RATES OF
UNSCATTERED X- AND GAMMA-RAY PHOTONS
EMERGING FROM MODEL SPHERES OF
SPECIAL NUCLEAR MATERIAL

Stephen Seltzer

National Institute of Standards and Technology
Gaithersburg, MD 20899

January 2009

U.S. DEPARTMENT OF COMMERCE
Carlos M. Gutierrez, Secretary

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY
Patrick Gallagher, Deputy Director


4.005000E-01
4.029000E-01
4.045000E-01
4.100000E-01
4.143000E-01
4.157640E-01
4.270000E-01
4.328000E-01
4.351000E-01
4.411000E-01
4.542000E-01
4.559600E-01
4.636000E-01
4.71 1000E-01
4.738000E-01
4.756000E-01
4.780000E-01
4.969000E-01
5.037000E-01
5.063000E-01

8
1.230000E-02
6.381001E-02
8.543100E-02
8.847100E-02
9.943201 E-02
1.001300E-01
1.024980E-01
1.408800E-01

75
1.270000E-02
1.650000E-02
1.900000E-02
2.360000E-02
2.450000E-02
2.551000E-02
2.736000E-02
2.996000E-02
3.583000E-02
3.819000E-02
4.415000E-02
4.635000E-02
5.090000E-02
5.273000E-02
5.460000E-02
5.719000E-02
6.050000E-02
6.365000E-02
7.190000E-02
7.272001E-02
7.415000E-02
7.734000E-02
8.767501E-02
9.088600E-02
9.684000E-02
1.008400E-01
1.021010E-01
1.026000E-01
1.028410E-01
1.057380E-01
1.245800E-01

3.100000E-05
2.300000E-05
3.500000E-05
6.899999E-05
5.400000E-05
1.730000E-02
1.900000E-05
8.000000E-06
1.200000E-05
1.900000E-05
2.400000E-05
1.100000E-05
8.000000E-06
1.200000E-05
1.900000E-05
1.900000E-05
1.200000E-05
1.200000E-05
1.200000E-05
1.200000E-05

7.099999E-02
2.630000E-03
1.700000E-05
2.800000E-05
3.400000E-06
6.400000E-06
2.400000E-06
2.100000E-04

3.150000E-01
3.000000E-03
3.800000E-03
4.700000E-05
5.100000E-05
1.170000E-03
1.030000E-01
1.090000E-03
1.620000E-04
1.600000E-03
6.499999E-04
2.230000E-03
1.550000E-05
8.500000E-04
7.700000E-04
2.990000E-04
6.500000E-05
5.000000E-04
1.900000E-05
3.700000E-05
2.400000E-04
7.300000E-04
7.500000E-03
1.220000E-02
9.500000E-04
3.000000E-04
1.500000E-03
7.000000E-05
2.860000E-03
1.090000E-03
4.800000E-05

PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233
PA233

TH232
TH232
TH232
TH232
TH232
TH232
TH232
TH232

PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231

31

1.443900E-01
1.988900E-01
2.300000E-01
2.430800E-01
2.456000E-01
2.460400E-01
2.557700E-01
2.584400E-01
2.601900E-01
2.731400E-01
2.773200E-01
2.836900E-01
3.000700E-01
3.026500E-01
3.129200E-01
3.271300E-01
3.300600E-01
3.407400E-01
3.515100E-01
3.544600E-01
3.571200E-01
3.593000E-01
3.638400E-01
3.793000E-01
3.847000E-01
3.870000E-01
3.916000E-01
3.955000E-01
3.981400E-01
4.078100E-01
4.103000E-01
4.270000E-01
4.350500E-01
4.380100E-01
4.868300E-01
4.910000E-01
5.014000E-01
5.097001E-01
5.161000E-01
5.358000E-01
5.467001E-01
5.718000E-01
5.830000E-01
6.090000E-01

55
9.200000E-03
1.025000E-02
1.330000E-02
1.720000E-02
1.910000E-02
2.564000E-02
4.286000E-02
4.408000E-02
5.857000E-02
6.386001 E-02
6.850000E-02
7.275100E-02
7.769001E-02
8.122800E-02
8.208700E-02
8.421400E-02

1.190000E-04
4.900000E-05
1.700000E-05
4.800000E-04
7.800000E-05
1.110000E-04
1.120000E-03
2.400000E-05
1.880000E-03
6.000000E-04
6.900000E-04
1.700000E-02
2.470000E-02
2.880000E-02
1.020000E-03
3.800000E-04
1.400000E-02
1.810000E-03
7.300000E-05
1.000000E-03
1.750000E-03
8.999999E-05
7.800000E-05
5.000000E-04
3.700000E-05
4.900000E-06
7.800000E-05
2.200000E-05
8.800000E-05
3.600000E-04
3.200000E-05
7.000000E-06
3.1 10000E-05
4.600000E-05
2.000000E-05
5.300000E-06
8.999999E-06
1.200000E-05
1.000000E-05
6.000000E-06
8.700000E-06
5.300000E-06
4.400000E-05
7.300000E-05

3.300000E-04
5.020000E-04
6.000000E-01
2.300000E-03
2.400000E-03
1.410000E-01
5.900000E-04
7.000000E-06
4.620000E-03
2.300000E-04
5.800000E-05
2.520000E-03
4.200000E-05
9.000000E-03
4.200000E-03
6.600000E-02

PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231
PA231

TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231
TH231


7.572001E-01 1.000000E-04
7.626000E-01 2.700000E-05
7.658000E-01 2.400000E-04
7.758300E-01 4.600000E-03
7.808000E-01 3.300000E-05
7.849301E-01 1.500000E-04
7.876000E-01 3.150000E-05
7.922000E-01 6.000000E-06
7.962200E-01 1.000000E-04
8.037701E-01 5.900000E-04
8.060001E-01 1.500000E-05
8.124000E-01 2.100000E-04
8.165001E-01 1.500000E-05
8.232000E-01 7.800000E-05
8.259500E-01 5.400000E-04
8.339000E-01 1.500000E-05
8.362001E-01 8.000001E-05
8.421900E-01 5.400000E-05
8.468601E-01 5.400000E-04
8.636000E-01 3.600000E-05
8.674001E-01 1.800000E-05
8.765001E-01 4.100000E-04
8.781000E-01 3.600000E-05
8.931000E-01 2.800000E-05
8.967100E-01 1.500000E-04
9.076100E-01 1.400000E-04
9.113000E-01 8.999999E-06
9.136000E-01 4.500000E-06
9.265000E-01 1.800000E-05
9.412001E-01 3.300000E-05
9.493001E-01 3.600000E-06
9.580001E-01 3.900000E-06
9.692001E-01 3.600000E-06
9.752001E-01 1.800000E-06
9.787000E-01 7.500000E-06
9.894001E-01 1.500000E-06
9.943000E-01 1.200000E-06
9.993001E-01 2.100000E-06

FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223
FR223

1.025100E+00 1.500000E-06 FR223

1
5.100001E-01 7.600000E-04

30
1.140000E-02 2.000000E-02
5.381000E-02 1.300000E-04
7.894800E-02 8.300000E-03
8.151700E-02 1.370000E-02
9.173001E-02 1.660000E-03
9.231500E-02 3.200000E-03
9.490000E-02 1.180000E-03
9.630001E-02 7.000000E-05
1.002500E-01 1.000000E-03
1.178200E-01 2.200000E-04
1.502100E-01 4.780000E-04
1.718300E-01 7.700000E-04
2.083000E-01 5.100000E-05
2.181200E-01 1.140000E-01
2.821200E-01 7.100000E-05
3.241000E-01 1.930000E-04
3.598600E-01 4.070000E-04
3.823400E-01 3.360000E-04
4.106400E-01 1.200000E-03

RN222

FR221
FR221
FR221
FR221
FR221
FR221
FR221
FR221
FR221
FR221
FR221
FR221
FR221
FR221
FR221
FR221
FR221
FR221
FR221

40

4.370000E-01 9.500000E-06
4.463000E-01 1.700000E-05
4.683000E-01 1.400000E-05
5.378000E-01 5.100000E-05
5.623000E-01 5.100000E-05
5.685000E-01 1.200000E-05
5.769001E-01 3.000000E-05
6.520000E-01 4.100000E-06
6.650000E-01 9.200000E-06
8.093000E-01 9.200000E-06
8.919001E-01 3.400000E-06

1
5.497300E-01 1.140000E-03

34

1.110000E-02 9.600000E-02
7.686301E-02 5.000000E-02
7.929000E-02 8.399999E-02
8.925600E-02 1.010000E-02
8.980700E-02 1.900000E-02
9.231701E-02 7.200000E-03
1.306000E-01 1.300000E-03
2.240000E-01 1.400000E-05
2.712300E-01 1.080000E-01
2.935600E-01 7.300000E-04
3.218000E-01 9.000000E-07
3.308000E-01 9.699999E-06
3.735000E-01 2.500000E-06
3.831000E-01 4.300000E-06
4.018100E-01 6.600000E-02
4.054000E-01 2.500000E-06
4.369000E-01 3.000000E-06
4.616000E-01 1.600000E-06
4.893000E-01 6.300000E-06
5.176000E-01 4.400000E-04
5.561000E-01 5.000000E-07
5.641000E-01 1.500000E-05
5.766000E-01 9.000000E-07
6.083000E-01 4.300000E-05
6.199000E-01 3.200000E-06
6.719000E-01 2.200000E-06
6.766600E-01 1.730000E-04
7.081000E-01 3.200000E-06
7.328000E-01 6,000000E-07
8.025000E-01 3.200000E-06
8.353000E-01 1.600000E-05
8.772001E-01 3.200000E-06
8.911000E-01 7.600000E-06
1.073700E+00 3.200000E-06

10

1.080000E-02 5.000000E-05
7.481501E-02 3.450000E-05
7.710700E-02 5.800000E-05
8.683001E-02 7.000000E-06
8.734901E-02 1.330000E-05
8.978400E-02 4.890000E-06
2.579000E-01 2.870000E-04
3.353300E-01 6.200000E-05
5.931000E-01 1.150000E-04
7.589000E-01 4.900000E-05

FR221
FR221
FR221
FR221
FR221
FR221
FR221
FR221
FR221
FR221
FR221

RN220

RN219
RN219
RN219
RN219
RN219
RN219
RN219
RN219
RN219
RN219
RN219
RN219
RN219
RN219
RN219
RN219
RN219
RN219
RN219
RN219
RN219
RN219
RN219
RN219
RN219
RN219
RN219
RN219
RN219
RN219
RN219
RN219
RN219

RN219

AT217
AT217
AT217
AT217
AT217
AT217
AT217
AT217
AT217
AT217


2.992000E-01 4.800000E-10
7.059001E-01 5,300000E-10
7.084200E-01 4.100000E-09
7.428100E-01 5.200000E-08
7.663900E-01 2.200000E-07
7.834001E-01 2.400000E-10
7.863000E-01 3.200000E-08
8.044001E-01 1.200000E-09
8.056000E-01 5,999999E-10
8.082500E-01 7.900000E-09
8.517001E-01 1.240000E-08
8.805000E-01 1.600000E-09
8.832300E-01 7.600000E-09
9.043000E-01 6.399999E-10
9.267200E-01 5.800000E-09
9.419001E-01 4.700000E-09
9.460000E-01 4.000000E-10
1.001030E+00 9.800000E-09
1.041800E+00 2.200000E-09
1.085400E+00 9.100000E-10

8
1.300000E-02 7.300000E-02
4.955000E-02 6.400000E-04
8.995701E-02 6.800000E-06
9.335000E-02 1.100000E-05
1.048190E-01 1,360000E-06
1.056040E-01 2.600000E-06
1.085820E-01 9,.900000E-07
1.135000E-01 1.020000E-04

28

1.381000E-02 9.900000E-04
1.390000E-02 6.200000E-01
2.634460E-02 2.430000E-02
3.319600E-02 1.300000E-03
3.854000E-02 4.000000E-03
4.342000E-02 2.400000E-04
5.101000E-02 3.400000E-03
5.954091E-02 3.450000E-01
6.483001E-02 1.282000E-02
6.976000E-02 9.500000E-06
9.706900E-02 1.540000E-01
1.010590E-01 2.450000E-01
1.029800E-01 6.400000E-05
1.133030E-01 3.070000E-02
1.142340E-01 5.810000E-02
1.174630E-01 2.270000E-02
1.646100E-01 1.860000E-02
2.080050E-01 2.120000E-01
2.218000E-01 2.120000E-04
2.344000E-01 2.050000E-04
2.675400E-01 7.120000E-03
2.927700E-01 2.500000E-05
3.091000E-01 2.700000E-06
3.323500E-01 1.200000E-02
3.353700E-01 9.510000E-04
3.377000E-01 8.899999E-05
3.686200E-01 3.920000E-04
3.709400E-01 1.073000E-03

PU238
PU238
PU238
PU238
PU238
PU238
PU238
PU238
PU238
PU238
PU238
PU238
PU238
PU238
PU238
PU238
PU238
PU238
PU238
PU238

U238
U238
U238
U238
U238
U238
U238
U238

U237
U237
U237
U237
U237
U237
U237
U237
U237
U237
U237
U237
U237
U237
U237
U237
U237
U237
U237
U237
U237
U237
U237
U237
U237
U237
U237
U237

26

54
5.180000E-03
8.220000E-03
1.330000E-02
2.937400E-02
3.632000E-02
4.653000E-02
5.710400E-02
6.259000E-02
6.390000E-02
7.049000E-02
7.454000E-02
8.647700E-02
8.799000E-02
9.228200E-02
9.464000E-02
9.586301E-02
1.061500E-01
1.075950E-01
1.084220E-01
1.087000E-01
1.114860E-01
1.154000E-01
1.177020E-01
1.311010E-01
1.342850E-01
1.399000E-01
1.432490E-01
1.514140E-01
1.533700E-01
1.552390E-01
1.624100E-01
1.691560E-01
1.705900E-01
1.761200E-01
1.808100E-01
1.868600E-01
1.914600E-01
1.932600E-01
1.946700E-01
1.949500E-01
1.968600E-01
1.999500E-01
2.016200E-01
2.029000E-01
2.091900E-01
2.122900E-01
2.140100E-01
2.226000E-01
2.299400E-01
2.378600E-01
2.489500E-01
2.570900E-01
2.624400E-01
2.796500E-01

9
1.300000E-02
4.946000E-02
8.995701E-02
9.335000E-02
1.048190E-01
1.056040E-01

2.220000E-03
9.000000E-02
4,930000E-01
1.412000E-01
5.000000E-05
1.040000E-03
3.540000E-03
6.000000E-05
1.080000E-04
1.080000E-04
1.200000E-04
1.240000E-01
1.670000E-03
1.660000E-02
6.150000E-03
2.680000E-02
4,899999E-04
3.330000E-03
6.300000E-03
6.800000E-04
2.440000E-03
2.600000E-05
1.690000E-03
8.569999E-04
6.700000E-04
4,600000E-05
4.430000E-03
2.320000E-03
6.100000E-05
8.890000E-04
3.270000E-04
6.330000E-04
2.000000E-04
1.200000E-04
1,580000E-04
3.000000E-05
1.920000E-04
4,370000E-04
3.300000E-04
1.770000E-03
2.080000E-04
5.300000E-05
3.930000E-04
4,800000E-05
1.420000E-04
1.510000E-03
3.620000E-04
2.000000E-05
1.100000E-04
5.690000E-04
5.000000E-05
6.400000E-05
4.71 0000E-05
1.090000E-04

9.000000E-02
7.800000E-04
1.240000E-05
2.000000)
2.500000E-06
4.700000E-06

NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237
NP237

U236
U236
U236
U236
U236
U236


The transport of photons was calculated with the Monte Carlo code ACCEPT from the
Integrated Tiger Series Version 3 (Halbleib et a/., 1992). The code was altered to simulate an
emission source uniformly distributed in the U or Pu sphere volume and to include unscattered
photons in the fluence scores. The spheres were assumed to be centered in a sphere of dry air
of density 1.197x 10° g/cm? (i.e., 20 °C, 101.325 kPa), and the fluence spectra were scored at a
radius of | m in an outer air shell 1 mm thick. Our knowledge of the transport properties of
photons (e.g., attenuation coefficients) and electrons (e.g., stopping powers) in U and in Pu does
not distinguish among isotopes, so atomic cross sections were used (Berger and Hubbell, 1987).
With up to 50 y of decay, the progenies with atomic numbers different from U or Pu are at
sufficiently low levels that they can be assumed not to alter the photon-transport properties of
the spheres.

Photon-source emission spectra can be obtained from the product of the calculated
activities in Table 2 and the emission probabilities in Appendix A. However, direct simulations
of the emission spectra in a Monte Carlo calculation would result in under-sampling of low-
intensity lines and very poor scoring statistics for any low-energy photons, i.e., the probability
of emergence from the surface of the heavy-metal sphere becomes vanishingly small for
photons emitted more than some few mean-free paths from the surface. Instead, the Monte
Carlo calculations were done for uniformly distributed, isotropic emission of monoenergetic
photons, with energies from 3.5 MeV for U and from 4.0 MeV for Pu, down to 30 keV for both
spheres. One can go to lower energies, but the emergence probability becomes very small, and
it was presumed that energies below those of the L-shell absorption-edge energies of U and Pu
would be of little interest. For emitted photon energies of 500 keV and below, the source
sampling was restricted to a volume of a spherical shell extending from about 7 mean-free paths
below the sphere surface out to the sphere surface, and the results normalized to the total
volume assuming that photons emitted at deeper source points have negligible probabilities of
emergence.

Because it is the fluence rate of the emergent photon lines that would be useful for
detection and identification of such nuclear material, this round of Monte Carlo calculations
included only photon transport and ignored the bremsstrahlung resulting from beta emission
and produced by secondary electrons set in motion by the source photons. These components
are estimated to make a small contribution to the continuum. However, the continuum
produced by source photons scattered in the spheres was scored, although not reported here.
The advantage of this approach based on monoenergetic photon transport is that uncertainties
can be controlled, and results for any source spectrum (but not sphere size) can be readily
evaluated; its disadvantage lies in the neglect of presumably relatively small bremsstrahlung
contributions to the continuum and to the production of characteristic x rays..

The line fluences at 1 m in air were based on 10° histories for each source energy, which
resulted in estimated relative standard deviations of the mean of 1 % or less. The results are
given in Table 3 and in Fig. 2. Note that for each monoenergetic source energy, there are
associated secondary-radiation line fluences of annihilation quanta (produced following pair
production) and of characteristic x rays (produced in photoelectric absorption).

10


1.E-05

U Sphere
1.E-06
*
€
6
8 1.£-07
<
o
3
ira
1.E-08
1.E-09
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 40
Photon Energy, MeV
1.E-05
Pu Sphere
1.E-06

Fluence, cm”
m
S
S

1.E-08

1.E-09

0.0 0.5 1.0 1.5 2.0 25 3.0 3.5 4.0 45
Photon Energy, MeV

Fig. 2. Fluence from monoenergetic photons at | m in air for the U and Pu spheres, normalized
to one internally emitted source photon (see Tables 3a and 3b).

13