Isomeric fission yields

The independent fission yields of isomeric states are important in the definition of inventories for decay-heat calculations. However, these data are sparse for all fission processes apart from the thermal fission of 235U. Modelling calculations are normally used to derive values, based on the partition of the independent fission yields of nuclides among their isomeric states using the spin distributions of the fission fragments and nuclear levels as fitting parameters.

Fig. 12. Peak parameters for A'(140)

Madland and England (1977) assumed that the spin distribution of the fission fragments after prompt-neutron emission could be represented by the equation:

P(J) = C x (2J + 1)e _[(4+1/2)/Jrms ]2,

in which Jrms defines the state of the spin distribution, and C is a constant. Fragments with J nearer the spin of a particular isomer state are defined as feeding that state. This model has been developed further by Rudstam and co-workers (IAEA-CRP, 2000): the probability that the spin will decrease by one unit is proportional to the density of nuclear states of spin J-1, while the probability that the spin will increase is proportional to the density of nuclear states of spin J+1. The ratio between the number of nuclear states of spin J-1 and those of spin J+1 is given by Z(J):

Z (J ) = -(2J^l Є (4 4 +2)/^

(2J + 3)

in which Jnuc is another spin parameter (defined effectively by the above equation). This approach results in a relative probability of Z/(1+Z) to decrease the spin by one unit, and a relative probability of 1/(1+Z) to increase the spin by one unit. Erroneous results will occur when the isomeric state is at a much higher energy than the ground state.

Equations have been derived to calculate the fractional independent isomeric yields (fiiy), and they can be modified to accommodate reductions in the excitation energy caused by the gamma-ray emissions. The available experimental data have been compared with the calculated fiiy values, particularly for the thermal fission of 235U. Various combinations of Jrms and Jnuc were adopted, and the best combinations were found to be:

Jrms of 6.50, and Jnuc of 6.00 for odd-mass nuclides;

Jrms of 6.00, and Jnuc of 1.00 to 2.00 for even-mass nuclides.

A value of 6.25 has been adopted for Jrms, and values of 6.00 (odd mass) and 2.00 (even mass) for Jnuc in comparing the fiiy data for the high-spin isomers listed in Table 6. Agreement between experimental and calculated values is judged to be satisfactory, although some nuclides exhibit significant discrepancies (e. g., 82As, 99Nb, 119Cd, 128Sb and 146La).

Table 6: Experimental and calculated fractional independent yields of the high-spin isomers

of nuclides formed in the thermal-fission of 235U

Nuclide

fiiy(high)

Nuclide

fiiy(high)

experimental

calculated

experimental

calculated

79Ge

1.00 ± 0.11

0.829

127In

0.87 ± 0.06

0.814

81Ge

0.70 ± 0.06

0.835

127Sn

0.90 ± 0.11

0.626

82As

0.17 ± 0.07

0.597

128In

0.30 ± 0.07

0.190

83Se

0.89 ± 0.07

0.816

128Sn

0.11 ± 0.07

0.209

84Br

0.30 ± 0.04

0.504

128Sb

0.61 ± 0.06

0.192

84Br

0.38 ± 0.04

0.504

129In

0.76 ± 0.07

0.815

90Rb

0.58 ± 0.05

0.659

129Sn

0.43 ± 0.06

0.621

90Rb

0.90 ± 0.01

0.659

130Sn

0.13 ± 0.02

0.212

99Nb

0.06 ± 0.14

0.819

130Sb

0.45 ± 0.11

0.190

113Ag

~1.00

0.847

132Sb

0.20 ± 0.02

0.190

115Ag

~1.00

0.846

132Sb

0.19 ± 0.03

0.190

116Ag

~1.00

0.391

133Te

0.78 ± 0.04

0.590

117Ag

~1.00

0.848

133Te

0.57 ± 0.04

0.590

118Ag

0.44 ± 0.10

0.388

133Te

0.61 ± 0.08

0.590

119Cd

0.39 ± 0.20

0.724

133I

0.07 ± 0.02

0.140

120Ag

0.85 ± 0.15

0.382

133Xe

0.75 ± 0.04

0.603

121Cd

0.89 ± 0.11

0.730

134Sb

0.19 ± 0.05

0.279

123Cd

0.68 ± 0.02

0.614

134i

0.20 ± 0.02

0.183

123In

0.94 ± 0.11

0.817

135Xe

0.65 ± 0.04

0.575

123Sn

1.00 ± 0.28

0.627

136i

0.79 ± 0.14

0.391

124In

0.86 ± 0.80

0.215

138Cs

0.58 ± 0.08

0.392

125Cd

0.66 ± 0.08

0.614

146La

0.06 ± 0.03

0.391

125In

0.88 ± 0.08

0.813

148Pr

0.12 ± 0.03

0.660

126In

0.42 ± 0.17

0.215

148Pm

0.71 ± 0.06

0.388

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