Production and Decay of Fission Products

We are going to assume that the fissile product has one mode of decay and does not do anything naughty such as undergo neutron capture. We can then write its rate of production as:

md6

where md19 is the decay constant for fission product N, md20 is the number of fissions per second and md21 is the fraction of fissions which produce fission product N. I have shown how to calculate md20 previously and md21 is given  in the data presented in Composition of Spent Fuel.

Again I am making the approximation that the rate of fission md20 is constant.

md7

 md8

md9

md10

md11

md12

md13

When t=0

md15

where N0 is the amount of the fissile product at time t=0.

md14

If we assume that there is none of that fissile product in the fresh fuel we get:

md16

md17

Although I have not been able to find this formula on the web a similar formula is given in http://www.ornl.gov/info/reports/1961/3445605157576.pdf

Below is a plot of this function with arbitrary units (i.e. I have not put in ‘real’ values for any of the constants. You can see that if the fissile product has a short half-life compared with the time that it is in the reactor the amount soon reaches an equilibrium – i.e. the rate of production equals the rate of decay. However, if the fission product has a longer half-life the amount continues to rise.

md18

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