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Recriticaility in the Fukushima nuclear reactor

Dear Reader,

Those of you who are following the story in the press may have heard of claims that one of the reactors had gone critical again. Now I would like to state that at this point after the melt downs I think that criticality is less likely than it was before the reactors were damaged by overheating. The uranium dioxide is now in the form of a big water free lump at the bottom of the pressure vessels. As the geometry is such that water can not be mixed between the uranium dioxide pellets it will be harder to moderate the fuel thus the fuel is more likely to stay subcritical compared with a core of intact fuel elements plus water.

One of the things which had made people think that the reactor had gone critical again is the observation of xenon-135, this is a shortlived (half life 9.14 hours) fission product, the thing which is important to understand that a short lived fission is not perfect evidence of criticality. This might seem odd but I will explain.

The reason is spontaneous fission, if we assume that the fuel in unit two has the same isotope signature as the stricken chernobyl reactor had back in 1987 and that both reactors contain the same amount of fuel then I can estimate how much xenon-135 will be formed by the fuel.

The chernobyl reactor was thought to contain 26 PBq of Cm-242, according to the chart of the nuclides 0.00062 % of curium-242 decays occur via spontaneous fission.

So as 1 PBq = 1000 TBq then every second we have 161.2 x 10^9 fission events per second due to the random spontaneous fission of the curium.

As the fission yields of the different products change as the energy of the state which undergoes fission increases, then we have to choose which fission yield to use with case. The data which I have does not have a listing for spontaneous fission of curium, but I will make an educated guess and use the data for Pu-239 with fast neutrons for the curium case.

The fission the xenon isotopes are

Xe-133, 6.9 %

Xe-135, 7.4 %

So we will have 11.9 x 10 ^9 atoms of Xe-135 formed per second in the fuel, if we make a dire assumption that all the xenon will be mobile then as the decay constant of Xe-135 is

(Decay constant = ln 2 / half life = 0.69 / 32904 seconds = 2.097 x 10^-5 s-1)

As activity is = number of atoms x decay constant

Then the activity of this xenon isotope released per second by the curium decay will be 0.25 MBq of activity, now if we ignore the decay of the xenon and a charcoal filter absorbs one hour’s worth of xenon then the filter will have about 900 MBq of activity on it. The activity of the filter will be higher as I have ignored the other actinide isotopes, many of these all also undergo spontanious fission.

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