# Why does the chain yield in nuclear fission sum up to 200%?

The question that you would like the fission yield tables to answer is

This isotope makes up some fraction of all the fission products; what is it?

Those fractions should add up to 100%.

The question that's being answered by these tables is slightly different:

What fraction of fission events produce this isotope?

Since fission usually produces two heavy fragments, the sum over all the fission fragments is approximately 200%. This is easier to *measure*, because you can tell how many fissions have occurred by looking only at the amount of uranium remaining in the fuel. Ensuring that you have accurately measured all of the myriad fission products is a lot trickier; for instance, some fraction of the fission products are noble gases, which might escape from the fuel assembly.

This approach is consistent with normalizations of convenience in other branching-ratio tabulations with multiple particles in the final state. For a specific example, consider

$$ \rm n + {}^{110}Cd \to {}^{111}Cd + \gamma $$

which is some fraction of what happens when you put thermal neutrons on natural cadmium. The gamma rays carry away a total energy of 7.0 MeV, which is the "neutron separation energy" for Cd-111. However the average energy of these photons is one or two MeV, and the Cd-111 has a couple of low-lying excitations through which most of these gamma-ray cascades pass. If we could count all of the gamma rays, the probabilities per neutron capture would add up to a few hundred percent. But in this particular case it's not possible to reliably measure the energies of all of the very soft gamma rays from the closely-spaced high-energy states, so the branching ratios in my reference are instead normalized to one of the more prominent transitions from a low-energy state. This confuses me every time I look it up (once every few years), because the calibration photon is assigned a relative intensity of 100%, but a different common photon is given a relative intensity of 274%.

1 reaction will produce 2 daughter nuclei.

So percentage per reaction sums up to 200%.

In your comment, you mention making it 0.5 and 0.5. This also a correct way because you are taking percentage per total product which will sum upto 100%.