I want to know why there is a maximum and then decrease.
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In nuclear and particle physics the only peaked energy spectra come from two body decays (spontaneous fission is a decay). One has a peak with a width due to measurement errors.
The neutrino was discovered because it was found that beta decay gave continuous spectra, no two body ones.
The particular shape of this decay is explained in the link, as it is easy to model since only electromagnetic and weak forces enter.
The functional form has a peak and diminution at the low and high energies.
In a fission fragmentation, there may be more than three fragments and the forces involved are the strong forces, the kinematics in the process will be more complicated than in the three body beta decay, but the balance of forces will give a similar form.