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Can someone explain why heavy nuclei prefer to go through $\alpha$-particle decay instead of nucleon decay?

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Nuclei are quantum mechanical "particles" composed out of protons and neutrons, which themselves are composed out of quarks and a sea of gluons and antiquarks. The basic holding "force" of this is the strong interaction force, modeled with QCD for the protons and neutrons, and a spill over force from the protons and neutrons called the strong nuclear force.

Quantum mechanical models have been developed which explain the decay and fission behavior of nuclei.

Hand waving: the alpha particle is very tightly bound, as seen in this binding energy curve, and in addition, it is stable. Thus within the "bag" containing the nucleons a stable configuration of alphas can exist in unstable nuclei, and the fission or decay into alphas may be energetically favored over the emission of a single nucleon, for a particular nucleus.

The models fit this behavior and can predict how other nuclei will fission or decay.

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