Nuclear Models
Although the standard model of physics is widely believed to completely describe the composition and behavior of the nucleus, theoretically generating predictions from it is much more difficult than for most other areas of particle physics. This is essentially because perturbation theory, a widely used mathematical tool, is not applicable to quantum chromodynamics (the theory of the strong force) at the energy scales relevant to the nucleus. As a result, experiments have historically been compared to relatively crude models which are necessarily imperfect. None of these models completely explain experimental data on nuclear structure.
The nuclear radius (R) is considered to be one of the basic quantities that any model must predict. For stable nuclei (not halo nuclei or other unstable distorted nuclei) the nuclear radius is roughly proportional to the cube root of the mass number (A) of the nucleus, and particularly in nuclei containing many nucleons, as they arrange in more spherical configurations:
The stable nucleus has approximately a constant density and therefore the nuclear radius R can be approximated by the following formula,
where A = Atomic mass number (the number of protons Z, plus the number of neutrons N) and r0 = 1.25 fm = 1.25 × 10−15 m. In this equation, the constant r0 varies by 0.2 fm, depending on the nucleus in question, but this is less than 20% change from a constant.
In other words, packing protons and neutrons in the nucleus gives approximately the same total size result as packing hard spheres of a constant size (like marbles) into a tight spherical or almost spherical bag (some stable nuclei are not quite spherical, but are known to be prolate).
Read more about this topic: Atomic Nucleus
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