Nuclear shells and magic numbers in a harmonic oscillator with orbit–orbit and spin–orbit terms, made by Bakken and placed on Wikicommons with a Creative Commons Attribution-Share Alike 3.0 Unported license, here: https://commons.wikimedia.org/wiki/File:Shells.png

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   John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Thursday, 10-Apr-2025 23:52:42 JST John Carlos Baez

   in reply to

   In nuclear physics, the magic numbers are

     2
     8 = 2+6
    20 = 2+6+12
    28 = 2+6+12+8
    50 = 2+6+12+8+22
    82 = 2+6+12+8+22+32
   126 = 2+6+12+8+22+32+44

   What's the big deal about this? I could explain it to you, but I'm just learning this stuff, so I'd basically be repeating the explanation here:

   https://en.wikipedia.org/wiki/Nuclear_shell_model

   The basic idea is this: neutrons and protons in nuclei form 'shells' somewhat like how electrons form shells in atoms... so a lot of the same math applies, namely the representation theory of the rotation group. But protons and neutrons interact so strongly that the patterns get complicated, even for fairly small nuclei. For the electrons in atoms, we can do surprisingly well at predicting the patterns in the periodic table by pretending they don't interact, until we reach rather large atoms.

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