Nuclear Magic Numbers and Exceptional Lie Algebras

Standard models of chemistry and nuclear physics accurately describe atomic behaviour via phenomenological frameworks: the Mayer-Jensen spin-orbit coupling for nuclear magic numbers, Pyykkö's relativistic kinematic treatment of the lanthanide contraction, and the $2(2\ell+1)$ rule for electron shell capacities. These frameworks are experimentally well-confirmed and are not challenged here.

This paper presents a speculative catalogue of structural coincidences between the numerical constants that appear in these frameworks and the geometry of the exceptional Lie algebras. Specifically, we observe that: (i) the cosmological abundance peak of Iron-56 shares its nucleon count with the dimension of the Freudenthal triple system of $E_7$; (ii) the electron shell capacities $2, 6, 10, 14$ coincide with dimensions of objects naturally associated to the normed division algebras $\mathbb{C}, \mathbb{H}, Sp(2), G_2$; and (iii) the nuclear magic numbers $2, 8, 20, 28, 50, 82, 126$ may admit an interpretation as closure counts of sub-geometries in Bruhat-Tits buildings.

We do not claim these coincidences constitute a derivation, nor that they supersede the standard explanations. We record them as a structured programme of open questions for specialists in exceptional Lie theory, nuclear structure, and algebraic chemistry, in the spirit of the Adelic Simplicial Architecture programme