Symmetry/asymmetry within a cylindrical lattice model of nuclear structure predicts cosmic abundance/scarcity

Abstract

Protons and neutrons are the smallest forms of measurable matter, and each nucleon has 3 up (+2/3) and down (-1/3) quarks. Quarks treated as point-like particles within polygonal geometries model the structures of stable nuclides through $^{36}$Ar. The model derives from the proton's radius (r=0.8414 fm), the hadron's prolate spheroid shape (from the $\Delta(1232)$ resonance), and the separation distance between bound nucleons ($\approx$0.8 fm, from the Argonne $v_{18}$ $NN$ potential). The prolate nucleon's spatial extent arises from its 3 quarks, which implies a qualitatively linear quark sequence. Spin-spin forces repel the like-flavored quarks to opposite ends of the nucleon, leaving the unlike quark in the middle. Quark-to-quark distance within the nucleon corresponds to the nucleon's radius. Nucleons link by quark-to-quark interactions to form proton-neutron short-range correlated pairs (pn SRC pairs), separated by a distance equal to the proton's radius. Alternating nucleons produce regularly alternating up/down quark sequences. We contemplate structures for each stable nuclide through $^{36}$Ar and include the one whose rotational radius (from the regular polygon radius formula) best correlates with its accepted charge radius (r(31)=0.98, p<0.001). Nucleon alternation makes pn SRC pairs and produces the equal numbers of protons and neutrons (Z=N) in the isotopes $^{4}_{2}$He, $^{12}_{6}$C, $^{14}_{7}$N, $^{16}_{8}$O, $^{20}_{10}$Ne, $^{24}_{12}$Mg, $^{28}_{14}$Si, and $^{32}_{16}$S, comprising 99.5% of stable baryonic matter. Bilateral structural symmetry emerges as a sensitive and specific predictor of cosmic abundance. Opposing deuteron-deuteron alternating quark charge sequences produce alternating and unequal electromagnetic fields capable of modelling the close-range attraction and far-range repulsion of the fusion potential curve and Coulomb potential energy barrier.