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

Abstract Protons and neutrons are the smallest forms of matter with measurable size, and each nucleon has a mix of three up (+2/3) and down (−1/3) quarks. Quarks are treated as point-like particles within polygon-based geometries in order to model the structures of stable nuclides through 36 Ar. The model derives ab initio from the proton’s radius (r = 0.8414 fm), the hadron’s prolate spheroid shape (from the transition to the nucleon’s first excited state (the ∆(1232) resonance), and the separation distance between bound nucleons (≈0.8 fm, from the Argonne v18 NN potential). The spatial extent of the prolate spheroid nucleon is assumed to arise from its three quarks, which implies a qualitatively linear quark sequence. Spin–spin forces repel the two like-flavored quarks to opposite ends of the prolate nucleon leaving the unlike quark in the middle. It then follows that the 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 SRCs), separated by a distance assumed equivalent to the proton’s radius. Alternating nucleons thus produce regularly alternating up/down point-like quark sequences. We contemplate various structures for each stable nuclide through <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mmultiscripts> <mml:mrow> <mml:mi mathvariant="normal">Ar</mml:mi> </mml:mrow> <mml:none/> <mml:none/> <mml:mprescripts/> <mml:mrow> <mml:mn>18</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>36</mml:mn> </mml:mrow> </mml:mmultiscripts> </mml:math> and include the one whose calculated rotational radius (derived from the radius formula of a regular polygon) best correlates with its IAEA-accepted charge radius (r(31) = .98, p&lt;.001). Nucleon alternation inherently makes pn SRC pairs, and produces the observed equal numbers of protons and neutrons (Z = N) found within isotopes <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mmultiscripts> <mml:mrow> <mml:mi mathvariant="normal">He</mml:mi> <mml:mo>,</mml:mo> </mml:mrow> <mml:none/> <mml:none/> <mml:mprescripts/> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>4</mml:mn> </mml:mrow> </mml:mmultiscripts> <mml:mmultiscripts> <mml:mrow> <mml:mi mathvariant="normal">C</mml:mi> <mml:mo>,</mml:mo> </mml:mrow> <mml:none/> <mml:none/> <mml:mprescripts/> <mml:mrow> <mml:mn>6</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>12</mml:mn> </mml:mrow> </mml:mmultiscripts> </mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mmultiscripts> <mml:mrow> <mml:mi mathvariant="normal">N</mml:mi> <mml:mo>,</mml:mo> </mml:mrow> <mml:none/> <mml:none/> <mml:mprescripts/> <mml:mrow> <mml:mn>7</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>14</mml:mn> </mml:mrow> </mml:mmultiscripts> </mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mmultiscripts> <mml:mrow> <mml:mi mathvariant="normal">O</mml:mi> <mml:mo>,</mml:mo> </mml:mrow> <mml:none/> <mml:none/> <mml:mprescripts/> <mml:mrow> <mml:mn>8</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>16</mml:mn> </mml:mrow> </mml:mmultiscripts> </mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mmultiscripts> <mml:mrow> <mml:mi mathvariant="normal">Ne</mml:mi> <mml:mo>,</mml:mo> </mml:mrow> <mml:none/> <mml:none/> <mml:mprescripts/> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>20</mml:mn> </mml:mrow> </mml:mmultiscripts> </mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mmultiscripts> <mml:mrow> <mml:mi mathvariant="normal">Mg</mml:mi> <mml:mo>,</mml:mo> </mml:mrow> <mml:none/> <mml:none/> <mml:mprescripts/> <mml:mrow> <mml:mn>12</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>24</mml:mn> </mml:mrow> </mml:mmultiscripts> </mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mmultiscripts> <mml:mrow> <mml:mi mathvariant="normal">Si</mml:mi> <mml:mo>,</mml:mo> </mml:mrow> <mml:none/> <mml:none/> <mml:mprescripts/> <mml:mrow> <mml:mn>14</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>28</mml:mn> </mml:mrow> </mml:mmultiscripts> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mmultiscripts> <mml:mrow> <mml:mi mathvariant="normal">S</mml:mi> </mml:mrow> <mml:none/> <mml:none/> <mml:mprescripts/>