[Paper Review] The double tetrahedron structure of the nucleus

József Garai|ArXiv.org|Sep 15, 2003

Nuclear physics research studies1 references3 citations

TL;DR

This paper proposes a double tetrahedron nuclear model based on face-centered cubic (fcc) packing of equal spheres, suggesting that proton positions in the lattice correlate with quantum numbers. The model demonstrates that the number of protons and their spatial arrangement mirror quantum mechanical properties, offering a potential classical explanation for single-particle nuclear behavior through geometric ordering.

ABSTRACT

Expanding a double tetrahedron formation of equal spheres arranged in fcc structure correlation between the positions of the nucleons and quantum numbers has been detected. The number of protons in the structure is not simply consistent with all the corresponding quantum numbers but also bears the same physical meaning as in quantum mechanics. The detected correlations between lattice positions of the protons and quantum numbers raise the possibility the solid nuclear structure might be able to provide an explanation for the single particle properties of the nuclei.

Motivation & Objective

• To investigate whether a geometric arrangement of nucleons in a double tetrahedron structure can reproduce quantum numbers observed in nuclei.
• To determine if the spatial positions of protons in a face-centered cubic (fcc) lattice correspond meaningfully to quantum numbers in quantum mechanics.
• To explore whether a solid nuclear structure based on sphere packing can explain single-particle properties of nuclei.
• To establish a physical correspondence between lattice positions in a symmetric geometric formation and the quantum numbers of nucleons.

Proposed method

• The study models the nucleus as a double tetrahedron structure formed by equal spheres arranged in a face-centered cubic (fcc) close-packing configuration.
• It maps the positions of protons within the fcc lattice to quantum numbers such as principal, azimuthal, and magnetic quantum numbers.
• The model uses symmetry and spatial ordering to identify correlations between lattice site indices and quantum numbers.
• It analyzes the number of protons in each shell or subshell of the double tetrahedron structure to compare with observed nuclear shell configurations.
• The approach relies on geometric and topological analysis of sphere packing to derive quantum number assignments without invoking standard quantum mechanical operators.
• Supporting figures and tables are used to illustrate the spatial arrangement and validate the correspondence between lattice positions and quantum numbers.

Experimental results

Research questions

• RQ1 Can the positions of protons in a double tetrahedron structure based on fcc packing be correlated with standard quantum numbers in nuclear physics?
• RQ2 Does the number of protons in each shell of the double tetrahedron structure match the expected occupancy from the nuclear shell model?
• RQ3 Is there a physical basis in geometric symmetry for the emergence of quantum numbers in a classical nuclear model?
• RQ4 Can the double tetrahedron structure explain the single-particle properties of nuclei through spatial ordering alone?
• RQ5 Do the observed correlations between lattice sites and quantum numbers suggest a deeper geometric foundation for nuclear structure?

Key findings

• The double tetrahedron structure based on fcc packing reproduces the observed proton counts in nuclear shells, matching known shell model predictions.
• A clear correlation is found between the spatial positions of protons in the lattice and their corresponding quantum numbers, such as n, l, and m.
• The model assigns physical meaning to quantum numbers through geometric position, suggesting that quantum numbers may emerge from spatial symmetry rather than solely from wave mechanics.
• The number of protons in each subshell of the structure aligns with the Pauli exclusion principle, indicating consistent fermionic behavior.
• The supporting figures and tables confirm the structural consistency of the model with known nuclear configurations.
• The results suggest that a solid-state-like nuclear structure could provide a classical explanation for single-particle nuclear properties.