Particles Physics and Atomic Matter

Abstract:This paper proposes a unified fractal model of matter, bridging the gap between high-energy particle physics and the periodic system of elements. We identify two distinct scaling laws governing the density and structural organization of matter: a Step-10 "Quantum Press" (1-10-100-1000) for the subatomic world and a Step-3 "Fractal Tree" (1-3-9-27-81-243) for the atomic architecture.The core of the study reveals a critical resonance point at the 14th level of material organization—identified as the element Uranium (Z=92). Our analysis demonstrates that at this junction, the theoretical density of the "Fractal Tree" reaches its limit of ~23.8 g/cm³, while the nuclear density simultaneously aligns with the 10¹⁴ g/cm³ threshold characteristic of the Omega-baryon (7th particle level).We argue that Uranium represents a phase transition where the atomic electron shell becomes redundant, and the material begins to behave as a relativistic macro-baryon. This convergence explains the onset of inherent instability and radioactivity as a collapse of the fractal shell, forcing the "substance" to revert to its "particle" state. The findings suggest that the limits of chemistry, discovered by Mendeleev, are in fact the fundamental density barriers sought by modern particle physics.