Elementary Energy-Quantum Sea Theory III

Abstract This paper develops a tier-1 to tier-2 (first-to-second tier) phase-transition closure of the elementary energy-quantum sea (EP-sea) program, extending the unified kinetic framework of Papers I–II to nuclear-scale "inner space" formation and decay phenomena. Key Theoretical Framework: EP-sea Background: Characterized by collision statistics and a fluctuation scale Θ (= Teff). Stability is organized by a unified visibility ratio χvis = ΔW / Θ (one e-fold criterion). Core-Shell Model: Introduces a coupled two-order-parameter model featuring a shell membrane field (χ1) and a core-lock field (χ2), constructing finite-size stabilized core-shell solutions representing nuclear interiors. Physical Implications: Double-Yukawa Potential: Linearization around stable solutions yields a two-mode spectrum with correlation lengths ξ2 ≪ ξ1. This leads to a two-scale effective kernel that naturally provides intermediate-range attraction plus short-range repulsion/saturation without adding a new fundamental force. Nuclear Decays: Formulated as rare-event barrier crossings within the EP-landscape: α-like emission: Corresponds to an outer-saddle (surface) escape channel. β-like / neutron rearrangement: Corresponds to an inner-saddle (core) branch-switch channel. Both are governed by Kramers/large-deviation scaling: Γ ~ Ω0 exp(-ΔW / Θ). Predictions & Benchmarks: The framework yields falsifiable trend-level benchmarks for saturation radii R(A) ~ r0A1/3 (with r0 ~ ξ2), binding-energy constraints, Geiger–Nuttall-type calibration templates for α decay, and explicit bounds on the environment sensitivity of decay windows under EP-background perturbations.