The Asymmetric Source Field Model (ASFM) for Atomic Valence A Deterministic Residual-Field Formalism for Valence Pattern Formation

Abstract We present the Asymmetric Source Field Model (ASFM) as a deterministic residual-field formalism for the reconstruction of atomic valence patterns in real space. In this approach, outer-shell structure is described through the interference topology of harmonically scaled spherical source fields generated by nucleonic emitters. A residual field is defined from a constructive component and a phase-shifted conjugate component with radial damping and controlled phase asymmetry. Stable outer-shell nodes are then identified on a three-dimensional voxel grid by a sweep-and-detect procedure over phase offset, damping, and node-selection parameters. For the light-element domain Z = 1–20, the number of stable residual nodes recovered in the outer-shell region reproduces the chemically expected valence organization, including single-valence cases, progressive p-shell filling, and noble-gas closure. In addition, a secondary comparison shows a strong correlation between simulated node amplitude and experimental first ionization energy, indicating that the residual-node topology is not only structurally informative but also linked to energetic trends. The formalism is intended as a real-space mathematical framework for valence pattern formation and residual-field organization, rather than as a reformulation of orbital quantum mechanics. In this sense, ASFM provides a deterministic structural model for analyzing chemically relevant outer-shell regularities and their relation to residual coherence geometry.