Atomic Physics & Structural Complexity

Analytical Hydrogen, Correlated Two-Electron Systems & Tabela Elementa

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Foundations Root · Atomic Physics, Isoelectronic Scaling & Shell Geometry

Public Status Boundary. All baseline atomic spectra and ground-state ionization energies presented in this corpus are strictly anchored to consensus experimental data from the NIST Atomic Spectra Database (NIST ASD) and CODATA. Authorial models such as Tabela Elementa and geometric shell derivations function as theoretical research architectures and active formalization targets.

$$\boxed{{\displaystyle \mathbf{\text{Single-electron analytical}}\ne \mathbf{\text{correlated many-electron}}}}$$$$\boxed{{\displaystyle \mathbf{\text{Independent-particle model}}\ne \mathbf{\text{correlated two-electron model}}}}$$$$\boxed{{\displaystyle \mathbf{\text{NIST ASD / CODATA}}=\mathbf{\text{VERSIONED EXTERNAL REFERENCE ANCHOR}}}}$$

Figure 5.1 — Atomic Complexity Ladder: Epistemic progression from exact Hydrogen baseline to correlated two-electron Helium (r12 interaction), isoelectronic scaling, and Tabela Elementa geometric shell ordering.

Maps structural complexity progression from analytical Hydrogen baseline to correlated Helium two-electron systems, H-like/He-like ions, and relativistic Tabela Elementa shell structures.

Credit: Ivan Pasev / GILC Research·CC BY-NC-SA 4.0·SCHEMATIC

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1. The Atomic Complexity Progression

Atomic structure in the Science of Fabric Reality ascends through four levels of physical complexity:

Tier	System / Domain	Physical Nature	Governing Physics	External Reference Anchor
1	Hydrogen Root ($Z=1$)	Exact 1-Electron	Analytical Coulomb model $E_n=-13.605693\text{ eV}/n^2$; experimental ionization $I_1=13.598434599702(12)\text{ eV}$	NIST ASD v5.11 / CODATA 2018
2	Helium System ($Z=2$)	Correlated 2-Electron	Inter-electronic Coulomb repulsion $r_{12}=|{\mathbf{r}}_1-{\mathbf{r}}_2|$, Hylleraas correlation; removal energy $I_1+I_2=79.005155\text{ eV}$	NIST ASD v5.11
3	Isoelectronic Sequences ($Z\ge 3$)	H-like / He-like Ions	$Z$-scaling, electron screening, relativistic fine-structure & QED Lamb shifts	CODATA / Atomic Data Tables
4	Tabela Elementa	Many-Body Periodic Shells	Geometric shell ordering, relativistic contraction, Madelung $n+\ell$ rule target	IUPAC Periodic Reference

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2. Epistemic Demarcation: Consensus vs Authorial Targets

To preserve rigorous scientific truth across the corpus:

2.1 Established External Consensuses

• Hydrogen Analytical Coulomb Model: Nonrelativistic infinite-nuclear-mass solution $E_n=-\frac{hc{R}_{\mathrm{\infty }}}{n^2}$ ($E_1=-13.605693\text{ eV}$); experimentally measured ground-state ionization energy $I_1=13.598434599702(12)\text{ eV}$ (NIST ASD v5.11, incorporating reduced mass, relativistic Dirac, and QED Lamb shift corrections).
• Helium Ground-State Benchmark: Independent Hartree-Fock limit $E_{\text{HF}}=-2.861680{\text{ E}}_h$ ($-77.8703\text{ eV}$); nonrelativistic correlated benchmark $E_{\text{corr-nonrel}}=-2.903724{\text{ E}}_h$ ($-79.0152\text{ eV}$); definitive correlation energy $E_{\text{corr}}=-0.042044{\text{ E}}_h$ ($-1.14409\text{ eV}$); NIST ASD total sequential two-electron removal energy $I_1+I_2=24.587389+54.417766=79.005155\text{ eV}$.
• Versioned Reference Anchors: All experimental comparators are tied to versioned metrological repositories ([NIST ASDv5.12] / [CODATA2022]).

2.2 Authorial Research Targets

• Geometric Shell Functional: Formulating the periodic shell progression ($s,p,d,f$) from relational boundary constraints without empirical parameter tuning.
• Madelung $n+\ell$ Rule Formalization: Seeking a first-principles derivation of shell filling order from invariant-preserving geometric packings.

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3. Atomic Physics Section Navigation

Explore the dedicated research sections:

• Hydrogen Root & Strong-Field Dynamics →
  Exact Coulomb baseline, time-dependent external laser field $H(t)$, TDSE solver, HHG spectrum, and detector uncertainty.
• Helium Atom & Two-Electron Correlation →
  Electron-electron Coulomb repulsion $r_{12}$, independent-particle vs correlated wavefunctions, and isoelectronic $Z$-scaling.
• LPFR Laboratory Interface →
  Multi-channel instrumentation loop, typed observable contracts, and pre-registered falsification criteria.
• FSR Thermophysics & Metrology →
  Radiative heat transfer, structured surface comparators, and cryogenic vacuum differential metrology.

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SOURCE AUTHORITY & BOUNDARY LOCK

This route enforces strict cryptographic and epistemic boundaries between consensus reference data, comparator theoretical literature, and authorial candidate predictions.

ESTABLISHED BASELINE

• NIST ASD v5.12 (2024-11-07)
  Spectroscopic energy levels and ionization thresholds for Z=1 to Z=118.
• CODATA 2022 (2025)
  Fundamental physical constants and Rydberg constant authority.

COMPARATOR LITERATURE

• Drake 2006 (2006)
  Two-electron correlation and Hylleraas non-relativistic benchmarks.

METROLOGY / DATA STANDARDS

• JCGM 100:2008 (GUM)
  Standard and combined uncertainty propagation.

AUTHORIAL EXTENSION BOUNDARY

VERSIONED_AUTHORITATIVE_EXTERNAL_REFERENCE

Atomic complexity ladder establishes consensus spectroscopic anchors. Geometric shell functionals and Madelung derivations are authorial research targets.

Explore Master Reference Atlas & Citations (BibTeX / CSL) →