# Cover letter — submission to *Progress in Physics*

Claes Johnson
KTH Royal Institute of Technology
SE-100 44 Stockholm, Sweden
claesjohnson@gmail.com

Date: 2026-07-13

To the Editors of *Progress in Physics*
(Dr. Pierre Millette; Dr. Andreas Ries)

Dear Editors,

I am pleased to submit for your consideration the manuscript

**"Unified Coulomb Theory for Atom and Nuclear Physics"**

for publication in *Progress in Physics* as a research article. In accordance with the journal's
guidelines the manuscript is submitted as a preliminary PDF; a LaTeX version prepared in the
`pip-template` will be provided upon acceptance.

**What the paper claims.** The manuscript advances a single thesis: that atomic and nuclear
structure are one and the same physics — opposite-sign charge clouds interacting by the Coulomb force
alone, on non-overlapping domains that meet at free boundaries and minimise the electrostatic energy
(the RealQM framework) — and that the two are related by a single operation, the interchange of
electron and proton, e⁻ ↔ p. Because the kinetic energy is written with the same form for both
species, this swap is an *exact symmetry* of the model rather than an analogy. Under it the ladder of
ordinary matter (atom → molecule → solid) maps term by term onto the nuclear ladder
(alpha → alpha-cluster → nuclear matter): closed electron shells (noble gases) correspond to closed
proton shells (the alpha and the magic nuclei), covalent bonds by shared electrons to nuclear bonds
by shared protons (alpha-cluster states / nuclear molecules), and condensed-matter saturation to
nuclear saturation.

**What is new and testable.** Built from a single repeating unit — a (2 electrons + 4 protons)
alpha — the computed alpha-conjugate binding-energy ladder reproduces the experimental binding
energies of ⁴He, ¹²C, ¹⁶O, …, ⁴⁰Ca to a uniform ~107 %, with near-constant binding per nucleon,
using no strong or weak force and no fitted parameter beyond a single energy scale fixed on the
deuteron. The paper also argues that alpha-clustering is *forced* (a monolithic nucleus over-binds as
Z², so extensive/saturating binding requires localising the Coulomb glue into alpha-sized packets),
and it reports a computed, free-boundary metastable alpha geometry.

**A foundational corollary.** Analysing the two scales that coexist in a single helium atom (an
ångström electron cloud around a femtometre nucleus) leads to the conclusion that it is *size*, not
mass, that is the electromagnetic variable: the same electron takes the proton's femtometre size in
the nucleus and a size 10⁵ times larger in the atom, at fixed charge, the difference registered
entirely in the kinetic energy. The mass appearing in the non-relativistic kinetic term ℏ²/2m is
therefore an artifact of that approximation — the physical kinetic energy being the mass-free ℏc/ℓ of
the relativistic regime — and mass proper, as rest energy, belongs to the gravitational sector.

**Why *Progress in Physics*.** The work is foundational and cross-disciplinary, bridging atomic and
nuclear physics from first principles and questioning a standard assumption (that nuclear binding
requires a strong force). It is parameter-free and openly falsifiable, and every computation is
reproducible: an open-source, browser-based (WebGPU) RealQM solver and all the simulations cited in
the paper — for both atoms and nuclei — are publicly available in an interactive gallery
(https://claes542.github.io/RealMolecule/gallery.html; source
https://github.com/Claes542/RealMolecule). I believe this fits the journal's scope for original,
independent, foundational physics.

**Declarations.** The manuscript is original, is not under consideration elsewhere, and has not been
previously published. There are no competing interests. The mathematical model and the physical
argument are my own; the numerical implementation was developed and run with AI assistance (Claude,
Anthropic), as stated in the Acknowledgements. A companion paper, *RealNucleus: Nuclear Binding as
Dual Coulomb Confinement*, provides the detailed nuclear computations summarised here and is cited
accordingly.

I would be glad to suggest reviewers or to provide any further material the editors may require.
Thank you for your consideration.

Sincerely,

Claes Johnson
KTH Royal Institute of Technology, Stockholm