The Departures Are a Shell Capacity: The Closures Refuse the Balance
Year: 2026
Type: preprint
Abstract: AF-2 evaluated the nuclear shell closures: the observed magic numbers 2, 8, 20, 28, 50, 82, 126 depart from the harmonic-oscillator closures 2, 8, 20, 40, 70, 112, 168 by −12, −20, −30, −42 at the four split closures — a debt the record meets with one fitted spin–orbit term. This paper attacks the departures as a two-face balance object in the frame's sense: if the sever's pair {200, 211} or its toll wrote the closures, the departure shares would land on owned balance forms. They do not — the battery in §1 refuses every form, nearest miss 9.11% against a 1% tolerance. What the departures are is printed in §2, exactly: 12, 20, 30, 42 are the pronic numbers k(k+1) for k = 3…6 — each departure equals the full capacity of one oscillator shell, one shell down. The spin–orbit intruder does not nudge the closures; it removes precisely one shell-capacity from each, in the oscillator's own combinatorics. The balance desk closes this address the way the Koide address was closed in the origination line: the phenomenon is real, its source is identified, and the source is not ours.
Author: Aldred, William Alexander
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225422815