The Weak Closure Travels, the Hard Step Does Not: An A-Scan of the Pairing Split
Year: 2026
Type: preprint
Abstract: AF-31 put declared BCS pairing on AF-27's computed Woods–Saxon spectrum and split the charge's word "sharpen" into two graded facts at A = 208: gap values sharpen (the weak light closures' two-quasiparticle gaps lift proportionally more than the heavy closures'), steps soften (the light closures smear where the heavy ones keep hard occupation steps). This paper re-runs the identical construction at A = 40, 90, 132 — the radius following the construction's own rule, Δ_emp(A) = 12/√A per A, AF-31's fixed-Δ scan carried as a cross-check — with the A = 208 rows reproducing AF-27/AF-31 as calibration (gaps 0.78/1.26/1.85/2.54 at κ_WS = 0.30; the AF-31 ratio pair 0.3071 → 0.6047 for G(28)/G(126) recomputed from this bench's prints). The hierarchy travels: 28 holds the smallest gap of any graded closure at every (A, κ_WS) in the scan — 2.08 MeV at A = 40 where the deep closures sit at 8–10 MeV, 1.29 at A = 132, 0.78 at 208 — and its value lift at Δ_emp is the largest at its A in eleven of twelve rows. The step half's strong form does not travel: G < Δ_emp occurs only at the single weakest point of the heaviest spectrum. And the scan finds a phenomenon AF-31 could not see: two of its A's close at the well's edge — the R(132) well binds exactly 126 states at all three strengths and the R(90) well exactly 82 at κ_WS = 0.30 — where the closure is the spectrum's boundary, not a gap in it, and the ratio instrument is undefined. Pairing is graded throughout by AF-31's control: it determines values, it does not place; no number here moves a closure's address.
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: W7225454225