Universal Z2/3/√(Qα) Scaling Law in Alpha Decay from Nuclei to Neutron-Star Mergers
Abstract
We establish a universal scaling law for α-decay half-lives based on the variable Xa = Za/√(Qα), which collapses experimental and theoretical data spanning over twenty orders of magnitude onto a single linear correlation. Global optimization over the complete set of even-even α emitters reveals a uniquely sharp optimum at a ≃ 2/3. This exponent is theoretically motivated by the leading geometric scaling of heavy nuclei and emerges quantitatively from the correlated nuclear systematics, driven by the correlated (Z, Qα) manifold of the nuclear chart. Strikingly, five structurally distinct semi-empirical models and an independent microscopic WKB calculation, when independently optimized with respect to the exponent a, yield values clustered around 2/3, while the corresponding a=2/3 correlations remain highly linear without refitting the original model parameters. This emergent scaling law implies smooth variations of decay times along the heavy r-process path. We demonstrate analytically that, given a roughly uniform distribution of this variable, the scaling law naturally supports a quasi-power-law radioactive heating rate (ε̇ ∝ t−1.24), consistent with full network calculations. Furthermore, integrating these scaling predictions directly into nuclear source terms for radiative-diffusion models yields multimessenger observables that accurately reproduce the kilonova AT2017gfo associated with the gravitational-wave event GW170817, demonstrating that the Z2/3/√(Qα) scaling coordinate provides a robust tool for modeling the radioactive engines of neutron-star mergers.
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BibTeX
@misc{anwer2026universal,
title = {{Universal $Z^2/3/\sqrtQ_α$ Scaling Law in Alpha Decay from Nuclei to Neutron-Star Mergers}},
author = {Hisham Anwer and B. Salah and A. R. Abdulghany},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25162},
eprint = {2609.25162},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25162},
}
RIS
TY - UNPB
TI - Universal Z^2/3/√(Q_α) Scaling Law in Alpha Decay from Nuclei to Neutron-Star Mergers
AU - Hisham Anwer
AU - B. Salah
AU - A. R. Abdulghany
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.25162
UR - https://arxiv.org/abs/2609.25162
AB - We establish a universal scaling law for α-decay half-lives based on the variable X_a = Z^a/√(Q_α), which collapses experimental and theoretical data spanning over twenty orders of magnitude onto a single linear correlation. Global optimization over the complete set of even-even α emitters reveals a uniquely sharp optimum at a ≃ 2/3. This exponent is theoretically motivated by the leading geometric scaling of heavy nuclei and emerges quantitatively from the correlated nuclear systematics, driven by the correlated (Z, Q_α) manifold of the nuclear chart. Strikingly, five structurally distinct semi-empirical models and an independent microscopic WKB calculation, when independently optimized with respect to the exponent a, yield values clustered around 2/3, while the corresponding a=2/3 correlations remain highly linear without refitting the original model parameters. This emergent scaling law implies smooth variations of decay times along the heavy r-process path. We demonstrate analytically that, given a roughly uniform distribution of this variable, the scaling law naturally supports a quasi-power-law radioactive heating rate (ε̇ ∝ t^−1.24), consistent with full network calculations. Furthermore, integrating these scaling predictions directly into nuclear source terms for radiative-diffusion models yields multimessenger observables that accurately reproduce the kilonova AT2017gfo associated with the gravitational-wave event GW170817, demonstrating that the Z^2/3/√(Q_α) scaling coordinate provides a robust tool for modeling the radioactive engines of neutron-star mergers.
ER -