dorsal/arxiv
View SchemaThe 1/3 Geometric Constant: Scale Invariance and the Origin of "Missing Energy" in 3D Quantum Fragmentation
| Authors | Jinzhen Zhu |
|---|---|
| Categories | |
| ArXiv ID | 2601.08255vv1 |
| URL | https://arxiv.org/abs/2601.08255 |
| License | http://creativecommons.org/licenses/by-nc-sa/4.0/ |
Abstract
We report a fundamental geometric constraint on the detection of kinetic energy release (KER) in three-dimensional quantum fragmentation. By investigating the sudden dissociation of Slater-type orbitals, physically motivated basis for localized states, we demonstrate that the ratio of the peak detected energy to the integrated mean, $R_E = E_{\text{peak}}/\langle E \rangle$, is strictly bounded below $0.5$ for all physical parameter spaces. We systematically map the behavior of $R_E$ across the orbital localization ($\zeta$) and effective repulsive charge ($Q$) landscape. Our results show that while $R_E$ exhibits sensitivity to the force-field geometry at atomic scales, it converges to a remarkably stable, scale-invariant constant of $\approx 0.33$ in the high-localization limit ($M \propto \zeta$) characteristic of subatomic ground states ($n=1$,$Q=1$). This $1/3$ geometric constant provides a provocative first-principles interpretation of the historical ``missing energy'' problem in nuclear physics. We suggest that the $1/3$ average energy ratio observed in Beta decay spectra may be a topological artifact of the $4\pi r^2$ volume weighting inherent to 3D wavefunctions, rather than exclusively a signature of undetected mass. This work establishes $R_E < 0.5$ as a universal geometric baseline for quantum simulations and offers a new framework for reconstructing the true energy budget in subatomic calorimetry by correcting for the intrinsic masking effects of 3D radial geometry.
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"abstract": "We report a fundamental geometric constraint on the detection of kinetic energy release (KER) in three-dimensional quantum fragmentation. By investigating the sudden dissociation of Slater-type orbitals, physically motivated basis for localized states, we demonstrate that the ratio of the peak detected energy to the integrated mean, $R_E = E_{\\text{peak}}/\\langle E \\rangle$, is strictly bounded below $0.5$ for all physical parameter spaces. We systematically map the behavior of $R_E$ across the orbital localization ($\\zeta$) and effective repulsive charge ($Q$) landscape. Our results show that while $R_E$ exhibits sensitivity to the force-field geometry at atomic scales, it converges to a remarkably stable, scale-invariant constant of $\\approx 0.33$ in the high-localization limit ($M \\propto \\zeta$) characteristic of subatomic ground states ($n=1$,$Q=1$). This $1/3$ geometric constant provides a provocative first-principles interpretation of the historical ``missing energy\u0027\u0027 problem in nuclear physics. We suggest that the $1/3$ average energy ratio observed in Beta decay spectra may be a topological artifact of the $4\\pi r^2$ volume weighting inherent to 3D wavefunctions, rather than exclusively a signature of undetected mass. This work establishes $R_E \u003c 0.5$ as a universal geometric baseline for quantum simulations and offers a new framework for reconstructing the true energy budget in subatomic calorimetry by correcting for the intrinsic masking effects of 3D radial geometry.",
"arxiv_id": "2601.08255",
"authors": [
"Jinzhen Zhu"
],
"categories": [
"physics.atom-ph"
],
"license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
"title": "The 1/3 Geometric Constant: Scale Invariance and the Origin of \"Missing Energy\" in 3D Quantum Fragmentation",
"url": "https://arxiv.org/abs/2601.08255",
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