dorsal/arxiv
View SchemaCrater Property in Two-Particle Bound States: When and Why
| Authors | Chi-Keung Chow |
|---|---|
| Categories | |
| ArXiv ID | physics/9910038 |
| URL | https://arxiv.org/abs/physics/9910038 |
| DOI | 10.1119/1.19482 |
| Journal | Am.J.Phys. 68 (2000) 546 |
Abstract
Crater has shown that, for two particles (with masses $m_1$ and $m_2$) in a Coulombic bound state, the charge distribution is equal to the sum of the two charge distributions obtained by taking $m_1\to\infty$ and $m_2\to\infty$ respectively, while keeping the same Coulombic potential. We provide a simple scaling criterion to determine whether an arbitrary Hamiltonian possesses this property. In particular we show that, for a Coulombic system, fine structure corrections preserve this Crater property while two-particle relativistic corrections and/or hyperfine corrections may destroy it.
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"abstract": "Crater has shown that, for two particles (with masses $m_1$ and $m_2$) in a\nCoulombic bound state, the charge distribution is equal to the sum of the two\ncharge distributions obtained by taking $m_1\\to\\infty$ and $m_2\\to\\infty$\nrespectively, while keeping the same Coulombic potential. We provide a simple\nscaling criterion to determine whether an arbitrary Hamiltonian possesses this\nproperty. In particular we show that, for a Coulombic system, fine structure\ncorrections preserve this Crater property while two-particle relativistic\ncorrections and/or hyperfine corrections may destroy it.",
"arxiv_id": "physics/9910038",
"authors": [
"Chi-Keung Chow"
],
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"physics.gen-ph",
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"doi": "10.1119/1.19482",
"journal_ref": "Am.J.Phys. 68 (2000) 546",
"title": "Crater Property in Two-Particle Bound States: When and Why",
"url": "https://arxiv.org/abs/physics/9910038"
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