dorsal/arxiv
View SchemaHyperspherical elliptic coordinates treatment of muon transfer from muonic hydrogen to atomic oxygen
| Authors | Arnaud Dupays, Bruno Lepetit, J. Alberto Beswick, Carlo Rizzo, Dimitar Bakalov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0612175 |
| URL | https://arxiv.org/abs/quant-ph/0612175 |
| DOI | 10.1103/PhysRevA.68.062506 |
| Journal | Phys. Rev. A, 68, 062506 (2003) |
Abstract
Quantum-mechanical calculations of muon transfer between muonic hydrogen and an oxygen nuclei for $s$ waves and collision energies in the range $10^{-3} - 10^3$ eV, are presented. Close-coupling time-independent Schr\"odinger equations, written in terms of hyperspherical elliptic coordinates were integrated along the hyper-radius to obtain the partial and total muon-transfer probabilities. The results show the expected Wigner-Bethe threshold behavior up to collision energies of the order of $10^{-2}$ eV and pronounced maxima at $10^2$ eV which can be interpreted in terms of crossings between potential energy curves corresponding to the entrance channel state $(\mu p)_{1s} + \mO$ and two product channels which asymptotically correlate to $p + (\mO\mu)_{n=5,6}$. The population of the final states with different orbital angular momenta is found to be essentially independent of energy in the range considered in this work. This can be attributed to a strong selection rule for the conservation of the quantum number associated to one of the elliptic hyperangles.
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"abstract": "Quantum-mechanical calculations of muon transfer between muonic hydrogen and\nan oxygen nuclei for $s$ waves and collision energies in the range $10^{-3} -\n10^3$ eV, are presented. Close-coupling time-independent Schr\\\"odinger\nequations, written in terms of hyperspherical elliptic coordinates were\nintegrated along the hyper-radius to obtain the partial and total muon-transfer\nprobabilities. The results show the expected Wigner-Bethe threshold behavior up\nto collision energies of the order of $10^{-2}$ eV and pronounced maxima at\n$10^2$ eV which can be interpreted in terms of crossings between potential\nenergy curves corresponding to the entrance channel state $(\\mu p)_{1s} + \\mO$\nand two product channels which asymptotically correlate to $p +\n(\\mO\\mu)_{n=5,6}$.\n The population of the final states with different orbital angular momenta is\nfound to be essentially independent of energy in the range considered in this\nwork. This can be attributed to a strong selection rule for the conservation of\nthe quantum number associated to one of the elliptic hyperangles.",
"arxiv_id": "quant-ph/0612175",
"authors": [
"Arnaud Dupays",
"Bruno Lepetit",
"J. Alberto Beswick",
"Carlo Rizzo",
"Dimitar Bakalov"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.68.062506",
"journal_ref": "Phys. Rev. A, 68, 062506 (2003)",
"title": "Hyperspherical elliptic coordinates treatment of muon transfer from muonic hydrogen to atomic oxygen",
"url": "https://arxiv.org/abs/quant-ph/0612175"
},
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