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Hyperspherical elliptic coordinates treatment of muon transfer from
muonic hydrogen to atomic oxygen
Arnaud Dupays, Bruno Lepetit, J. Alberto Beswick, Carlo Rizzo, Dimitar Bakalov
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.
- oai_identifier:
- oai:arXiv.org:quant-ph/0612175
- categories:
- quant-ph
- comments:
- 6 pages, 7 figures
- doi:
- 10.1103/PhysRevA.68.062506
- arxiv_id:
- quant-ph/0612175
- journal_ref:
- Phys. Rev. A, 68, 062506 (2003)
- created:
- 2006-12-20
Full article ▸
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