Muonic–electronic negative hydrogen ion: circular states
- 1 September 2013
- journal article
- Published by Canadian Science Publishing in Canadian Journal of Physics
- Vol. 91 (9), 715-721
- https://doi.org/10.1139/cjp-2013-0077
Abstract
We studied a system consisting of a proton, a muon, and an electron (a μpe system), the muon and the electron being in circular states. We demonstrated that in this case, the muonic motion can represent a rapid subsystem while the electronic motion can represent a slow subsystem – the result that might seem counterintuitive. We used a classical analytical description to find the energy terms for the quasi molecule where the muon rotates around the axis connecting the immobile proton and the immobile electron (i.e., dependence of the energy of the muon on the distance between the proton and electron). We found that there is a double-degenerate energy term. We demonstrated that it corresponds to stable motion. We also conducted an analytical relativistic treatment of the muonic motion and found that the relativistic corrections are relatively small. Then we unfroze the slow subsystem and analysed a slow revolution of the axis connecting the proton and electron. We derived the condition required for the validity of the separation into rapid and slow subsystems. Finally, we showed that the spectral lines, emitted by the muon in the quasi molecule, μpe, experience a red shift compared to the corresponding spectral lines that would have been emitted by the muon in a muonic hydrogen atom (in the μp-subsystem). The relative values of this red shift, which is a “molecular” effect, are significantly greater than the resolution of available spectrometers and thus can be observed. Observing this red shift should be one of the ways to detect the formation of such muonic–electronic negative hydrogen ions.Keywords
This publication has 16 references indexed in Scilit:
- Experimental confirmation of circular Rydberg states with projectile-like ionsJournal of Physics B: Atomic, Molecular and Optical Physics, 2009
- Dissociative electron attachment to muonic hydrogen:Physical Review A, 2008
- Plasma screening within Rydberg atoms in circular statesThe European Physical Journal D, 2008
- Magnetic stabilization of a Rydberg quasimolecule in circular statesPhysical Review A, 2006
- Circular Rydberg states of hydrogenlike systems in collinear electric and magnetic fields of arbitrary strengths: an exact analytical classical solutionThe European Physical Journal D, 2004
- Astrophysical detection of heavy-particle-induced spectral shifts in muonic ironPhysical Review D, 2002
- Are Crossings of Energy Levels and Charge Exchange Really Quantum Phenomena?Physical Review Letters, 2000
- A purely classical description of crossings of energy levels and spectroscopic signatures of charge exchangeJournal of Physics B: Atomic, Molecular and Optical Physics, 2000
- High-resolution VUV spectroscopy ofin the region near thethresholdPhysical Review A, 2000
- Muon catalysed fusionContemporary Physics, 1990