Muonic–electronic quasi molecules based on a fully stripped multicharged ion

Abstract

In our previous paper (Can. J. Phys. 91, 715 (2013) doi: 10.1139/cjp-2013-0077 ) we studied a system consisting of a proton, a muon, and an electron; the muon and the electron being in circular states. The study was motivated by numerous applications of muonic atoms and molecules, where one of the electrons is substituted by the heavier lepton μ–. We demonstrated that in such a μpe quasi molecule, the muonic motion can represent a rapid subsystem while the electronic motion can represent a slow subsystem — a result that may seem counterintuitive. In other words, the muon rapidly revolves in a circular orbit about the axis connecting the proton and electron while this axis slowly rotates following a relatively slow electronic motion. 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 present paper we generalize this study by replacing the proton in the μpe quasi molecule by a fully stripped ion of nuclear charge Z > 1. We show that in this case, just as in the previously studied case of Z = 1, the muonic motion can represent a rapid subsystem while the electronic motion can represent a slow subsystem. For this to be valid, the ratio of the muonic and electronic angular momenta should be slightly greater than in the case of Z = 1. We demonstrate that the binding energies of the muon for Z > 1 are much greater than for Z = 1 at any finite value of the nucleus–electron distance. Finally we show that the red shift of the spectral lines emitted by the muon (compared to the spectral lines of the corresponding muonic hydrogen-like ion of nuclear charge Z) decreases as Z increases. However, the relative red shift remains within the spectral resolution of available spectrometers at least up to Z = 5. Observing this red shift should be one of the ways to detect the formation of the quasi molecules, μZe.

Classical Dynamics of Muonic-Electronic Helium and Heliumlike Ions: The Allowance for the Eccentricity of the Muon and Nucleus Orbits

“…where W is defined in Equation ( 9) and [P, Q] are the Poisson brackets, is the time-independent term for the effective potential. On substituting Ω from Equation (7) in Equation ( 12), we get:…”

Classical description of charge exchange involving He-like or Li-like ions in Rydberg states in plasmas

“…We also performed an exact numerical solution to this problem. From the scaling formula for R, k=(μL 2 /Z)r with μ given by equation (19). Equation (17), after being squared, is a fourth-degree polynomial with respect to p and has a real positive analytical solution for p which depends on r: p 0 =p(w, b, r).…”

“…Later applications of these results included the following studies: the magnetic stabilization of such one-electron Rydberg quasimolecules (hereafter, RQ1) [10], the electric-fieldcaused enhancement of the ionization of the RQ1 and of charge exchange [11,12], the effect of the screening by plasma electrons on the classical energy terms of RQ1 [13,14], the application to the problem of continuum lowering in plasmas [13][14][15], the effect of a laser field on RQ1 [16], and the attachment of an electron to a muonic hydrogen atom [17,18] or to a muonic hydrogenic ion [19]. All these studies were summarized in review [20].…”

“…In papers [8, 10-14, 17, 18] the studies were focused at Circular Rydberg States (CRS) of the QR1 systems (the analysis in papers [9,16,19] went beyond CRS). CRS of atomic and molecular systems, with only one electron, correspond to |m|=(n−1)?1, where n and m are the principal and magnetic electronic quantum numbers, respectively.…”