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

2014 ◽  
Vol 92 (11) ◽  
pp. 1405-1410 ◽  
Author(s):  
N. Kryukov ◽  
E. Oks
Keyword(s):  
Hydrogen Atom ◽  
Spectral Resolution ◽  
Nuclear Charge ◽  
Muonic Hydrogen ◽  
Binding Energies ◽  
Red Shift ◽  
Spectral Lines ◽  
Angular Momenta ◽  
Electronic Motion ◽  
Slow Subsystem

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.

Muonic–electronic negative hydrogen ion: circular states

2013 ◽  
Vol 91 (9) ◽  
pp. 715-721 ◽  
Author(s):  
N. Kryukov ◽  
E. Oks
Keyword(s):  
Analytical Description ◽  
Muonic Hydrogen ◽  
Red Shift ◽  
Spectral Lines ◽  
Hydrogen Ion ◽  
Hydrogen Ions ◽  
Energy Term ◽  
Electronic Motion ◽  
Relativistic Treatment ◽  
Slow Subsystem

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.

II—Observations on the Structure of the Hydrogen Lines Hα and Hβ

1924 ◽  
Vol 43 ◽  
pp. 37-42
Author(s):  
A. E. M. Geddes
Keyword(s):  
Fine Structure ◽  
Hydrogen Atom ◽  
Doppler Effect ◽  
Nuclear Charge ◽  
Direct Proof ◽  
Spectral Lines ◽  
Balmer Series ◽  
A Value ◽  
The Doppler Effect ◽  
Hydrogen Lines

According to Sommerfeld's theory of the fine structure of spectral lines, the magnitude of the separation of the doublets for all the members of the Balmer series of hydrogen should be constant, and have a value of 0·365 cm.−1. Now, owing to the extreme lightness of the hydrogen atom, a direct proof of Sommerfeld's theory by observation of the hydrogen lines is a somewhat difficult undertaking. At ordinary temperatures the Doppler effect is considerable, so that the lines are broadened out and the components of the doublets tend to overlap. The atom of helium, however, is four times as heavy as that of hydrogen, while the nuclear charge is double, so in consequence the separation of the doublets should be, according to the theory, sixteen times as great.

scholarly journals Nuclear Structure Evolution Reflected from Local Relations

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2253
Author(s):  
Man Bao ◽  
Qian Wei
Keyword(s):  
Nuclear Charge ◽  
Binding Energies ◽  
Structure Evolution ◽  
Α Decay ◽  
Charge Radii ◽  
Coexistence Phase ◽  
Nuclear Masses ◽  
Quadrupole Deformation Parameter ◽  
Nuclear Structures ◽  
Physical Quantities

The structure evolution of nuclei which are in connection with symmetry breaking is one of the important problems not only for nuclear structures, but also for astrophysics and the spectroscopy of exotic nuclei. Many physical quantities can provide useful information of a shell structure, such as nuclear masses and nuclear charge radii. This paper introduces three kinds of local relations, i.e., the NpNn scheme respectively for the quadrupole deformation parameter and the excitation energy of the first 2+, 4+, 6+ states, the (αN′n+N′p) relation for nuclear charge radii and α decay energies, and the so-called “nonpairing” relation for binding energies and nuclear charge radii. All these relations reflect the evolution of nuclear structures, involving shells, subshells, shape coexistence, phase transition and the Wigner effect. Some results from different models can be verified with each other.

Twinkle, Twinkle Little Star

2019 ◽  
pp. 46-53
Author(s):  
Nicholas Mee
Keyword(s):  
Nineteenth Century ◽  
Quantum Mechanics ◽  
Chemical Composition ◽  
Hydrogen Atom ◽  
Periodic Table ◽  
Chemical Properties ◽  
Spectral Lines ◽  
Exclusion Principle ◽  
Middle Years ◽  
Absorption Of Light

The emission and absorption of light by atoms produces discrete sets of spectral lines that were a vital clue to unravelling the structure of atoms and their elucidation was an important step towards the development of quantum mechanics. In the middle years of the nineteenth century Bunsen and Kirchhoff discovered that spectral lines can be used to determine the chemical composition of stars. Following Rutherford’s discovery of the nucleus, Bohr devised a model of the hydrogen atom that explained the spectral lines that it produces. His work was developed further by Pauli, who postulated the exclusion principle in order to explain the structure of other types of atom. This enabled him to explain the layout of the Periodic Table and the chemical properties of the elements.

scholarly journals Investigations concerning plasma parameters and population inversion in laser-produced counterstreaming plasmas

1991 ◽  
Vol 9 (2) ◽  
pp. 501-515 ◽  
Author(s):  
P. Glas ◽  
M. Schnürer
Keyword(s):  
Computational Analysis ◽  
Nuclear Charge ◽  
Gain Coefficient ◽  
Spectral Lines ◽  
Interaction Zone ◽  
Electron Number ◽  
Plasma Parameters ◽  
X Ray ◽  
Spatial Intensity Distribution ◽  
Resonance Transitions

We investigated the case where two laser-produced plasmas collide nearly head on. Special attention was devoted to the fundamentals necessary to realize a coherent X-ray source. A gas-dynamic computational analysis was performed to understand the evolution of the density, the temperature, and the velocity of merging plasmas. The spatial intensity distribution of selected spectral lines reveals that the interaction of plasmas of different nuclear charge and charge state is not strictly collision dominated. Using spectral line intensity ratios, we determined electron temperatures and electron number densities, as well as the intensity inversion on the 4–1 to 3–1 resonance transitions of [He]-like Al. Inversion occurs in the vicinity of the targets if identical materials are used (Al–Al) and is possibly indicated in the interaction zone for different ones (Al–Cu), too. The inversion factors (and the gain coefficient) for the 4–3 transition of [He]-like Al at about 130 Å were estimated.

Coincidental spectral lines for the hydrogen atom

1993 ◽  
Vol 23 (3) ◽  
pp. 465-468 ◽  
Author(s):  
Daniel W. Wyss ◽  
Walter Wyss
Keyword(s):  
Hydrogen Atom ◽  
Spectral Lines

scholarly journals Proton polarizability and lamb shift in the muonic hydrogen atom

2000 ◽  
Vol 63 (5) ◽  
pp. 845-849 ◽  
Author(s):  
A. P. Martynenko ◽  
R. N. Faustov
Keyword(s):  
Hydrogen Atom ◽  
Lamb Shift ◽  
Muonic Hydrogen

scholarly journals Revolution of Charged Particles in a Central Field of Attraction with Emission of Radiation

2020 ◽  
Vol 3 (1) ◽  
Keyword(s):  
Circular Orbit ◽  
Center Of Mass ◽  
Orbital Plane ◽  
Hydrogen Gas ◽  
Spectral Lines ◽  
Electronic Charge ◽  
Central Field ◽  
Angular Momenta ◽  
Stable Circular Orbit ◽  
Common Center

A particle of mass nm, carrying the electronic charge -e, revolves in an orbit through angle ψ at distances nr from a center of force of attraction, with angular momenta nL perpendicular to the orbital plane, where n is an integer greater than 0, m the electronic mass and r1 is the radius of the first circular orbit. The equation of motion of the nth orbit of revolution is derived, revealing that an excited particle revolves in an unclosed elliptic orbit, with emission of radiation at the frequency of revolution, before settling down, after many cycles of ψ, in a stable circular orbit. In unipolar revolution, a radiating particle settles in a circular orbit of radius nr1 round a positively charged nucleus. In bipolar revolution, two radiating particles of the same mass nm and charges e and –e, settle in a circular stable orbit of radius ns1 round a common center of mass, where s1 is the radius of the first orbit. Discrete masses nm and angular momenta nL lead to quantization of the orbits outside Bohr’s quantum mechanics. The frequency of radiation in the bipolar revolution is found to be in conformity with the Balmer-Rydberg formula for the spectral lines of radiation from the atom hydrogen gas. There is a spread in frequency of emitted radiation, the frequency in the final circle being the highest, which might explain hydrogen fine structure, as observed with a diffraction grating of high resolution. The unipolar revolution is identified with the solid or liquid state of hydrogen and bipolar revolution with the gas state.

Sign in / Sign up

Export Citation Format

Share Document