Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0810.2898 · Europhysics Letters (EPL)

Hyperfine level splitting for hydrogen-like ions due to rotation-spin coupling

I. M. Pavlichenkov

Published Feb 1, 2009• 10 citations
arXivHTMLPDF

Abstract

The theoretical aspects of spin-rotation coupling are presented. The approach is based on the general covariance principle. It is shown that the gyrogravitational ratio of the bare spin- and the spin-1 particles is equal unity. That is why spin couples with rotation as an ordinary angular momentum. This result is the rigorous substantiation of the cranking model. To observe the phenomenon, the experiment with hydrogen-like ions in a storage ring is suggested. It is found that the splitting of the 1 2 S 1/2 , F =1/2 hyperfine state of the 140 Pr 58+ and 142 Pm 60+ ions circulating in the storage ring ESR in Darmstadt along a helical trajectory is about 4.5 MHz. We argue that such splitting can be experimentally determined by means of the ionic interferometry.

DOI
10.1209/0295-5075/85/40008

Related papers

Spin-rotation coupling and Thomas precession of ions in a storage ring

Gaetano Lambiase, G. Papini

We discuss the role of spin-rotation coupling and Thomas precession in the decay of hydrogen-like heavy ions that are injected in a storage ring. We find that the decay curve has a time modulation that vanishes if the magnetic field also disappears. The results can be applied to the recently reported modulation in the decay of the hydrogen-like ions 140Pr58+, 142Pm60+ and 122I52+, where rotation couples to the spins of electron and nucleus. Spin-rotation coupling and Thomas precession also generate oscillations in the decay of a muon bound to a nucleus rotating in a storage ring.

Journal of Physics Conference Series•Jun 10, 2013•1 citation

Electromagnetic Backgrounds and Angular-Momentum Barriers in Gravitomagnetic Searches with Hydrogen-Like Ions

Leonardo A. Pachon

Hydrogen-like ions cannot usefully bound the gyrogravitational ratio $χ$: in ${}^{95}$Mo$^{41+}$ gravity shifts the hyperfine constants by fractions of $10^{-39}$--$10^{-38}$ with the tensor structure of the hyperfine interaction, centroids cancel it, and the $2p$ lines are 1.3 eV wide. Isotopes with spin can, however, enter the King plots that search for new bosons: for the cadmium clock line, the second-order hyperfine shift of ${}^{111}$Cd is $-0.96$~MHz, and a specific difference with ${}^{113}$Cd reduces it to about $2$~Hz after calculable anomaly and third-order corrections.

quant-pharXiv:2604.20717•Apr 23, 2026

Determination of the Spin-Rotation Fine Structure of He2+

Paul Jansen, Luca Semeria, Frédéric Merkt

Measuring spin-rotation intervals in molecular cations is challenging, particularly so when the ions do not have electric-dipole-allowed rovibrational transitions. We present a method, based on an angular-momentum basis transformation, to determine the spin-rotational fine structure of molecular ions from the fine structure of high Rydberg states. The method is illustrated by the determination of the so far unknown spin-rotation fine structure of the fundamentally important He_{2}^{+} ion in the X ^{2}Σ_{u}^{+} state. The fine-structure splittings of the v^{+}=0, N^{+}=1, 3, and 5 levels of He_{2}^{+} are 7.96(14), 17.91(32), and 28.0(6) MHz, respectively. The experiment relies on the use of single-mode cw radiation to record spectra of high Rydberg states of He_{2} from the a ^{3}Σ_{u}^{+} metastable state.

Physical Review Letters•Jan 26, 2018•12 citations

Radio-frequency Faraday effect in atomic hydrogen

Jack Finkel

Expressions for the angle of the Faraday rotation in atomic hydrogen, at radio frequencies, that are valid for all temperatures and magnetic field strengths are developed taking into account the electron-proton spin interactions. Simplified expressions for the rotation are also given for the special cases when the Zeeman splitting is much greater than or much smaller than the hyperfine splitting and when the two splittings are equal. A numerical result is given for the latter case at the hyperfine resonance frequency, 1420 MHz.

Journal of Physics B Atomic and Molecular Physics•Mar 28, 1985•0 citations

Rotational symmetry of space, rotation operators, conservation laws, and spin and orbital angular momenta in quantum mechanics

Masud Mansuripur

Quantization of spin and orbital angular momenta in standard quantum mechanics is rooted in the fundamental rotational symmetry of space in conjunction with the results of experiments on atomic and subatomic particles conducted with the Stern-Gerlach apparatus. We explain some of the most important features of spin and orbital angular momenta as inescapable consequences of elementary Stern-Gerlach experiments viewed in light of the rotational symmetry of space. The rotation operator is first derived for spin-½ particles, then extended to spin-1 particles by treating the case of a hydrogen atom in its ground state, where the spin of the proton combines with that of the electron to create a spin-1 triplet state. Along the way, we examine the evolution of a particle’s spin state under an applied magnetic field, where the interaction energy arises from the existence of a magnetic dipole moment for each particle in proportion to its spin angular momentum. Whereas a constant magnetic field B0 causes the particle’s magnetic moment to gyrate around the direction of B0, it will be seen that the presence of a small oscillating magnetic field perpendicular to B0 brings about the so-called Rabi oscillations, which involve periodic flippings of the particle’s spin orientation. In the case of a hydrogen atom in its ground state, the interaction between the magnetic dipole moments of the proton and the electron splits the ground state between a lower energy singlet having a net angular momentum of zero (spin-0 state), and a higher energy triplet having a total angular momentum of ħ (spin-1 state). This hyperfine splitting is the source of the well-known 21-cm line observed in the spectrum of the hydrogen atom, which arises from transitions between the atom’s singlet and triplet states. In the final section, we put forward an argument (originally made by Richard Feynman) that ties the rotational symmetry of space to the conservation of angular momentum in quantum mechanics. The argument is, in fact, quite general, enabling one to deduce other conservation laws from various inherent symmetries of quantum mechanical systems.

Spintronics•Oct 4, 2024•0 citations

Hyperfine energy levels of alkali-metal dimers: Ground-state homonuclear molecules in magnetic fields

J. Aldegunde, Jeremy M. Hutson

We investigate the hyperfine energy levels and Zeeman splittings for homonuclear alkali-metal dimers in low-lying rotational and vibrational states, which are important for experiments designed to produce quantum gases of deeply bound molecules. We carry out density-functional theory calculations of the nuclear hyperfine coupling constants. For nonrotating states, the zero-field splittings are determined almost entirely by the scalar nuclear spin-spin coupling constant. By contrast with the heteronuclear case, the total nuclear spin remains a good quantum number in a magnetic field. We also investigate levels with rotational quantum number $N=1$, which have long-range anisotropic quadrupole-quadrupole interactions and may be collisionally stable. For these states the splitting is dominated by nuclear quadrupole coupling for most of the alkali-metal dimers and the Zeeman splittings are considerably more complicated.

arXiv:0810.4709•Physical Review A•Jan 6, 2009•40 citations
The theoretical aspects of spin-rotation coupling are presented. The approach is based on the general covariance principle. It is shown that the gyrogravitational ratio of the bare spin- and the spin-1 particles is equal unity. That is why spin couples with rotation as an ordinary angular momentum. This result is the rigorous substantiation of the cranking model. To observe the phenomenon, the experiment with hydrogen-like ions in a storage ring is suggested. It is found that the splitting of the 1 2 S 1/2 , F =1/2 hyperfine state of the 140 Pr 58+ and 142 Pm 60+ ions circulating in the storage ring ESR in Darmstadt along a helical trajectory is about 4.5 MHz. We argue that such splitting can be experimentally determined by means of the ionic interferometry.
We discuss the role of spin-rotation coupling and Thomas precession in the decay of hydrogen-like heavy ions that are injected in a storage ring. We find that the decay curve has a time modulation that vanishes if the magnetic field also disappears. The results can be applied to the recently reported modulation in the decay of the hydrogen-like ions 140Pr58+, 142Pm60+ and 122I52+, where rotation couples to the spins of electron and nucleus. Spin-rotation coupling and Thomas precession also generate oscillations in the decay of a muon bound to a nucleus rotating in a storage ring.
Hydrogen-like ions cannot usefully bound the gyrogravitational ratio χχχ: in 95{}^{95}95Mo41+^{41+}41+ gravity shifts the hyperfine constants by fractions of 10−3910^{-39}10−39--10−3810^{-38}10−38 with the tensor structure of the hyperfine interaction, centroids cancel it, and the 2p2p2p lines are 1.3 eV wide. Isotopes with spin can, however, enter the King plots that search for new bosons: for the cadmium clock line, the second-order hyperfine shift of 111{}^{111}111Cd is −0.96-0.96−0.96~MHz, and a specific difference with 113{}^{113}113Cd reduces it to about 222~Hz after calculable anomaly and third-order corrections.
Measuring spin-rotation intervals in molecular cations is challenging, particularly so when the ions do not have electric-dipole-allowed rovibrational transitions. We present a method, based on an angular-momentum basis transformation, to determine the spin-rotational fine structure of molecular ions from the fine structure of high Rydberg states. The method is illustrated by the determination of the so far unknown spin-rotation fine structure of the fundamentally important He_{2}^{+} ion in the X ^{2}Σ_{u}^{+} state. The fine-structure splittings of the v^{+}=0, N^{+}=1, 3, and 5 levels of He_{2}^{+} are 7.96(14), 17.91(32), and 28.0(6) MHz, respectively. The experiment relies on the use of single-mode cw radiation to record spectra of high Rydberg states of He_{2} from the a ^{3}Σ_{u}^{+} metastable state.
Expressions for the angle of the Faraday rotation in atomic hydrogen, at radio frequencies, that are valid for all temperatures and magnetic field strengths are developed taking into account the electron-proton spin interactions. Simplified expressions for the rotation are also given for the special cases when the Zeeman splitting is much greater than or much smaller than the hyperfine splitting and when the two splittings are equal. A numerical result is given for the latter case at the hyperfine resonance frequency, 1420 MHz.
Quantization of spin and orbital angular momenta in standard quantum mechanics is rooted in the fundamental rotational symmetry of space in conjunction with the results of experiments on atomic and subatomic particles conducted with the Stern-Gerlach apparatus. We explain some of the most important features of spin and orbital angular momenta as inescapable consequences of elementary Stern-Gerlach experiments viewed in light of the rotational symmetry of space. The rotation operator is first derived for spin-½ particles, then extended to spin-1 particles by treating the case of a hydrogen atom in its ground state, where the spin of the proton combines with that of the electron to create a spin-1 triplet state. Along the way, we examine the evolution of a particle’s spin state under an applied magnetic field, where the interaction energy arises from the existence of a magnetic dipole moment for each particle in proportion to its spin angular momentum. Whereas a constant magnetic field B0 causes the particle’s magnetic moment to gyrate around the direction of B0, it will be seen that the presence of a small oscillating magnetic field perpendicular to B0 brings about the so-called Rabi oscillations, which involve periodic flippings of the particle’s spin orientation. In the case of a hydrogen atom in its ground state, the interaction between the magnetic dipole moments of the proton and the electron splits the ground state between a lower energy singlet having a net angular momentum of zero (spin-0 state), and a higher energy triplet having a total angular momentum of ħ (spin-1 state). This hyperfine splitting is the source of the well-known 21-cm line observed in the spectrum of the hydrogen atom, which arises from transitions between the atom’s singlet and triplet states. In the final section, we put forward an argument (originally made by Richard Feynman) that ties the rotational symmetry of space to the conservation of angular momentum in quantum mechanics. The argument is, in fact, quite general, enabling one to deduce other conservation laws from various inherent symmetries of quantum mechanical systems.
We investigate the hyperfine energy levels and Zeeman splittings for homonuclear alkali-metal dimers in low-lying rotational and vibrational states, which are important for experiments designed to produce quantum gases of deeply bound molecules. We carry out density-functional theory calculations of the nuclear hyperfine coupling constants. For nonrotating states, the zero-field splittings are determined almost entirely by the scalar nuclear spin-spin coupling constant. By contrast with the heteronuclear case, the total nuclear spin remains a good quantum number in a magnetic field. We also investigate levels with rotational quantum number N=1N=1N=1, which have long-range anisotropic quadrupole-quadrupole interactions and may be collisionally stable. For these states the splitting is dominated by nuclear quadrupole coupling for most of the alkali-metal dimers and the Zeeman splittings are considerably more complicated.