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arXiv:2604.20717

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

Leonardo A. Pachon

quant-phgr-qcnucl-thSubmitted Apr 22, 2026• Announced Apr 23, 2026• Revised Oct 19, 2026 (v2)

v1 · Apr 22, 2026 v2 · Oct 19, 2026

Abstract

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.

Comments: 4 pages, 1 figure, 1 table, plus 9 pages of Supplemental Material. Substantially revised version. The spin-quadrupole shift and the projected laboratory bound of v1 are withdrawn: hydrogen-like ions cannot usefully test the gravitational coupling of nuclear spin. New: use of isotopes with spin in King plots, with a CI+MBPT calculation for the cadmium clock line

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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.

We present the first measurements of the [Xe]4f75d16s6p$\;^{11}{F_J}$11FJ excited state hyperfine coefficients and isotope shifts of spin-forbidden transitions of atomic gadolinium (Gd) at 726 and 743 nm in a hollow cathode gas discharge. In addition, we performed a King Plot analysis to determine specific mass shift and field shift constants for these lines. Moreover, we observed King Plot nonlinearity for the 743 nm transition, which is an effect recently proposed to aid in searches for hypothetical new light bosons. Spectroscopic results obtained from this study will facilitate the development of more efficient isotope separation techniques, enable narrowband laser cooling of Gd for novel dipolar physics investigations, and foster technological advances in high precision atomic clocks and quantum enhanced metrology.

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.

Spectroscopy of the 411-nm transition in

{}^{171}{\mathrm{Yb}}^{+}

has been performed and the feasibility of its use as an optical frequency standard has been demonstrated. The

{}^{2}{S}_{1/2}(F=0, {m}_{F}=0){--}^{2}{D}_{5/2}(F=2, {m}_{F}=0)

frequency, at zero-magnetic field, has been measured to be 729 487 779 566(153) kHz. This transition is free from the first-order Zeeman shift and has a measured second-order shift of +0.38(8) Hz/(\ensuremath{\mu}

{\mathrm{T})}^{2}

. In addition, the hyperfine structure of the

{}^{2}{D}_{5/2}

level has been deduced by driving the other hyperfine components of the 411-nm transition, showing it to be inverted. The

{}^{2}{D}_{5/2}

hyperfine splitting, measured to be -191(2) MHz, implies an A factor of -63.6(7) MHz. These data taken in conjunction with previous work yield an isotope shift of ${\ensuremath{\nu}}_{171}\ensuremath{-}{\ensuremath{\nu}}_{172}=+1317.1(1.3)\mathrm{MHz}$ for this transition between the 171 and 172 isotopes.