Electromagnetic Backgrounds and Angular-Momentum Barriers in Gravitomagnetic Searches with Hydrogen-Like Ions
quant-ph, gr-qc, nucl-th
Submitted: 2026-04-22
Updated: 2026-10-19
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 The spin-quadrupole shift and the projected laboratory bound of v1 are withdrawn: hydrogen-like ions cannot usefully test the gravitational coupling of nuclear spin.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
License: http://creativecommons.org/licenses/by/4.0/
The gist: 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
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.
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