Hyperfine Level Splitting for Hydrogen-Like Ions due to Rotation-Spin Coupling

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-1/2 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 ${}^{140}{\mathrm{Pr}}^{58+}$ and ${}^{142}{\mathrm{Pm}}^{60+}$ 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.

6 pages, final version

References in corpus (3)

• Observation of Non-Exponential Orbital Electron Capture Decays of Hydrogen-Like ${}^{140}$Pr and ${}^{142}$Pm Ions
• Measurement of the ${\beta }^{+}$ and orbital electron-capture decay rates in fully-ionized, hydrogen-like, and helium-like ${}^{140}$Pr ions
• Observable frequency shifts via spin-rotation coupling

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