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

TL;DR

This paper presents a theoretical analysis of spin-rotation coupling in hydrogen-like ions, showing that spin couples with rotation as angular momentum, and proposes an experiment to observe hyperfine level splitting due to this effect.

Contribution

It provides a rigorous theoretical foundation for spin-rotation coupling and suggests an experimental method to measure hyperfine splitting in hydrogen-like ions.

Findings

Gyrogravitational ratio of spin-1/2 and spin-1 particles is unity.

Hyperfine splitting of about 4.5 MHz predicted for specific ions.

Proposes ionic interferometry as a method for experimental detection.

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 $^{140}{\rm Pr}^{58+}$ and $^{142}{\rm Pm}^{60+}$ 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.