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

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-\frac{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 1²S_1/2, F=1/2 hyperfine state of the ¹⁴⁰Pr⁵⁸⁺ and ¹⁴²Pm⁶⁰⁺ 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.