Nuclear Recoil Correction in Hydrogen-like Atoms

Our aim is to calculate the nuclear recoil correction to the hyperfine splitting within the framework of HPQED theory [1]. An exact formula was derived in Ref. [2]. However, due to the complexity of this expression, it has not yet been calculated numerically. As a first step we have developed a numerical method based on the DKB basis [3] for solving the Dirac equation, following Shabaev’s numerical approach. Using this method, we calculated the nuclear recoil correction to the Lamb shift both for muonic and electronic hydrogen-like atoms. Our purpose is to apply this method to the hyperfine splitting. This effect is unknown for light hydrogen-like atoms.

[1]: K. Pachucki, V.A. Yerokhin, Phys. Rev. A 110, 032804 (2024)

[1]: K. Pachucki, Phys. Rev. A 109, 052822 (2024)

[3]: V. M. Shabaev et al., Phys. Rev. Lett. 93, 130405 (2004)