Nuclear recoil correction to the hyperfine splitting in atomic systems

TL;DR

This paper derives a formula for nuclear recoil corrections to hyperfine splitting in light atoms, highlighting the importance of nuclear structure effects beyond simple Hamiltonian models.

Contribution

It provides a compact formula for $O(Z\alpha)$ recoil corrections and emphasizes the need for realistic nuclear structure modeling.

Findings

Derived a compact formula for recoil corrections

Showed significance of nuclear structure effects in light atoms

Highlighted limitations of Hamiltonian-based descriptions

Abstract

We consider leading $O(m/M)$ nuclear recoil corrections to the hyperfine splitting in light atomic systems. Due to the singularity of hyperfine interactions, the electromagnetic form factors of the nucleus have to be introduced as a function of the four-momentum square, which goes beyond the Hamiltonian description of the system. We present a compact formula for $O(Z\,\alpha)$ recoil corrections and indicate the importance, especially for light atoms, of a more realistic description of the nuclear structure effects.