Empirical determination of the hyperfine anomaly in cesium and improved tests of atomic theory in precision atomic searches for new physics

The finite distribution of the nuclear magnetic moment across the nucleus gives an important contribution to the hyperfine structure known as the Bohr-Weisskopf (BW) effect. We have obtained an empirical value of -0.24(18)% for this effect in the ground and excited s states of atomic cesium-133. This value is found from historical muonic atom measurements in combination with our muonic-atom and atomic many-body calculations. The effect differs by 0.5% in the hyperfine structure from the value found using the uniform magnetization distribution, which has been commonly employed in the community over the last several decades, and it supports the validity of the nuclear single-particle model. This result is important for the testing and development of atomic theory towards the 0.1% uncertainty level in precision atomic searches for new physics, in particular for atomic parity violation in cesium.