Empirical Determination of the Bohr-Weisskopf Effect in Cesium and Improved Tests of Precision Atomic Theory in Searches for New Physics

The finite distribution of the nuclear magnetic moment across the nucleus gives a 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 ${}^{133}\mathrm{Cs}$. 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 precision heavy-atom community over the last several decades. We also deduce accurate values for the BW effect in other isotopes and states of cesium. These results enable cesium atomic wave functions to be tested in the nuclear region at an unprecedented 0.2% level, and are needed for the development of precision atomic many-body methods. This is important for increasing the discovery potential of precision atomic searches for new physics, in particular for atomic parity violation in cesium.

Figure 1

Product of $1s$ radial wave functions $fg$ for H-like and muonic ${}^{133}\mathrm{Cs}$ as a function of radial distance $r/R_m$, where $R_m$ is nuclear magnetic radius, alongside $F(r)/r^2$ that describes the nuclear magnetization distribution in ball, SP, SP-WS models. Values $fg$ are scaled to be unity at $r=R_m$.