Diamagnetic correction to the ${}^{9}$Be${}^{+}$ ground-state hyperfine constant

Diamagnetic correction to the $^{9}$ Be $^{+}$ ground-state hyperfine constant

N. Shiga, W. M. Itano, and J. J. Bollinger

Phys. Rev. A 84, 012510 – Published 22 July 2011

Abstract

We report an experimental determination of the diamagnetic correction to the $^{9}$ Be $^{+}$ ground state hyperfine constant $A$ . We measured $A$ $=$ $- 625 008 837.371 (11)$ Hz at a magnetic field $B$ of 4.4609 T. Comparison with previous results, obtained at lower values of $B$ (0.68 T and 0.82 T), yields the diamagnetic shift coefficient $k$ $=$ $2.63 (18) \times 10^{- 11}$ T $^{- 2}$ , where $A (B) = A_{0} (1 + k B^{2})$ . The zero-field hyperfine constant $A_{0}$ is determined to be $- 625 008 837.044 (12)$ Hz. The $g$ -factor ratio ${g_{I}}^{'} / g_{J}$ is determined to be $2.134 779 852 7 (10) \times 10^{- 4}$ , which is equal to the value measured at lower $B$ to within experimental error. Upper limits are placed on some other corrections to the Breit-Rabi formula. The measured value of $k$ agrees with theoretical estimates.