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

TL;DR

This paper precisely measures the diamagnetic correction to the hyperfine constant of $^9$Be$^+$ in a high magnetic field, providing experimental data that confirms theoretical estimates and refines fundamental atomic parameters.

Contribution

The study provides the first high-field measurement of the diamagnetic correction to the $^9$Be$^+$ hyperfine constant, improving accuracy of atomic models and fundamental constants.

Findings

Measured hyperfine constant $A$ at 4.4609 T with high precision.

Determined diamagnetic shift coefficient $k$ = $2.63(18) imes 10^{-11}$ T$^{-2}$.

Confirmed the $g$-factor ratio matches previous low-field measurements.

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 $A(B)=A_0\times (1+k B^2)$. The zero-field hyperfine constant $A_0$ is determined to be $-625\,008\,837.044(12)$ Hz. The $g$-factor ratio ${g_I}^\prime/g_J$ 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.