Universal binding and recoil corrections to bound state g factors in hydrogenlike ions

Hyperfine splitting of P-states in light muonic ions

We calculate hyperfine structure intervals for P–states in muonic ions of lithium, beryllium and boron. To construct the particle interaction operator in momentum space we use the tensor method ofprojection operators on states with definite quantum numbers of total atomic momentum F and total muonmomentum j. We take into account vacuum polarization, relativistic, quadruple and structure corrections of orders α4, α5 and α6. The obtained numerical values of hyperfine splittings can be used for a comparison with future experimental data.

Recoil Effect on the g Factor of Li-Like Ions

The nuclear recoil effect on the g factor of Li-like ions is evaluated. The one-electron recoil contribution is treated within the framework of the rigorous QED approach to the first order in the electron-to-nucleus mass ratio m/M and to all orders in the parameter αZ. These calculations are performed in a range Z=3-92. The two-electron recoil term is calculated for low- and middle-Z ions within the Breit approximation using a four-component approach. The results for the two-electron recoil part obtained in the Letter strongly disagree with the previous calculations performed using an effective two-component Hamiltonian. The obtained value for the recoil effect is used to calculate the isotope shift of the g factor of Li-like ^{A}Ca^{17+} with A=40 and A=48 which was recently measured. It is found that the new theoretical value for the isotope shift is closer to the experimental one than the previously obtained value.

Isotope dependence of the Zeeman effect in lithium-like calcium

The magnetic moment μ of a bound electron, generally expressed by the g-factor μ=−g μ_Bs ħ⁻¹ with μ_B the Bohr magneton and s the electron's spin, can be calculated by bound-state quantum electrodynamics (BS-QED) to very high precision. The recent ultra-precise experiment on hydrogen-like silicon determined this value to eleven significant digits, and thus allowed to rigorously probe the validity of BS-QED. Yet, the investigation of one of the most interesting contribution to the g-factor, the relativistic interaction between electron and nucleus, is limited by our knowledge of BS-QED effects. By comparing the g-factors of two isotopes, it is possible to cancel most of these contributions and sensitively probe nuclear effects. Here, we present calculations and experiments on the isotope dependence of the Zeeman effect in lithium-like calcium ions. The good agreement between the theoretical predicted recoil contribution and the high-precision g-factor measurements paves the way for a new generation of BS-QED tests.

In addition to hyperfine splitting effects, isotope shifts of atomic electronic energy levels allow the investigation nuclear properties. Here, the authors study the isotope dependence of the Zeeman effect in litihium-like calcium isotopes in a Penning-trap setup and find good agreement with QED calculations.