Zeeman Correction Research Articles

Magnetic Interactions of One-Electron Atoms and of Positronium

This paper constitutes a continuation of previous work on magnetic interactions of one-electron atoms. In earlier papers the magnetic moment of a hydrogenic atom in its ground state was calculated, including radiative and nuclear-mass corrections. In this work the ${g}_{J}$ and ${g}_{I}$ factors are calculated for arbitrary hydrogenic states, including radiative and nuclear-mass corrections. The magnetic moment of a hydrogenic atom is obtained for any state. An extensive analysis of the Zeeman levels of positronium is carried out for the $n=1$ and $n=2$ states, including higher-order corrections. For the $n=1$ state, the results confirm the validity of the Breit---Rabi formula with $g$ factors in agreement with those given in an earlier paper by Grotch and Hegstrom. The annihilation diagram is included in the analysis but does not lead to any additional correction terms (to the accuracy we are working with). The Zeeman corrections in the $n=1$ state are relevant to the precise experimental determination of the positronium hyperfine structure. The analysis of the $n=2$ state Zeeman structure of positronium is similar to that carried out by Brodsky and Parsons for the $n=2$ states of hydrogenic atoms. Although the results in the hydrogenic case were immediately applicable to Lamb-shift measurements, the present results are not yet applicable since at present there is no experimental data on the excited states of positronium.

Hyperfine Structure ofHg193*,Hg195, andHg195*by Zeeman-Level Crossings

Hyperfine-structure measurements by optical detection of Zeeman-level crossings in the $6s6p^{3}P_{1}$ state were made with natural-linewidth precision in three radioactive isotopes of mercury. The magnetic dipole ($A$) and electric quadrupole ($B$) interaction constants in Mc/sec implied by these measurements (without second-order hyperfine corrections, but including second-order Zeeman and cross-Zeeman hyperfine corrections) are: ${\mathrm{Hg}}^{195}$ (9.5-h half-life)$A(^{3}P_{1})=15813.46\ifmmode\pm\else\textpm\fi{}0.23$ ${\mathrm{Hg}}^{195*}$ (isomer, 40 h)$A(^{3}P_{1})=\ensuremath{-}2368.04\ifmmode\pm\else\textpm\fi{}0.08$ $B(^{3}P_{1})=\ensuremath{-}782.45\ifmmode\pm\else\textpm\fi{}0.86$ ${\mathrm{Hg}}^{193*}$ (isomer, 11 h)$A(^{3}P_{1})=\ensuremath{-}2399.69\ifmmode\pm\else\textpm\fi{}0.06$ $B(^{3}P_{1})=\ensuremath{-}724.8\ifmmode\pm\else\textpm\fi{}90.0.$ The ${g}_{J}$ factor for the $^{3}P_{1}$ state of ${\mathrm{Hg}}^{199}$ is obtained from a new level-crossing measurement. The value, including second-order Zeeman and Zeeman-hyperfine corrections, is ${{g}_{J}}^{\ensuremath{'}}=1.486118\ifmmode\pm\else\textpm\fi{}0.000016$; 37\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ of this is the total contribution from ${g}_{I}$ and the second-order corrections. Our value is in substantial agreement with a recent measurement in the even Hg isotopes. The measured ratio of the $A$ factors of ${\mathrm{Hg}}^{195}$ and ${\mathrm{Hg}}^{199}$ with all second-order corrections (resulting from interaction with neighboring fine-structure levels) included is combined with the value for the ratio of the magnetic moments in an external field obtained by Walter and Stavn to yield the Bohr-Weisskopf hfs anomaly between ${\mathrm{Hg}}^{195}$ and ${\mathrm{Hg}}^{199}$, which is calculated to be $^{195}\ensuremath{\Delta}^{199}(^{3}P_{1})=0.1476(76)%$. The contribution to the anomaly from the ${s}_{\frac{1}{2}}$ electron is extracted and used to estimate admixture coefficients in the single-particle model of the nucleus with configuration mixing. These turn out to be satisfactorily small for the configurations assumed.

Hyperfine Structure ofHg197andHg199

The hyperfine structure of the $^{3}P_{1}$ state of ${\mathrm{Hg}}^{197}$ and ${\mathrm{Hg}}^{199}$ has been measured by a microwave-optical experiment. This involves optical excitation to the desired state, paramagnetic resonance in this state, and an optical method of detecting the paramagnetic resonance. The paramagnetic resonances were obtained between different $F$ levels as a function of magnetic field. Quadratic Zeeman corrections were estimated by second-order perturbation theory and the corrected transition frequencies were then extrapolated to zero field. The zero-field hyperfine-structure splittings in the $^{3}P_{1}$ state are ${\mathrm{Hg}}^{197}(F=\frac{3}{2} \mathrm{to} F=\frac{1}{2})=23086.37(2)$ Mc/sec, ${\mathrm{Hg}}^{199}(F=\frac{3}{2} \mathrm{to} F=\frac{1}{2})=22128.56(2)$ Mc/sec. Hyperfine-structure constants $A$ are obtained which are correct to second order. These are combined with the known nuclear magnetic moments to give the hyperfine-structure anomaly in the $^{3}P_{1}$ state: $\ensuremath{\Delta}(^{3}P_{1}, {\mathrm{Hg}}^{199}, {\mathrm{Hg}}^{201})=\ensuremath{-}0.00147(1)$, and the anomaly of the hyperfine-structure interaction for the $6s$ electron in the $^{3}P_{1}$ state: $\ensuremath{\Delta}({s}_{\frac{1}{2}}, {\mathrm{Hg}}^{199}, {\mathrm{Hg}}^{201})=\ensuremath{-}0.00175(9)$.