Hyperfine Structure of ${\mathrm{Hg}}^{193*}$, ${\mathrm{Hg}}^{195}$, and ${\mathrm{Hg}}^{195*}$ 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)$A\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)=15813.46\mathrm{}\pm 0.23$ ${\mathrm{Hg}}^{195*}$ (isomer, 40 h)$A\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)=-2368.04\mathrm{}\pm 0.08$ $B\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)=-782.45\mathrm{}\pm 0.86$ ${\mathrm{Hg}}^{193*}$ (isomer, 11 h)$A\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)=-2399.69\mathrm{}\pm 0.06$ $B\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)=-724.8\mathrm{}\pm \mathrm{90.0.}$ 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 ${g_J}^{\prime }=1.486118\mathrm{}\pm 0.000016$; 37×${10}^{-6\mathrm{}}$ 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 ${}_{}{}^{195}{}_{}{}^{}\Delta _{}^{199}{}_{}{}^{}\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)=0.1476\mathrm{}\left(76\right)\%$. 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.