Calculation of parity-nonconserving effects in forbiddenM1transitions in cesium

Calculations are presented of the $E1\mathrm{}$ amplitude expected in forbidden $M1\mathrm{}$ transitions of Cs if parity conservation is violated in the neutral weak $e-N$ interaction, as proposed in a number of gauge models, including that of Weinberg and Salam. Valence electron wave functions are generated as numerical solutions of the Dirac equation in a Tietz central potential, and are used to calculate excited-state lifetimes, hfs splittings, and Stark $E1\mathrm{}$ transition amplitudes. These are compared with experiment and are in good agreement. Contributions to the $6{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ $g$-factor anomaly and to the forbidden $6{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-7\mathrm{}{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ and $6{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-8\mathrm{}{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ transitions from relativistic effects, Breit interaction, interconfiguration interaction, and hfs mixing are calculated, and it is found that this theoretical description is not entirely adequate. The parity-nonconserving $E1\mathrm{}$ amplitude ${\mathcal{E}}_{\mathrm{PN}}$ for the $6{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-7\mathrm{}{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ and $6{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-8\mathrm{}{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ transitions is evaluated. The results ${\mathcal{E}}_{\mathrm{PN}}\mathrm{}(6S-7S)=i3.50\mathrm{}\times {10}^{-11\mathrm{}} Q_W\left|{\mu }_B\right|$ and ${\mathcal{E}}_{\mathrm{PN}}\mathrm{}(6S-8S)=i1.48\mathrm{}\times {10}^{-11\mathrm{}}{Q}_W\left|{\mu }_B\right|$ are obtained. With a measured value of the $M1\mathrm{}$ amplitude