Calculation of parity-nonconserving effects in the6P122−7P122forbiddenM1transition in thallium

Abstract

Calculations are presented of the $E1\mathrm{}$ amplitude expected in the $6{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}-7\mathrm{}{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ forbidden $M1\mathrm{}$ transition in Tl 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 to the Dirac equation in a modified Tietz central potential. These wave functions are used to calculate allowed $E1\mathrm{}$ oscillator strengths, hfs splittings, and Stark $E1\mathrm{}$ transition amplitudes. These results are compared with experiment and the agreement is generally good. The relativistic $6{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}-7\mathrm{}{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ $M1\mathrm{}$ transition amplitude $\mathcal{m}$ is also calculated, and corrections due to interconfiguration mixing, Breit interaction, and hfs mixing are included. The result, ${\mathcal{m}}_{\mathrm{theor}}=(-3.2\mathrm{}\pm 1.0)\times {10}^{-5\mathrm{}}\frac{\mathrm{}\left|e\right|\mathrm{}\hslash }{2m_{e}c}$, is in agreement with the experimental value, ${\mathcal{m}}_{\mathrm{expt}}=(-2.11\mathrm{}\pm 0.30)\times {10}^{-5\mathrm{}}\frac{\mathrm{}\left|e\right|\mathrm{}\hslash }{2m_{e}c}$. The parity-nonconserving $E1\mathrm{}$ amplitude ${\mathcal{E}}_{\mathrm{PN}}$ is calculated, and a value for the circular dichroism, $\delta \simeq \frac{2\mathrm{Im}\left({\mathcal{E}}_{\mathrm{P}\mathrm{N},\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{o}}\right)}{{\mathcal{m}}_{\mathrm{expt}}}=2.6\mathrm{}\times {10}^{-3\mathrm{}}$, is obtained. Parity-nonconserving effects in other Tl transitions are discussed.