Calculation of parity-nonconserving optical rotation in atomic bismuth

A Dirac-Hartree-Fock potential has been used to evaluate all zeroth- and first-order effects on the parity-nonconserving optical rotation for the 876-nm and 648-nm transitions in Bi. For the 876-nm transition, the zeroth-order result is -9.6×${10}^{-8\mathrm{}}$ for the ratio $R=\frac{\mathrm{Im}\mathrm{}\left(E1\mathrm{}\right)\mathrm{}}{M1\mathrm{}}$, and the result after addition of the first-order effect is -7.0×${10}^{-8\mathrm{}}$. The ratios for the 648-nm transition are -12.8×${10}^{-8\mathrm{}}$, respectively. To obtain more accurate results, the parity-nonconserving parts of the orbitals were then obtained in a self-consistent procedure by including the weak parity-nonconserving interaction in the one-particle Hamiltonian of the Hartree-Fock equations. Similarly, the electric-dipole functions were modified by taking into account the shielding of the external electric field due to a polarization of the core electrons. Re-evaluation of the first-order diagrams using these functions changes the ratio to $R=-8.3\mathrm{}\times {10}^{-8\mathrm{}}$ for the 876-nm transition and to $R=-11.1\mathrm{}\times {10}^{-8\mathrm{}}$ for the 648-nm transition.