It is proposed to obtain precise theoretical values for amplitudes of the parity non-conserving transitions in heavy atoms induced by exchange of neutral Z particles between the nucleus and the atomic electrons, thereby permitting the determination of the Weinberg angle from atomic physics experiments. The amplitudes are obtained with a relativistic version of many-body perturbation theory. The multiple sums occurring in higher order are evaluated with finite-basis techniques. All orders methods have been devised and will be applied to cesium. With energies, transition amplitudes, and hyperfine constants accurate to 1% the parity non conserving amplitudes can be obtained with errors at the 1% level.
