Precise theoretical values for the amplitudes of parity non-conserving transitions in heavy atoms induced by exchange of neutral Z particles between the nucleus and electrons will be studied. This will permit a determination of the Weinberg angle from atomic physics experiments. The amplitudes are calculated using a relativistic version of many-body perturbation theory. The multiple sum over states needed in evaluating higher order effects are performed using finite basis set techniques often in conjunction with the solution of partial differential equations. With energies, transition amplitudes and hyperfine constants accurate to 1% the parity non-conserving amplitudes can also be obtained with errors at the 1% level.
