New theoretical methods are developed, within the framework of relativistic many-body theory, to treat parity nonconservation (PNC) in heavy atoms. The goal of this research is to improve the accuracy of PNC amplitudes in atoms and ions of experimental interest. Reducing the error in PNC calculations leads to more accurate experimental weak charges QW, quantities that depend on atomic theory and in turn provide valuable tests of the standard electroweak model. Precise calculations of the nuclear spin-dependent PNC amplitudes provide data needed to extract accurate anapole moments from PNC experiments. These in turn shed light on inconsistencies between constraints on weak nucleon-nucleon coupling constants obtained from the experimental anapole moment of cesium and those obtained from other nuclear PNC measurements. To improve calculations of PNC matrix elements, an indirect method that eliminates truncation errors is developed to perform sums over intermediate states. This method leads to a large set of inhomogeneous linear equations, similar to the singles-doubles (SD) equations developed earlier by this group.
