Atomic parity-nonconservation (PNC) provides a unique test of extensions to the Standard Model of elementary-particle physics. The accuracy of the measured PNC amplitude in atomic cesium has been recently improved to 0.3%. In order to provide quantitatively important constraints on "new physics" the 1% uncertainty of the relevant atomic-structure calculations has to be reduced accordingly.

I will discuss the prospects for improving ab initio relativistic many-body calculations of PNC amplitudes in heavy alkali-metal systems. At the accuracy level below 1% new physical effects beyond Coulomb correlations become important. In particular I will demonstrate that Breit and negative-energy state corrections to PNC amplitudes amount to 0.6% in Cs and 1.1% in Fr. These corrections reduce the 2.5 S Standard Model deviation [Bennett and Wieman, Phys. Rev. Lett. 82, 2484 (1999)] in the weak charge of Cs to 1.7 S.

I will also discuss one of the "by-products" of the PNC activity - calculations of dispersion coefficients for alkali-metal dimers with an unprecedented accuracy. The long-range atomic interactions sensitively determine properties of Bose-Einstein Condensates of dilute atomic gases.