Relativistic many-body calculations in atoms and parity violation in caesium

It is shown that the use of relativistic Hartree-Fock equations in an external field, Brueckner orbitals and many-body perturbation theory provides, as a rule, an accuracy to 1-3% in atomic calculations. To control the accuracy, the energy levels and the fine and hyperfine structure intervals as well as the E1 amplitudes for s-p transitions in Cs have been calculated. The parity-violating E1 amplitude for the 6s-7s transition has been found: (7s mod D z mod 6s)=(0.88+or-0.03)*10 -11 (-Q w /N)(-iea B ), where Q w is the weak charge of the nucleus and N is the number of neutrons. Previous experimental data make it possible to find the weak nuclear charge of 133 Cs, Q W =-73.4+or-8.1+or-6, and the Weinberg angle sin 2 theta w =0.237+or-0.036+or-0.03.