Relativistic theory of parity violation in many-electron atoms

We present a theoretical framework for the calculation of parity-mixing effects of the weak interaction in many-electron atoms which is based on first principles. The starting point is an external-field no-pair Hamiltonian H₊ which allows for a consistent treatment of effects coming from virtual electron-positron pairs and can be used as a basis for a systematic program of calculations. We show that the matrix element M for parity-violating E1 transitions, given by quantum electrodynamics, gets an appreciable contribution M^pair from states involving an extra electron-positron pair. However on eliminating the velocity operator α in favor of the length operator iωr, we find cancellations which result in an accurate formula for M involving only the positive-energy N-electron eigenstates of H₊ as intermediate states and the length form, iωr · ε{lunate}, of the dipole operator. We discuss the implications of our results for calculations of amplitudes for parity-violating radiative E1 transitions in many-electron atoms. Our analysis includes a study of the effects coming from the weak electron-electron interaction as well as those arising from the weak electron-nucleus interaction.