## Abstract

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.

Original language | English (US) |
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Pages (from-to) | 149-178 |

Number of pages | 30 |

Journal | Annals of Physics |

Volume | 127 |

Issue number | 1 |

DOIs | |

State | Published - Jun 1980 |

### Bibliographical note

Funding Information:One of us (J.H.) thanks the National Science Foundation for a predoctoral fellowship. Another (J.S.) thanks the National Research Council of the National Academy of Sciences for partial support and Dr. A. Temkin for his hospitality at the Laboratory for Solar Physics and Astronomy of the Goddard Space Flight Center. This work was also supported in part by the National Science Foundation and by the Department of Energy.