### 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 |

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### Cite this

*Annals of Physics*,

*127*(1), 149-178. https://doi.org/10.1016/0003-4916(80)90152-9