EFFECT OF FINAL-STATE INTERACTIONS IN ALLOWED BETA-DECAYS .1. GENERALFORMALISM

In this work the beta decay of a nucleus hosted in an atomic or a mole cular system is considered. A formalism is derived that allows the cal culation of the changes in the beta spectrum that are caused by the Co ulombic final-state interaction of the beta electron (or positron) wit h all molecular electrons as well as nuclei. Explicit formulas are der ived for the matrix elements occurring in a perturbational treatment u p to the pure first-order correction term, and different approximation s are discussed. The result obtained in this work is especially applic able to cases where the decaying nucleus is part of a molecular system . In contrast to previous works a complete partial-wave analysis of th e interaction operator has been performed, and for the first time expl icit results are derived for all partial waves. The total symmetric co ntribution agrees (for atoms) with previous results and confirms the e arly work of Rose. However, the nonspherical contributions are of the same order of magnitude as the total symmetric contribution and have t herefore to be taken into account, if the Rose correction is applied. This can be done in a very simple way, since the correction turns out to be (approximately) proportional to the number of electrons but othe rwise completely independent of the atomic or molecular system under c onsideration. In the case of molecular systems also the contribution o f the spectator nuclei has to be considered, since this contribution i s again of the same order of magnitude as the correction term given by Rose. It is shown that the interaction with the decaying nucleus (tha t leads to the occurrence of the Fermi function) is very well approxim ated within the present perturbational approach, where it is treated i n the same way as the interaction with the other particles.