The First Forbidden β-Decay

Abstract

The energy spectrum, longitudinal polarization, and various β-γ correlations, with and without measurement of β or γ-ray polarizations, and calculated for the first forbidden β-decay. The theoretical expressions include finite nuclear size effects, in the form of a simple modification of older expressions. A short discussion of relevant Coulomb functions is presented. Interference from so-called third forbidden transitions is also included. The expressions are presented in a reasonably accurate expansion such that the energy dependence, dependence on real and imaginary parts of coupling constants, and dependence on independent nuclear matrix elements, are clearly revealed. Possibilities for testing the time reversal invariance of the interaction are discussed. The β-γ directional correlation is probably most useful for this purpose among the various possibilities in the first forbidden transition. The transverse β polarization is probably not useful for this purpose (it may, however, be used to determine nuclear matrix elements). Determination of other general properties of the β-decay interaction from first forbidden decays is probably even more difficult. Special information that might, however, be obtained from examination of a 0-0 transition is discussed. It is proposed that there is a fruitful field for determining properties of specific nuclei by measurement of several properties of a single decay. Both accurate and simplified expressions are presented to show what may be looked for. Absolute measurement of γ polarization following β-decay and measurement of the β-γ correlation and its energy dependence are very promising experiments; as are of cource, (the widely known) accurate spectrum and longitudinal polarization measurements. A special discussion is presented of the RaE case, where it is pointed out that accurate longitudinal polarization measurements could be very helpful.