On the theory of beta-radioactivity IV : The polarization of beta-rays emitted by aligned nuclei in allowed transitions

Abstract

The consequences of alignment of nuclei, which show allowed ß-transitions, are investigated. A general formula is derived for the transition probability of an allowed β-transition, in which the direction of emission of electron and neutrino, the polarization of the electron and the orientation of the nuclear spin are taken into account. The calculations have been made for a Hamiltonian for the β-interaction, which is an arbitrary "mixture" of the five invariants of the Dirac theory. The influence of the nuclear charge has, however, been neglected. From this formula the following results are immediately obtained:

The angular distribution of the β-radiation remains spherically symmetric if the nuclei are aligned, so that the alignment cannot be detected in this way.

The emitted β-radiation is polarized and the degree of polarization follows from the general formula. If we take the special case that the interaction Hamiltonian is of the tensor or the axial vector type and if the β-rays are emitted perpendicular to the direction of the nuclear spin of completely aligned nuclei with nuclear spin ji, the degree of polarization is given by: a) 1/Eif ji = jf + 1, b) 1/E(ji + 1), if ji = jf,c)ji/E(ji + 1), if ji = ji - 1. (E is the relativistic energy of the electrons, E ≈ 1 for small kinetic energies; jf gives the spin of the final nucleus).