Internal Ionization during Beta Decay

In nuclear $\beta$ decay, atomic excitation, including ionization, can occur because of (i) imperfect overlap of parent and daughter orbital electron wave functions, and (ii) scattering of atomic electrons by the $\beta$ particle ("direct collisions"). In order to evaluate the relative importance of these two processes and test the possible role of nuclear matrix elements in orbital-electron ejection, published work on the subject has been reviewed. New measurements have been performed determining the total probability of $K$ ionization in the $\beta$ decay of ${\mathrm{Tc}}^{99}$ [(4.8±0.3)×${10}^{-4\mathrm{}}$ per $\beta$] and ${\mathrm{Pm}}^{147}$ [(9.3±1.4)×${10}^{-5\mathrm{}}$ per $\beta$]. The $K$ ionization probability as a function of $\beta$ energy has also been measured; a strong energy dependence is found, in disagreement with the traditional wave-function overlap theory. This theory is improved by including phase-space considerations, using relativistic electron wave functions in the calculation of the pertinent matrix elements, and paying careful attention to the antisymmetrization of the final-state wave function. The predictions of the modified wave-overlap theory agree very well with experiment. Direct collisions appear to play only a minor role. The calculations indicate that the ionization probability is inhibited in forbidden decay. A possible change in the shape factor for transitions accompanied by internal ionization is predicted.