K-Shell Internal Ionization Accompanying Beta Decay

Internal ionization in the $K$ shell during nuclear $\beta$ decay has been studied experimentally as well as theoretically. The subsequent $K$ x rays were measured in coincidence with emitted electrons for various segments of the $\beta$ spectra of ${}_{}{}^{147}{}_{}{}^{}\mathrm{Pm}$ and ${}_{}{}^{63}{}_{}{}^{}\mathrm{Ni}$, using $4\pi$ detection geometry for these electrons; the sources were mounted in the electron detectors. The energy-dependent ionization probability $P_K\left(E_{\beta }^0\right)$ was measured as a function of $E_{\beta }^0$, where the parameter $E_{\beta }^0$ is defined as a sum of energies of the $\beta$ particle and emitted $K$ electron plus the $K$-shell binding energy of the daughter atom. This energy-dependent and the simultaneously measured total ionization probabilities have been found to be in fairly good agreement with theoretical values calculated by the theory developed based on a relativistic one-step treatment of electron shakeoff. From this result it has been established that electron shakeoff is the predominant mechanism even for electrons ($\beta$ particles and $K$ electrons) emitted with very low energies. As to the total ionization probability, it is pointed out that the theoretical values calculated by the simple wave-function-overlap theory using self-consistent-field wave functions should be improved by multiplying by a correction factor, a function of $B_K$ and $E_0$, where $B_K$ is the $K$-shell binding energy of the daughter atom and $E_0$ is the ordinary maximum kinetic energy of $\beta$ rays. The theoretical treatment of the phenomenon and future fruitful experiments to be hoped for are also discussed.