K-shell ionization in the electron and positron decays ofCu64

The total $K$-ionization probabilities accompanying the ${\beta }^{+}$ and ${\beta }^{-}$ decays of ${}_{}{}^{64}{}_{}{}^{}\mathrm{Cu}$, $P_K\left({\beta }^{+}\right)$, and $P_K\left({\beta }^{-}\right)$ were determined from coincidence and singles $K$ x-ray spectra of Ni and Zn to be (13.2 ± 0.8) × ${10}^{-4\mathrm{}}$ and (11.9 ± 0.8) × ${10}^{-4\mathrm{}}$, respectively, using a high resolution Si(Li) photon spectrometer. $\frac{P_K\left({\beta }^{+}\right)}{P_K\left({\beta }^{-}\right)}$ was measured directly and independently to be 1.26 ± 0.10, in fair agreement with the ratio of the separate measurements 1.11 ± 0.10. While the average ratio is in agreement with the shaking theory of Isozumi, Shimizu, and Mukoyama, the individual values are a factor of ∼ 1.5 larger than their predictions. A similar approximately twofold excess over the Isozumi, Shimizu, and Mukoyama hydrogenic-wave-function-based predictions has been observed for almost all cases of $K$-shell shaking in ${\beta }^{-}$ decay, and now also for this first reported measurement in ${\beta }^{+}$ decay. The measured ratio is the first experimental evidence affirming the previously recognized and acknowledged error of a factor of 2 (excess) for shakeoff in ${\beta }^{-}$ decay (but not in ${\beta }^{+}$ decay) in the theory of Law and Campbell. No evidence was found for a postulated Ni $K$ vacancy production mechanism, in which the positron annihilates with a $K$ electron internal to the parent atom, exceeding a few percent of $K$ shaking in positron decay.