Direct Interaction Mechanism in the Ionization FollowingβDecay

A method of estimating the contribution of the direct interaction mechanism (d.i.m.) to the ionization process in $\beta$ decay is proposed. It is restricted to the same energy range $E_{\beta }\gg E_b$ ($E_{\beta }$ is the kinetic energy of the $\beta$-particle, $E_b$ is the binding energy of the atomic electron) as the conventional theory, but is based on independent information emerging from experimental impact cross-section data. Following Williams, the ionization by external impact is ascribed to two factors: (a) direct collisions, corresponding to low impact parameters; (b) glancing ("photoeffect") collisions corresponding to large impact parameters. We assume that the contribution of factor (a) to the ionization cross section is the same both in external impact and in $\beta$ decay, and evaluate the contribution of factor (b) to the impact cross section by means of the Weizsäcker-Williams method. By subtracting this contribution from the experimental impact cross section, we get the d.i.m. cross section. We apply this procedure to the calculation of the d.i.m. ionization probabilities $P_{\mathrm{d}.\mathrm{i}.\mathrm{}}$ of the following $\beta$-active isotopes: ${\mathrm{Na}}^{22}$, ${\mathrm{P}}^{32}$, ${\mathrm{Y}}^{90}$, ${\mathrm{Pr}}^{143}$, ${\mathrm{Ne}}^{23}$, and ${\mathrm{Ar}}^{41}$. In opposition to the predictions of the conventional theory, according to which $\delta \equiv \frac{P_{\mathrm{d}.\mathrm{i}.\mathrm{}}}{P_s}\ll 1$, ($P_s$ is the shake-off probability), our results, although approximative, suggest that the $K$-shell ionization probabilities are affected, sometimes in a decisive manner, by the d.i.m.; we get for ${\mathrm{Y}}^{90}1<\mathrm{}\delta <2\mathrm{}$ and for ${\mathrm{Pr}}^{143}2<\mathrm{}\delta <4\mathrm{}$. This conclusion is in line with independent experimental results by Charpak, Suzor, and Spighel on low-energy electrons accompanying $\beta$ decay. Further experiments to check this conclusion are proposed, and possible explanations of the failure of the theory are suggested.