Inner-shell ionization during nuclearβdecay

A theory is developed of the ionization of inner-shell electrons during $\beta$ decay. For allowed transitions it is shown that in the lowest order of the coupling constants the transition amplitude for the process is a sum of two terms, one of which attributes the ionization process to the sudden change in nuclear charge, and the other to a virtual scattering of an inner-shell electron by the emerging $\beta$ particle. For the $K$-shell specific calculations are carried out using nonrelativistic hydrogenic wave functions and a Coulomb Green's function due to Glauber and Martin. Results whose relative accuracy is of order $Z\alpha$ are obtained for energy spectra, angular correlation functions, and the total internal ionization probability; numerical results are presented for the nuclides ${}_{}{}^{63}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{107}{}_{}{}^{}\mathrm{Pd}$, and ${}_{}{}^{151}{}_{}{}^{}\mathrm{Sm}$. The role of the virtual-scattering mechanism is assessed and a comparison with other recent theoretical work is made.