Effects of Radioactive Disintegrations on Inner Electrons of the Atom

The probability that nuclear emission of an alpha- or beta-particle causes ionization of a K or L electron of the atom is calculated by time-dependent perturbation theory using nonrelativistic Coulomb wave functions. Beta-emission (electron or positron) causes an ionization probability of 0.64Z² and 2.1Z² per beta in the K and L shells, respectively. (The K shell result agrees with Migdal and Feinberg; the L shell result disagrees with Migdal.) The use of nonrelativistic wave functions causes an appreciable underestimate in the ionization probability for K electrons of heavy atoms. Screening corrections for the use of Coulomb wave functions would increase the ionization probabilities by a factor of 1.4 for K electrons and by a factor of 3 or 4 for L electrons. Migdal's result for dipole electronic transitions caused by nuclear alpha-decay are reduced by a factor 25 (for the case of Po²¹⁰) because of nuclear recoil. Quadrupole matrix elements such as (r^-3)_1s,n^'d are evaluated by a new method developed by H. A. Bethe. This method uses the Sommerfeld integral representation for the continuum n^'d wave function. Quadrupole transitions are negligible for K electrons, but are the predominant effect for L electrons. The calculated ionization probabilities for Po²¹⁰ are 10^-7 and 1.1×{}10^-4 per alpha in the K and L shells, respectively. For alpha-decay, screening corrections and higher multipole transitions would both increase the ionization probability for L electrons. Madansky and Rasetti's measurements of photons from RaE are consistent with our calculations, but Bruner's measurements on Sc⁴⁴ are not. Grace's interpretation of K x-rays from Po²¹⁰ is consistent with the calculation of this paper, while Barber and Helm's interpretation is not. Rubinson and Bernstein find 8 times the L x-ray yield from Po²¹⁰ we have calculated for Coulomb wave functions.