Screening effects in radiative orbital electron capture by an atomic nucleus

Using the results of an analytic perturbation theory for screened Coulomb wave functions, closed-form expressions are given for screening corrections to internal bremsstrahlung accompanying nuclear capture from ns and $2p$ states within nonrelativistic dipole approximation. The analytic perturbation theory is based on the expansion of the potential in the interior of an atom as a series of the form V(r)=-(a/r)[1+V₁λr+V₂(λr)²+V₃(λr)³+], where a=Zα, λ is a Z-dependent small parameter characterizing the screening, and the coefficients Vₖ are of order unity. The nonrelativistic screened Coulomb Green's function, needed for the calculations of the matrix elements, is obtained as a series in λ with analytic coefficients. The screening correction to radiative capture from ns-states, in agreement with the arguments of Glauber and Martin, is simply the energy independent, multiplicative factor of the ratio of screened to unscreened bound state normalization. In radiative capture from the $2p$ state there are additional energy dependent screening corrections, largest near the resonance at an energy corresponding to characteristic x-ray radiation (due to the shift of the resonance energy position with screening), which decrease to less than 1% for photon energies several times larger than the energy of the resonance. The relation between the screening corrections to radiative capture from the $2p$ state at resonance and to the 2p-1s bound-bound radiative transition serves as a check of the calculation. From the screened Green's function the Fermi-Segr\`e formula, connecting the ns-bound state energy shifts and the bound state normalizations, is rederived, together with a generalization to arbitrary angular momentum states.RADIOACTIVITY Screening corrections to internal bremsstrahlung accompanying nuclear capture of an orbital electron from ns and $2p$ states within nonrelativistic dipole approximation.