Electron Screening Corrections to Beta-Decay Spectra

The corrections to the Fermi function $F(Z, W)$ which arise from the screening of the Coulomb field of the nucleus by the atomic electrons have been investigated using a Hulthén model for the screened field. The resulting problem is exactly solvable for the Schrödinger and Klein-Gordon equations. The results agree with those obtained by Rose and by Longmire and Brown using a modification of the WKB method, and disagree markedly with those obtained by Reitz by numerical integration of the Dirac equation. The latter results appear to be incorrect. The screening corrections are sufficiently small for light nuclei as not to affect materially present tests for the universal Fermi interaction and conserved vector current hypotheses for beta decay, but may become significant for low-energy beta transitions in heavy nuclei.