Remarks concerning the O(Zα2) corrections to Fermi decays, conserved-vector-current predictions, and universality

Abstract

Finite-nuclear-size contributions to the O(Z${\ensuremath{\alpha}}^{2}$) corrections to Fermi decays are studied for realistic nuclear-charge distributions. In conjunction with the results of Koslowsky et al. and recent papers by the author and Zucchini and by Jaus and Rasche, these refinements lead to an average value scrFt=3070.6\ifmmode\pm\else\textpm\fi{}1.6 s for the accurately measured superallowed Fermi transitions. Correspondingly, ${V}_{\mathrm{ud}}$=0.9744\ifmmode\pm\else\textpm\fi{}0.0010 and ${V}_{\mathrm{ud}}$${}^{2}$+${V}_{\mathrm{us}}$${}^{2}$+${V}_{\mathrm{ub}}$${}^{2}$=0.9979\ifmmode\pm\else\textpm\fi{}0.0021 in good agreement with the three-generation standard model at the level of its quantum corrections. The agreement with conserved-vector-current predictions is very good, with each of the eight transitions differing from the average by <1\ensuremath{\sigma}. The consequences of using two other calculations of the nuclear mismatch correction ${\ensuremath{\delta}}_{c}$, Wilkinson's microscopic analysis and the recent results of Ormand and Brown, are briefly discussed. A useful upper bound on scrFt, independent of the ${\ensuremath{\delta}}_{c}$ calculation, is given.