Atomic screening effects on electron-neutrino angular correlation and β-decay asymmetry in allowed transitions

Atomic screening effects on the electron-neutrino angular correlation coefficient a0 and the β asymmetry coefficient A0, in allowed transitions, are studied. It has long been known that the dominant screening effect on the spectrum is the replacement, in the factor which represents the phase space of the β particle, of W, the energy with which the β particle emerges, by W-V0, the energy with which it is born; V0 is the energy of interaction of the β particle at the origin with the potential generated there by the atomic electrons. [One also replaces the momentum p=p(W) by p'=p(W-V0).] One might well expect a similar result for screening effects on a0 and A0, which include the influence of the nuclear Coulomb potential---and this intuitive expectation is shown to be the case. One need merely replace the velocity of emergence v=v(W) in the correlation functions by the velocity at birth, v'=v(W-V0). As for the case of the spectrum, the effect can be obtained by using a static approximation, with the atomic electrons unaffected by the β particle, and with the screening potential treated to second order; the effect of virtual or real excitation of the atomic electrons is negligible. The screening effect is of order 10-4 for most superallowed and mirror image transitions (presently, both theory and experiment for superallowed transitions---with implications for electro-weak theory and the standard model---give ft values accurate to about one part in 103); it can be as large as 20% for some pure Gamow-Teller transitions, for which the nuclear matrix element does not enter into the analysis of a0 and A0