The change of the Fermi matrix element of the $\beta$ decay of ${\mathrm{O}}^{14}$ to the first excited state of ${\mathrm{N}}^{14}$ from its value $\sqrt{2}$ due to Coulomb corrections is re-estimated. It is shown, that for pure $1p$-shell states the reduction is between 0.02 and 0.20%. Configuration mixing in the $1p$ shell may increase these figures considerably.

Instead of arbitrary admixtures of higher configurations, a collective model for the presumably most important of such admixtures is considered: the model of a "breathing state" (radial density oscillation). It is shown that for sufficiently low values of the energy of the first excited breathing state compatible with experimental data for the level spectrum of the mass-14 system, the $\beta$-decay matrix element may be reduced by as much as five percent. In view of the lack of present knowledge about the breathing state and nuclear compressibility for light nuclei, it is concluded that the discrepancy between the measured values of the vector and $\mu$-meson decay coupling constants of $\beta$ decay may well be due to such an effect.

• Received 25 January 1962

DOI:https://doi.org/10.1103/PhysRev.128.841