Beta decays and related processes in theA=14nuclei

We present an analysis of the processes ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}\left({}_{}{}^{14}{}_{}{}^{}\mathrm{O}\right)\to {}_{}{}^{14}{}_{}{}^{}\mathrm{N}+e^{-}\left(e^{+}\right)+{\overline{\nu }}_e\left({\nu }_e\right)$ and ${\mu }^{-}+{}_{}{}^{14}{}_{}{}^{}\mathrm{N}\to {\nu }_{\mu }+{}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ (ground state) on the basis of an "elementary particle" treatment and of a "microscopic" treatment including the nucleons-only impulse approximation and the meson exchange. The elementary particle treatment in conjunction with data on $e^{-}+{}_{}{}^{14}{}_{}{}^{}\mathrm{N}\to e^{-}+{}_{}{}^{14}{}_{}{}^{}\mathrm{N}_{}^{*}{}_{}{}^{}$ (2.31 MeV), conserved vector current, partially conserved axialvector current, and a possible second-class axial current, yields $50 invsec <{\left[\Gamma \right({\mu }^{-}+{}_{}{}^{14}{}_{}{}^{}\mathrm{N}\to {\nu }_{\mu }+{}_{}{}^{14}{}_{}{}^{}\mathrm{C} \left(\mathrm{ground}\mathrm{state}\right)\left)\right]}_{\mathrm{stat}.\mathrm{av}.\mathrm{}}<70\mathrm{} invsec$ and $95 invsec <{\left[\Gamma \right({\mu }^{-}+{}_{}{}^{14}{}_{}{}^{}\mathrm{N}\to {\nu }_{\mu }+{}_{}{}^{14}{}_{}{}^{}\mathrm{C} \left(\mathrm{ground}\mathrm{state}\right)\left)\right]}_{F=\frac{1}{2}}<210\mathrm{} invsec$. The microscopic treatment leads to the conclusion that the nucleons-only-impulse-approximation and meson-exchange contributions to the ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}\left({}_{}{}^{14}{}_{}{}^{}\mathrm{O}\right)\to {}_{}{}^{14}{}_{}{}^{}\mathrm{N}+e^{-}\left(e^{+}\right)+{\overline{\nu }}_e\left({\nu }_e\right)$ amplitude may well be opposite in sign and comparable in magnitude so that the destructive interference between them contributes significantly to the anomalously small values of $\Gamma \left({}_{}{}^{14}{}_{}{}^{}\mathrm{C}\right({}_{}{}^{14}{}_{}{}^{}\mathrm{O})\to {}_{}{}^{14}{}_{}{}^{}\mathrm{N}+e^{-}(e^{+})+{\overline{\nu }}_e({\nu }_e\left)\right)$ and ${\left[\Gamma \right({\mu }^{-}+{}_{}{}^{14}{}_{}{}^{}\mathrm{N}\to {\nu }_{\mu }+{}_{}{}^{14}{}_{}{}^{}\mathrm{C} \left(\mathrm{ground}\mathrm{state}\right)\left)\right]}_{\mathrm{stat}.\mathrm{av}.\mathrm{},F=\frac{1}{2}}$.