Pseudoscalar Interaction in Nuclear Beta Decay

The experiments on the allowed beta transitions, which lead almost uniquely to the $V-1.2A$ interaction, do not have any bearing on a possible contribution from the pseudoscalar interaction. To determine whether or not any contribution from the pseudoscalar interaction is really needed, an examination has been made of the $\beta$ longitudinal polarization and the $\beta$ shape factor in the 0→0 (yes) beta transitions. The theoretical polarization for the mixture of the pseudoscalar and the axial vector interactions has been developed. In this work, the formulation of the pseudoscalar interaction as given by Rose and Osborn has been used. The numerical results on the $\beta$ longitudinal polarization and the shape factor depend on two parameters, namely, the coupling constant ratio, $\frac{C_P}{M{C}_A}$, and $\lambda$, the ratio of the two relevant nuclear matrix elements. $M$ is the nucleon mass in units of the electron mass. The electronic functions occurring in the theoretical formulas for these effects are tabulated for ${\mathrm{Pr}}^{144}$ ($0^{-}$ → $0^{+}$) and ${\mathrm{Ho}}^{166}$ ($0^{-}$ → $0^{+}$). All the electronic radial functions were computed considering the nucleus as a sphere of a uniform charge distribution with a nuclear radius as $1.2A^{\frac{1}{3}}\times {10}^{-13\mathrm{}}$ cm, and taking into account the finite deBroglie wavelength effect. The results of extensive numerical analysis are presented. We conclude that the absence of the pseudoscalar interaction is consistent with the existing experimental data. The value of $\frac{C_P}{M{C}_A}$, which also gives a satisfactory fit to the experimental data depends on $\lambda$. The upper limit of the value of $\left|\frac{C_P}{M{C}_A}\right|$ is found to be 0.05 for $\left|\lambda \right|=200\mathrm{}$. In this work, time-reversal invariance is assumed valid for the weak as well as the strong interactions, and the two-component theory of the neutrino has been used.