An analysis of 515 decays $K^{+}\to {\pi }^0+e^{+}+\nu$ in a Freon-filled bubble chamber is described. The events were kinematically overdetermined so that a complete reconstruction of each decay was possible. All decay configurations were detectable except for those with positron momentum less than 5 $\frac{\mathrm{MeV}}{c}$. The data are satisfactorily described by a pure vector interaction. The energy dependence of the vector form factor $f_{+}$ is given by $\left|f_{+}\right(q^2\left)\right|=\left|\mathrm{}{f}_{+}\mathrm{}\right(0\left)\right| \frac{M^2}{(M^2-q^2)}$, with $M={{810}_{-140\mathrm{}}}^{+320\mathrm{}}$ MeV, or equivalently, $\left|f_{+}\right(q^2\left)\right|=\left|\mathrm{}{f}_{+}\mathrm{}\right(0\left)\right|\times [1+\lambda (\frac{q^2}{{M_{\pi }}^2}\left)\right]$, with $\lambda ={{0.028}_{-0.014\mathrm{}}}^{+0.013\mathrm{}}$. In the Callan-Treiman relationship for $K_{l2\mathrm{}}$ and $K_{l3\mathrm{}}$ decays, this value of $\lambda$ leads to the prediction that $\xi =0.0\mathrm{}\pm 0.1 or -2.0\mathrm{}\pm 0.1$. Upper limits for scalar and tensor currents are given. Systematic biases inherent in the heavy-liquid-chamber technique are discussed.

• Received 27 February 1967

DOI:https://doi.org/10.1103/PhysRev.159.1187