Measurement of the Branching Ratio and Positron Momentum Spectrum for the DecayK0→π0+e++ν

The branching ratio and positron momentum spectrum have been measured for the ${K_{e3\mathrm{}}}^{+}$ decay mode. The shape of the momentum spectrum, containing 17 000 events, is consistent with pure vector coupling with a form-factor momentum dependence given by ${\lambda }^{+}=0.08\mathrm{}\pm 0.04$. Upper limits on a possible mixture of scalar or tensor coupling are, respectively, $\left|\frac{f_S}{f_{+}}\right|<\mathrm{}0.23\mathrm{}$ and $\left|\frac{f_T}{f_{+}}\right|<\mathrm{}0.58\mathrm{}$. The branching ratio is found to be (4.92±0.21)%, based on 960 events. The semileptonic $\Delta I=\frac{1}{2}$ rule is tested by comparing the ${K_{e3\mathrm{}}}^{+}$ and ${K_{e3\mathrm{}}}^0$ rates. We conclude that the present data on $K_{e3\mathrm{}}$ decays are in disagreement with this rule.