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We report results from an experiment designed to test the conserved vectorcurrent (CVC) hypothesis by measuring the shape of the $\beta$-decay spectrumfor the allowed $0^+\rightarrow 1^+$ ground state decay of $^{14}$O.Measurements of the spectrum intensity were obtained with a superconductingbeta spectrometer and will be reported for positron kinetic energies rangingfrom 1.9 to 4.0 MeV. After dividing out phase space, Coulomb, and othercorrection factors, the resulting shape function has a negative slope ofseveral per cent per MeV. We define a parameter $a'$, which is essentially ameasure of the average slope of the shape function over the energy range of themeasurements, and determine its value to be $a' = -0.0290 \pm 0.0008$ (stat.)$\pm 0.0006$ (syst.). The measured slope parameter is in good agreement withpredictions from shell model calculations that respect CVC.

Measurement of the Shape Factor for the Beta Decay of $^{14}$O