No 17 keV neutrino: Admixture < 0.073% (95% C.L.)

To solve the controversial issue concerning the possible existence of a 17 keV neutrino with a 1% admixture in nuclear $\beta$ decay, we searched directly for any evidence of a production-threshold effect. The ${}_{}{}^{63}{}_{}{}^{}\mathrm{Ni}$ $\beta$ spectrum was measured with a magnetic spectrometer, with very high statistics along with a fine energy scan over a narrow energy region around the expected threshold. The obtained mixing strength was ${\mathrm{}\left|U\right|\mathrm{}}^2=[-0.011\mathrm{}\pm 0.033(\mathrm{stat})\pm 0.030(\mathrm{syst}\left)\right]\%$, very consistent with zero, and decisively excluding the existence of a 17 keV neutrino admixing at the 1% level with the electron neutrino. The corresponding upper limit was set at ${\mathrm{}\left|U\right|\mathrm{}}^2<0.073\%$ (95% C.L.). A new limit was also obtained for a wider mass range: ${\mathrm{}\left|U\right|\mathrm{}}^2<0.15\%$ (95% C.L.) for 10.5 to 25.0 keV neutrinos.