A phenomenological analysis is presented of inverse-$\beta$ (IB) experiments on proton targets performed at 6.5, 8.7, and 11.2 m from reactor sources and of a deuteron-disintegration experiment at 11.2 m. The analysis leads to the conclusion that either there is a statistically significant distance dependence of the ${\overline{\nu }}_e$ spectra measured in these experiments or that at least three of the four experiments have unstated sources of error or seriously understated errors. We find that this distance dependence can be accounted for by neutrino oscillations. The distance dependence is exhibited in the normalization-independent ratio of low- to high-energy halves of the spectrum. The ratios at the three distances, taken in paris, differ by greater than 3 standard deviations. The entire analysis is done without using any theoretically calculated spectra. We find that no distance-independent spectrum can account for the 8.7- and 11.2-m IB experiments with a confidence level (C.L.) >0.026. Assuming neutrino oscillations rather than experimental errors are the cause of the distance dependence exhibited by the data we search for and find simple two-component neutrino-oscillation fits to the data with a gain in C.L. over the no-oscillation best fits by factors ranging from ∼5 to ∼15. These joint oscillation $2\nu$ solutions have the ($\delta m^2$, ${sin}^{2}2\theta$) values: (0.95±0.10 e${\mathrm{V}}^2$, 0.32±0.11), (2.34±0.23 e${\mathrm{V}}^2$, 0.20±0.07), and (3.75±0.27 e${\mathrm{V}}^2$, 0.25±0.08). Under the $3\nu$ hypothesis the solutions have the values $\delta {m^2}_{12}={0.88}_{-0.24\mathrm{}}^{+0.16\mathrm{}}$ e${\mathrm{V}}^2$ and $\delta {m^2}_{13}=2.39\mathrm{}\pm 0.30$ e${\mathrm{V}}^2$, with amplitudes ${0.17}_{-0.08\mathrm{}}^{+0.13\mathrm{}}$ and 0.16±0.08, respectively. The limits quoted correspond to 90% C.L. obtained by including the reactor ${\overline{\nu }}_e$ spectral range from inversion of the $e^{-}$ spectrum from the fission of ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$ and by disregarding the 6.5-m experiment on the grounds that it has poor statistics for analysis of its differential spectrum. Each one of these solutions is within the 68%-C.L. allowed region in the ($\delta m^2$, ${sin}^{2}2\theta$) space of the analysis by Boehm et al. of their own experiment at 8.7 m. The above oscillation parameters are within the allowed limits from accelerator experiments. Our observation of the difference between the 8.7- and 11.2-m IB experiments on proton targets may constitute new evidence for ${\overline{\nu }}_e$ oscillations, provided the experiments are correct.

• Received 4 January 1982

DOI:https://doi.org/10.1103/PhysRevD.27.58