Are Neutrino Oscillations Compatible with the Decaying Neutrino Theory for the Ionisation of Hydrogen in the Interstellar Medium

Recent Super-Kamiokande data have greatly strengthened the hypothesis that the atmospheric neutrino anomaly is mainly due to nearly maximal oscillations between $\nu_{\mu}$ and either $\nu_{\tau}$ or a sterile neutrino $\nu^s_{\mu}$.In this letter we point out that the decaying neutrino theory for the ionisation of hydrogen in the interstellar medium, in conjunction with the assumption that the cosmological constant $\lambda$ is zero, requires these oscillations to be between $\nu_{\mu}$ and $\nu^s_{\mu}$. This requirement can be tested by forthcoming Super-Kamiokande measurements. A further requirement can be derived if the solar neutrino deficit is energy dependent and if both it and the LSND data are also due to neutrino oscillations. In that case the decaying neutrino theory alone (without any assumption about the value of $\lambda$) requires both that the atmospheric anomaly is due to $\nu_{\mu}-\nu^s_{\mu}$ oscillations and that the solar neutrino oscillations are between $\nu_e$ and a second sterile neutrino $\nu^s_e$. This latter requirement can be tested by forthcoming SNO and BOREXINO measurements. If these are also $\nu_{\tau}-\nu^s_{\tau}$ oscillations the decay line would be split into two lines of nearly equal intensity and spacing less than $\sim$ 0.2 eV.