  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.
