Test of $\nu_{\mu} \to \nu_x$ oscillations and determination of $\Delta m^2$ using the $L/E$ method on atmospheric neutrino data

We point out that the measurement of the $L/E$ distribution of atmospheric neutrino events with sufficient resolution in order to observe the characteristic modulations of neutrino oscillations would provide a unique way to test the $\numunux$ oscillations nature of the atmospheric neutrino anomaly\cite{kamatmo} in the parameter range $5\times 10^{-4} < \Delta m^2 < 2\times 10^{-3}\rm\ eV^2$. With an integrated exposure of a few tens of kiloton-year, this method can cover the lower part of the $\Delta m^2$ region of the currently allowed atmospheric neutrino solution\cite{superkamiokande} and is therefore complementary to the one explorable with planned long-baseline neutrino beam experiments (e.g. Refs. \cite{icarus,icarusprop}). We stress that experimentally this method relies on the ability to measure high energy muons ($E_\mu>5\rm\ GeV$). A large magnetized calorimeter of several kilotons would be ideally suited for this measurement. The existing LEP detectors augmented with atmospheric neutrino triggers could also be used to perform such a study.