Solving Degeneracies at a $\beta$-Beam by Combining Ions

We study how the eightfold-degeneracy in the ($\theta_{13},\delta$) plane observed in $\gamma \sim 100$ $\beta$-beams can be reduced by periodically changing the ions in the storage ring. This ``ions cocktail'' allows to change the neutrino energy, at fixed $\gamma$, by choosing ions with different decay energies. We propose to combine the standard $^6$He and $^{18}$Ne beams with $^8$Li and $^8$B ones. These latter two ions have peaked $\nu_e \to \nu_\mu$ oscillation probabilities for $\gamma = 100$ at a baseline $L \sim 700$ Km. At this distance and this $\gamma$ the oscillation probability of $^6$He and $^{18}$Ne neutrinos is at its second maximum. This setup is particularly suited for large enough values of $\theta_{13}$ (within reach at T2K-I) and it allows solving most of the eightfold-degeneracy, measuring $\theta_{13}, \delta$ and the sign of the atmospheric mass difference for values of $\theta_{13} \geq 5^\circ$.