${\theta }_{13}$, $\delta$ and the neutrino mass hierarchy at a $\gamma =350$ double baseline Li/B $\beta$-Beam

We consider a $\beta$-Beam facility where ${}^8$Li and ${}^8$B ions are accelerated at $\gamma =350$, accumulated in a 10 Km storage ring and let decay, so as to produce intense ${\bar{\nu }}_e$ and ${\nu }_e$ beams. These beams illuminate two iron detectors located at $L\simeq 2000$ Km and $L\simeq 7000$ Km, respectively. The physics potential of this setup is analysed in full detail as a function of the flux. We find that, for the highest flux ($10 \times 10^{18}$iondecaysperyearperbaseline),thesensitivityto$\theta_{13}$reaches$\sin^2 2 \theta_{13} \geq 2 \times10^{-4}$; the sign of the atmospheric mass difference can be identified, regardless of the true hierarchy, for ${\sin }^{2}2{\theta }_{13}\ge 4\times {10}^{-4}$; and, CP-violation can be discovered in 70% of the $\delta$-parameter space for $\sin^2 2 \theta_{13} \geq 10^{-3}$,havingsomesensitivitytoCP-violationdownto$\sin^2 2 \theta_{13} \geq 10^{-4}$for$|\delta| \sim 90^\circ$.