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Using Heavy Quark Effective Theory with non-perturbatively determinedparameters in a quenched lattice calculation, we evaluate the splittingsbetween the ground state and the first two radially excited states of the $B_s$system at static order. We also determine the splitting between first excitedand ground state, and between the $B_s^*$ and $B_s$ ground states to order$1/m_b$. The Generalized Eigenvalue Problem and the use of all-to-allpropagators are important ingredients of our approach.

HQET at order $1/m$: II. Spectroscopy in the quenched approximation