The possibility of the existence of excited S-symmetry states of positronic lithium and beryllium, resulting from the positron attachment to high-spin P parent atomic states, is examined and confirmed with variational calculations in the basis of explicitly correlated Gaussian functions. The unexpectedly different order of the energies of the S and P states is explained by the formation of the positronium cluster structure and associated disappearance of the destabilizing centrifugal force. The annihilation properties of newly discovered states are discussed in the context of prospective experimental detection.

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