Positronic beryllium: accurate energies and leading relativistic corrections in the ground and lowest excited states

One of the long standing questions of positron physics and chemistry is the existence of electronically stable positron-atom and positron-molecule complexes. From the theoretical and computational viewpoint, reliable identification of states, especially metastable ones, in which a positron can be attached to an atom, is challenging due to very weak binding energies and nontrivial structure of the complexes. A few years ago we predicted the stability against dissociation of an excited P-state of Be. The fact that both the ground and excited states are stable against dissociation in conjunction with their notably different lifetimes opens up an interesting possibility of measuring resonant positron-atom annihilation and providing experimental evidence for the existence of positron-atom complexes. In this work we have undertaken another, more comprehensive study of this system. We have performed considerably more accurate calculations of the binding energies and other relevant properties, such as the electron-positron annihilation rates. In particular, we have computed the leading relativistic corrections and show how they change the tiny binding energies of the ground and first excited states of the e⁺-Be complex.