Lithium and sodium atoms can interact with positronium to from a positronic alkali atom in which the ion core of the alkali atom loosely binds to positronium. The systems are suitable to investigate mechanisms of positron binding to atoms because the systems can be described with a three-body model and atomic interactions are included in a model potential between the ion core and the valence electron in the atoms. In order to clarify the details of the loosely bound states, we estimated relativistic effects by reconstructing the model potential. A major contribution to the relativistic effects on the binding energy are ascribed to the electron in the alkali atomic orbital whose contribution to the total wavefunction is small. It was found that the relativistic effects appear largely in the binding energy and geometry of LiPs + and NaPs + compared with those of Li and Na atoms.
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