Abstract
The [Formula: see text] atomic state problem is solved in a suitable numerical approach based on Sturmian functions, which is able to account for both the strong short range nuclear potential (for both the local and nonlocal) and the long range Coulomb force and to provide directly the wave function of protonium with complex eigenvalues [Formula: see text]. The small hyperfine-splittings and decay widths of the 1s and 2p levels of the [Formula: see text] atomic states are studied in the latest version of the Paris [Formula: see text] potential. It is found that the potential needs to be modified at energies around the [Formula: see text] threshold.
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