Relativistic correction to the 1sσ and 2pσ electronic states of the H2+ molecular ion and the moleculelike states of the antiprotonic helium He+(p)over-bar

Effective potentials of the relativistic Breit-Pauli corrections for the 1s sigma(g) and 2p sigma(u) electron states of the H-2(+) molecular ion and the 1s sigma, 2s sigma, and 3p sigma states of the antiprotonic helium atom He+ p are calculated within the Born-Oppenheimer approximation. The variational expansion with randomly chosen exponents has been used for numerical studies. The results obtained for the Breit-Pauli effective potentials are accurate up to ten significant digits for the H-2(+) molecular ion and eight digits for the He+ p atom. (c) 2006 American Institute of Physics.