Relativistic correction to the 1ssigma and 2psigma electronic states of the H2 + molecular ion and the moleculelike states of the antiprotonic helium He+ -p.

Effective potentials of the relativistic Breit-Pauli corrections for the 1ssigma(g) and 2psigma(u) electron states of the H(2) (+) molecular ion and the 1ssigma, 2ssigma, and 3psigma 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.