Relativistic corrections of order mα6 to the two-centre problem

Effective potentials of the relativistic m alpha(6) order correction for the ground state of the Coulomb two-centre problem are calculated. They can be used to evaluate the relativistic contribution of that order to the energies of hydrogen molecular ions or metastable states of the antiprotonic helium atom, where precision spectroscopic data are available. In our studies we use the variational expansion based on randomly chosen exponents that permits us to achieve high numerical accuracy.