Some asymptotic formulae for one-electron two-center problem

Asymptotic formulae of some expectation values related to the relativistic corrections in inverse powers of the internuclear distance R for the lsσ _g electron state of hydrogen molecular ion H₂⁺ and the lsσ molecule-like state of antiprotonic helium atom He⁺ are obtained with the use of the first-order perturbation function. Using these asymptotic formulae, the relativistic correction of order mα⁶ for these states in reciprocal powers of the internuclear distance R is derived to accuracy of (R ⁻⁴). The article is published in the original.