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 <i>R </i>for the 1<i>sσ</i><sub><i>g</i></sub><i> </i>electron state of hydrogen molecular ion H<sub>2</sub><sup>+</sup> and the 1<i>sσ </i>molecule-like state of antiprotonic helium atom He<sup>+</sup>p are obtained with the use of the first-order perturbation function. Using these asymptotic formulae, the relativistic correction of order <i>mα</i><sup><i>6</i></sup><i> </i>for these states in reciprocal powers of the internuclear distance <i>R </i>is derived to accuracy of <i>О</i>(R<sup>-4</sup>).