The two Coulomb centres problem at large centre separation

The case of large centre separation R in the two Coulomb centres problem is treated with the help of a comparison method. A multipole expansion for the energy in reciprocal powers of R is obtained up to O( R -5 ). Particular attention is paid to quasi-crossings of the energy curves. Their position and the splitting of the curves is found. It is shown that these quasi-crossings correspond to a Coulomb series for a charge equal to the difference between the charges of the centres.