The two Coulomb centres problem at small inter-centre separations

Abstract

The case of small inter-centre separations R in the two Coulomb centres problem is treated with the help of asymptotic methods. Particular attention is paid to the logarithmic terms in the expansions for the energy. It is shown that they correspond to the complicated behaviour of the wavefunctions near the origin. The agreement between the asymptotic formulae and the numerical results is discussed. An expression for the phaseshift in the continuum is obtained.