Quantal Two-Centre Coulomb Problem treated by means of the Phase-Integral Method III. Quantization Conditions in the General Case Expressed in Terms of Complete Elliptic Integrals. Numerical Illustration

In this paper we take up the quantal two-centre problem where the Coulomb centres have arbitrary positive charges. In analogy with the symmetric case, treated in the second paper of this series of papers, we use the knowledge on the quasiclassical dynamics to express the contour integrals in the first- and third-order approximations of the phase-integral quantization conditions, given in the first paper of this series of papers, in terms of complete elliptic integrals. For various values of the distance between these charges the accuracy of the formulas obtained is illustrated by comparison with available numerically exact results.