J M Peek et al 2007 J. Phys. B: At. Mol. Opt. Phys. 40 565 doi:10.1088/0953-4075/40/3/012
J M Peek1, T Kereselidze2, I Noselidze2 and J Kielkopf3
Show affiliationsThe eigenfunctions for an electron in the Coulomb field of two nuclei with arbitrary charge are considered in the Born–Oppenheimer approximation. This forced separation of electron and nuclear variables introduces the magnitude of the internuclear separation R as a parameter. An eigenfunction approaches a hydrogenic ion as R approaches zero and the standard phase convention is applied there. The separated-atom phase is deduced and found to depend on the R = 0 eigenparameters. This is contrary to expectations. These results are used to investigate the sign of the dipole matrix element in the two limits of R. The even/odd number of zeros for a transition over 0 ≤ R < ∞ is thereby determined. These results are related to existing numerical data and one omission is identified. Predictions are given. The phase arguments predict sequences of transitions that must have similar properties. One such sequence is investigated. A sum rule result shows a deep minimum exists as a function of R. This result is related to an unusual minimum previously predicted for the photoionization of H2+.
31.15.-p Calculations and mathematical techniques in atomic and molecular physics
33.70.Ca Oscillator and band strengths, lifetimes, transition moments, and Franck-Condon factors
Issue 3 (14 February 2007)
Received 15 June 2006, in final form 4 December 2006
Published 24 January 2007
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