Periodic orbits of the hydrogen molecular ion
Department of Physics, Hunan Normal University, Hunan, 410081, China
Wuhan Institute of Physics, The Chinese Academy of Sciences, Wuhan, 430071, China
2 Department of Physics and Atmospheric Science, Drexel University, Philadelphia, PA19104, USA
Published online: 15 June 1999
Based on our previous work [Yiwu Duan, J.M. Yuan, C.G. Bao, Phys. Rev. A 52, 3497 (1995)], we study deeply the periodic orbits of the hydrogen molecular ion within the Born-Oppenheimer approximation (BOA). The Thiele-Burrau's transformation is introduced to regularize the singularities associated with the Coulomb potential terms and to transform the problem into a direct product of a pendulum and an anharmonic oscillator. This facilitates the analysis of the bifurcation properties of the periodic orbits. Some more details are also given about the calculation of the semiclassical density-of-state distribution using the Berry-Tabor formula.
PACS: 03.65.Sq – Semiclassical theories and applications / 31.10.+z – Theory of electronic structure, electronic transitions, and chemical binding
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1999