2004/02/20 by Gerald V. Dunne, C. Gauthier, Christopher S. Gauthier
Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Atomic and Molecular Physics #Laser-Matter Interactions and Applications #hep-th #math-ph #math.MP #physics.atom-ph #quant-ph
paper · pdf · doi:10.1103/physreva.69.053409
published as Phys. Rev. A 69, 053409 (2004) · 26 pp, 10 figures, latex; Revision: normalization (factor of 1/2) of field-free plots corrected -- figs 4,8,10. Ionization case unaffected. References added
arxiv created 2004/02/20 · openalex publication_date 2004/05/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a simple exact analytical solution, using the Weyl-Titchmarsh-Kodaira spectral theorem, for the spectral function of the one-dimensional diatomic molecule model consisting of two attractive \ensuremathδ-function wells in the presence of a static external electric field. For sufficiently deep and far apart wells, this molecule supports both an even and an odd state, and the introduction of a static electric field turns these bound states into quasibound states which are Stark-shifted and broadened. The continuum spectrum also inherits an intricate pattern of resonances which reflect the competition between resonant scattering between the two atomic wells and between the linear potential and one or both atomic well(s). All results are analytic and can be easily plotted. The relation between the large orders of the divergent perturbative Stark-shift series and the nonperturbative widths of quasibound levels is studied.