High-precision nonadiabatic calculations of dynamic polarizabilities and hyperpolarizabilities for low-lying vibrational-rotational states of hydrogen molecular ions

Li-Yan Tang, Zong-Chao Yan, Ting-Yun Shi, and James F. Babb
Phys. Rev. A 90, 012524 – Published 29 July 2014

Abstract

The static and dynamic electric multipolar polarizabilities and second hyperpolarizabilities of the H2+, D2+, and HD+ molecular ions in the ground and first excited states are calculated nonrelativistically using explicitly correlated Hylleraas basis sets. The calculations are fully nonadiabatic; the Born-Oppenheimer approximation is not used. Comparisons are made with published theoretical and experimental results, where available. In our approach, no derivatives of energy functions nor derivatives of response functions are needed. In particular, we make contact with earlier calculations in the Born-Oppenheimer calculation where polarizabilities were decomposed into electronic, vibrational, and rotational contributions and where hyperpolarizabilities were determined from derivatives of energy functions. We find that the static hyperpolarizability for the ground state of HD+ is seven orders of magnitude larger than the corresponding dipole polarizability. For the dipole polarizability of HD+ in the first excited state the high precision of the present method facilitates treatment of a near cancellation between two terms. For applications to laser spectroscopy of trapped ions we find tune-out and magic wavelengths for the HD+ ion in a laser field. In addition, we also calculate the first few leading terms for long-range interactions of a hydrogen molecular ion and a ground state H, He, or Li atom.

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  • Received 28 May 2014

DOI:https://doi.org/10.1103/PhysRevA.90.012524

©2014 American Physical Society

Authors & Affiliations

Li-Yan Tang1,2, Zong-Chao Yan1,2,3, Ting-Yun Shi1, and James F. Babb2

  • 1State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics and Center for Cold Atom Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, People's Republic of China
  • 2ITAMP, Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, Massachusetts 02138, USA
  • 3Department of Physics, University of New Brunswick, Fredericton, New Brunswick, Canada E3B 5A3

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Vol. 90, Iss. 1 — July 2014

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