The static and dynamic polarisability, and the Stark and black-body radiation frequency shifts of the molecular hydrogen ions H2+, HD+, and D2+

Abstract

We calculate the DC Stark effect for three molecular hydrogen ions in the non-relativistic approximation. The effect is calculated both in dependence on the rovibrational state and in dependence on the hyperfine state. We discuss special cases and approximations. We also calculate the AC polarisabilities for several rovibrational levels, and therefrom evaluate accurately the black-body radiation shift, including the effects of excited electronic states. The results enable the detailed evaluation of certain systematic shifts of the transitions frequencies for the purpose of ultra-high-precision optical, microwave or radio-frequency spectroscopy in ion traps.

References in corpus (15)

• Addressing and manipulation of individual hyperfine states in cold trapped molecular ions and application to HD^{+} frequency metrology
• Cold Atom Clocks, Precision Oscillators and Fundamental Tests
• Millisecond Pulsars as Tools of Fundamental Physics
• Oklo Constraint on the Time-Variability of the Fine-Structure Constant
• 35 Years of Testing Relativistic Gravity: Where do we go from here?
• Precision Spectroscopy of Atomic Hydrogen and Variations of Fundamental Constants
• Fundamental units: physics and metrology
• Astrophysical constraints on hypothetical variability of fundamental constants
• Molecular Dynamics Simulation of Sympathetic Crystallization of Molecular Ions
• Vibrational spectroscopy of H2+: hyperfine structure of two-photon transitions
• The electric quadrupole moment of molecular hydrogen ions and their potential for a molecular ion clock
• Observation of a rotational transition in trapped and sympathetically cooled molecular ions
• Vibrational spectroscopy of H2+: precise evaluation of the Zeeman effect
• Infrared dynamic polarizability of HD+ rovibrational states
• Precision spectroscopy of the molecular ion HD+: control of Zeeman shifts

Cited by in corpus (14)

• Proton-Electron Mass Ratio from Laser Spectroscopy of HD${}^{+}$ at the Part-Per-Trillion Level
• Lorentz and CPT tests with hydrogen, antihydrogen, and related systems
• Proton-electron mass ratio by high-resolution optical spectroscopy of ion ensembles in the resolved-carrier regime
• Rotational spectroscopy of cold, trapped molecular ions in the Lamb-Dicke regime
• Penning-trap mass measurements of the deuteron and the HD+ molecular ion
• CPT tests with the antihydrogen molecular ion
• High-precision nonadiabatic calculations of dynamic polarizabilities and hyperpolarizabilities for the lowlying vibrational-rotational states of hydrogen molecular ions
• Vibronic spectroscopy of sympathetically cooled CaH${}^{+}$
• Prospects for Polar Molecular Ion Optical Probe of Varying Proton-Electron Mass Ratio
• Canceling spin-dependent contributions and systematic shifts in precision spectroscopy of the molecular hydrogen ions
• The leading term of the He$-\bar{p}\mbox{He}^+$ long-range interaction
• Light one-electron quasi-molecular ions within the finite-basis-set method for the two-center Dirac equation
• Leading order relativistic corrections to the dipole polarizability of the hydrogen molecular ions
• The Stark effect in molecular Rydberg states: Calculation of Rydberg-Stark manifolds of H${}_2$ and D${}_2$ including fine and hyperfine structures