Quadrupole transitions in the bound rotational–vibrational spectrum of the deuterium molecular ion

The systematic shifts of the transition frequencies in the molecular hydrogen ions are of relevance to ultra-high-resolution radio-frequency, microwave and optical spectroscopy of these systems, performed in ion traps. We develop the ab-initio description of the interaction of the electric quadrupole moment of this class of molecules with the static electric field gradients present in ion traps. In good approximation, it is described in terms of an effective perturbation hamiltonian. An approximate treatment is then performed in the Born-Oppenheimer approximation. We give an expression of the electric quadrupole coupling parameter valid for all hydrogen molecular ion species and evaluate it for a large number of states of H + 2 , HD + , and D + 2 . The systematic shifts can be evaluated as simple expectation values of the perturbation hamiltonian. Results on radio-frequency (M1), one-photon electric dipole (E1) and two-photon E1 transitions between hyperfine states in HD + are reported.For two-photon E1 transitions between rotationless states the shifts vanish. For a large subset of rovibrational one-photon transitions the absolute values of the quadrupole shifts range from 0.3 to 10 Hz for an electric field gradient of 10 8 V/m 2 . We point out an experimental procedure for determining the quadrupole shift which will allow reducing its contribution to the uncertainty of unperturbed rovibrational transition frequencies to the 1 × 10 -15 relative level and, for selected transitions, even below it. The combined contributions of black-body radiation, Zeeman, Stark and quadrupole effects are considered for a large set of transitions and it is estimated that the total transition frequency uncertainty of selected transitions can be reduced below the 1 × 10 −15 level.

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“…[21]. Recently, the quadrupole transition moments for D + 2 have been reported [22]. After developing the general theory in Sec.…”

Section: Introductionmentioning

confidence: 99%

The electric quadrupole moment of molecular hydrogen ions and their potential for a molecular ion clock

Bakalov

Schiller

2013

Appl. Phys. B

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“…where a 0 , t 0 = a 0 /αc, and E 0 = 2Ry are the atomic units of length, time, and energy. The comparison with the values calculated by H. O. Pilon [8] with different methods for a partly overlapping selection of transitions shows good agreement for the lower excited states, and indications of possible discrepancy of the order of 10 −4 for the higher vibrational excitations. Juxtaposition with the analogous Table II of Ref.…”

Section: Numerical Resultsmentioning

confidence: 53%

“…( 16), Einstein coefficients, A v ′ L ′ →vL for selected E2 transitions between the ro-vibrational states |vL and |v ′ L ′ of D + 2 , and, for comparison, the results of H.O. Pilon [8] when available.…”

Section: Electric Quadrupole Transitionsmentioning

confidence: 99%

“…Of main interest in the case of homonuclear MHIs (H + 2 , D + 2 ) are the electric quadrupole (E2) spectra. The first calculations in the approximation of spinless particles were performed back in 1953 by Bates and Poots [5], followed by works of Posen et al [6], Pilon and Baye [7], and Pilon [8]. The hyperfine structure (HFS) of the E2-spectral lines of H + 2 was first considered in [9] and systematically investigated in [10].…”

Section: Introductionmentioning

confidence: 99%

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Hyperfine structure and electric quadrupole transitions in the deuterium molecular ion

Danev,

Bakalov,

Korobov

et al. 2020

Preprint

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Molecular hydrogen ions are of metrological relevance due to the possibility of precise theoretical evaluation of their spectrum and of external-field-induced shifts. In homonuclear molecular ions the electric dipole E1 transitions are strongly suppressed, and of primary laser spectroscopy interest is the electric quadrupole (E2) transition spectrum. In continuation of previous work on the H + 2 ion, we report here the results of the calculations of the rate of laser-induced electric quadrupole transitions between a large set of ro-vibrational states of D + 2 . We also present an evaluation of the hyperfine structure that corrects errors in previous publications in the literature. The effects of the laser polarization in the hyperfine and Zeeman structure of the E2 transition spectrum are treated in detail.

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Nuclear critical charge for two-electron ion in Lagrange mesh method

Pilón

Turbiner

2015

Physics Letters A

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The Schroedinger equation for two electrons in the field of a charged fixed center $Z$ is solved with the Lagrange mesh method for charges close to the critical charge $Z_{cr}$. We confirm the value of the nuclear critical charge $Z_{cr}$ recently calculated in Estienne et al. {\em Phys. Rev. Lett. \bf 112}, 173001 (2014) to 11 decimal digits using an inhomogeneous (non-uniform) three-dimensional lattice of size $70 \times 70 \times 20$. We show that the ground state energy for H$^-$ is accurate to 14 decimals on the lattice $50 \times 50 \times 40$ in comparison with the highly accurate result by Nakashima-Nakatsuji, {\it J. Chem. Phys. \bf 127}, 224104 (2007).Comment: 6 pages, no figure

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Quadrupole transitions in the bound rotational–vibrational spectrum of the deuterium molecular ion

Cited by 8 publications

References 18 publications

The electric quadrupole moment of molecular hydrogen ions and their potential for a molecular ion clock

The electric quadrupole moment of molecular hydrogen ions and their potential for a molecular ion clock

Hyperfine structure and electric quadrupole transitions in the deuterium molecular ion

Nuclear critical charge for two-electron ion in Lagrange mesh method

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