High-precision spectroscopy of hydrogen molecular ions

Zhong, Zhen-Xiang; Tong, Xin; Zhou, Yan; Shi, Ting-Yun

doi:10.1088/1674-1056/24/5/053102

Cited by 20 publications

(14 citation statements)

References 145 publications

(261 reference statements)

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“…Analyzing a variety of systematic effects, such as the AC and DC Stark effects on the transition frequency [75,76], the redistribution of rotational sub-states due to black-body radiation in molecular dynamics simulations, and the analysis of hyperfine line strengths at the magnetic sub-state level, the experimental result on the R(2) line of the (1,0) [62] bands are included in Table 1. Attempts to measure transitions in the (6,0) band have not yet resulted in accurate values [77]. Work is in progress to measure the spectrum of H + 2 in an ion trap [78], which is more difficult than probing HD + where electric dipole transitions are allowed, unlike for the homo-nuclear species.…”

Section: Laser Precision Metrology Of Hd + and H +mentioning

confidence: 99%

Physics beyond the Standard Model from hydrogen spectroscopy

Ubachs

Koelemeij

Eikema

et al. 2016

Journal of Molecular Spectroscopy

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Spectroscopy of hydrogen can be used for a search into physics beyond the Standard Model. Differences between the absorption spectra of the Lyman and Werner bands of H 2 as observed at high redshift and those measured in the laboratory can be interpreted in terms of possible variations of the proton-electron mass ratio µ = m p /m e over cosmological history. Investigation of some ten of such absorbers in the redshift range z = 2.0 − 4.2 yields a constraint of |∆µ/µ| < 5 × 10 −6 at 3σ. Observation of H 2 from the photospheres of white dwarf stars inside our Galaxy delivers a constraint of similar magnitude on a dependence of µ on a gravitational potential 10 4 times as strong as on the Earth's surface. While such astronomical studies aim at finding quintessence in an indirect manner, laboratory precision measurements target such additional quantum fields in a direct manner. Laser-based precision measurements of dissociation energies, vibrational splittings and rotational level energies in H 2 molecules and their deuterated isotopomers HD and D 2 produce values for the rovibrational binding energies fully consistent with quantum ab initio calculations including relativistic and quantum electrodynamical (QED) effects. Similarly, precision measurements of high-overtone vibrational transitions of HD + ions, captured in ion traps and sympathetically cooled to mK temperatures, also result in transition frequencies fully consistent with calculations including QED corrections. Precision measurements of inter-Rydberg transitions in H 2 can be extrapolated to yield accurate values for level splittings in the H + 2 -ion. These comprehensive results of laboratory precision measurements on neutral and ionic hydrogen molecules can be interpreted to set bounds on the existence of possible fifth forces and of higher dimensions, phenomena describing physics beyond the Standard Model.

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Section: Laser Precision Metrology Of Hd + and H +mentioning

confidence: 99%

Physics beyond the Standard Model from hydrogen spectroscopy

Ubachs

Koelemeij

Eikema

et al. 2016

Journal of Molecular Spectroscopy

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“…Table I demonstrate convergence of this key quantity for the two vibrational states v = 4 and v = 10. The first case is needed to compare our numbers with previously obtained results by [14,15], in the latter case v = 4 was the largest vibrational state considered. While in general there is a very good agreement between our data and the data from [14], in case of the Hylleraas variational calculations it was observed that precision is going down rather rapidly with increase of the vibrational quantum number v. And already in case of the (L = 3, v = 4) state we see some discrepancy, and we presume that it is primarily due to the difficulty in determining of the real uncertainty in the calculations.…”

Section: Resultsmentioning

confidence: 95%

“…So far, systematic calculation of the leading order relativistic and radiative corrections were obtained in [12][13][14][15]. In all the cases the vibration quantum number has been restricted to v = 4.…”

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confidence: 99%

Leading-order relativistic corrections to the rovibrational spectrum of H2+ and HD+ molecular ions

2019

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High-precision variational calculations of the operators for the relativistic corrections in the leading mα 4 order are presented. The ro-vibrational states in the range of the total orbital angular momentum L = 0−4 and vibrational quantum number v = 0−10 for the H + 2 and HD + molecular ions are considered. We estimate that about ten significant digits are obtained. This high precision is required for making theoretical predictions for transition frequencies at the level of 10 −12 relative uncertainty.

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“…VII D and VII E can be used to calculate relativistic corrections to the electron spinorbit and spin-spin tensor interaction coefficients of the hyperfine Hamiltonian in a one-electron molecular system. Here, we present corrections to the spin-orbit coefficient in both H + 2 [8] and HD + [7] for a few transitions studied in recent or ongoing experiments [2,4,6,24].…”

Section: Numerical Results and Conclusionmentioning

confidence: 99%

Hyperfine structure in the H$_2^+$ and HD$^+$ molecular ions at $mα^6$ order

Korobov,

Karr,

Haidar

et al. 2020

Preprint

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A complete effective Hamiltonian for relativistic corrections at orders mα 6 and mα 6 (m/M ) in a one-electron molecular system is derived from the NRQED Lagrangian. It includes spin-independent corrections to the energy levels and spin-spin scalar interactions contributing to the hyperfine splitting, both of which had been studied previously. In addition, corrections to electron spin-orbit and spin-spin tensor interactions are newly obtained. This allows improving the hyperfine structure theory in the hydrogen molecular ions. Improved values of the spin-orbit hyperfine coefficient are calculated for a few transitions of current experimental interest. I. INTRODUCTIONHigh-resolution spectroscopy of the hydrogen molecular ions H + 2 and HD + may contribute significantly to the determination of fundamental constants such as the proton-electron mass ratio m p /m e [1]. A pure rotational transition in HD + has recently been measured with a relative uncertainty of 1.3 × 10 −11 [2]. The experimental accuracy of ro-vibrational transition frequencies is expected to reach a few parts per trillion in the near future using spectroscopy in the Lamb-Dicke regime [2][3][4] or in a Doppler-free geometry [5,6]. While information on fundamental constants is obtained from comparison of spin-averaged transition frequencies with theoretical predictions, the hyperfine splitting of ro-vibrational lines also allows for precise tests of theory.So far, the hyperfine structure of H + 2 and HD + has been calculated within the Breit-Pauli approximation [7, 8], taking into account the anomalous magnetic moment of the electron. All terms at orders mα 4 and mα 5 are included, so that the theoretical accuracy of the hyperfine coefficients is of order α 2 ∼ 5 × 10 −5 . Higherorder corrections to the largest coefficients, i.e. the spin-spin Fermi contact interaction, were later calculated in [9,10], which allowed to get excellent agreement with available RF spectroscopy data in H + 2 [11] at the level of ∼ 1 ppm. The following step to improve the hyperfine structure theory is to evaluate higher-order corrections to the next largest coefficients, i.e. the electron spin-orbit and spin-spin tensor interaction, starting with relativistic corrections at the mα 6 order.With this aim, we derive in the present work the complete effective Hamiltonian for the hydrogen molecular ions at the mα 6 and mα 6 (m/M ) orders, following the NRQED approach [12][13][14]. Then, we use it to calculate numerically the corrections to the electron spin-orbit interaction for a few transitions studied in ongoing experiments. The paper is organized as follows: in Secs. II and III, we recall the expression of the NRQED Lagrangian and associated interaction vertices. We then systematically derive the effective potentials, which are organized in three categories: tree-level interactions involving the exchange of a Coulomb or transverse photon (Sec. IV), terms due to retardation in the transverse photon exchange (Sec. V), and finally those coming from a seagull diagram with simul...

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High-precision spectroscopy of hydrogen molecular ions

Cited by 20 publications

References 145 publications

Physics beyond the Standard Model from hydrogen spectroscopy

Physics beyond the Standard Model from hydrogen spectroscopy

Leading-order relativistic corrections to the rovibrational spectrum of H2+ and HD+ molecular ions

Hyperfine structure in the H$_2^+$ and HD$^+$ molecular ions at $mα^6$ order

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