Related papers: Higher-order corrections to the spin-orbit and spi…
We consider higher-order corrections to hyperfine coefficients related to the spin-orbit and spin-spin tensor interactions in hydrogen molecular ions. The $m\alpha^7 \ln(\alpha)$-order radiative correction is derived in the NRQED framework.…
The largest hyperfine interaction coefficients in the hydrogen molecular ion HD$^+$, i.e. the electron-proton and electron-deuteron spin-spin scalar interactions, are calculated with estimated uncertainties slightly below 1~ppm. The…
We report on progress in calculation of the spin-orbit interaction for the HD$^+$ molecular ion. This interaction is currently the largest source of theoretical uncertainty in determination of the hyperfine structure of rovibrational…
A complete effective Hamiltonian for relativistic corrections at orders $m\alpha^6$ and $m\alpha^6(m/M)$ in a one-electron molecular system is derived from the NRQED Lagrangian. It includes spin-independent corrections to the energy levels…
Precise numerical calculation of radiofrequency intervals between hyperfine sublevels of the $(37,35)$ state of the antiprotonic helium-4 atom is presented. Theoretical consideration includes the QED corrections of order $m\alpha^6$ to the…
The relativistic second-order corrections at orders $m\alpha^6$ and $m\alpha^6(m/M)$ in hydrogen molecular ions are calculated. Convergence of numerical results is studied, which allows estimating the relative numerical uncertainty to be…
High-precision variational calculations of the operators for the relativistic corrections in the leading $m\alpha^4$ order are presented. The ro-vibrational states in the range of the total orbital angular momentum $L\!=\!0\!-\!4$ and…
The major goal of the high-precision studies of ro-vibrational states in the hydrogen molecular ions is to provide an alternative way for improving the electron-to-proton mass ratio, or the atomic mass of electron. By now the complete set…
The m\alpha^6(m/M) order corrections to the hyperfine splitting in the H_2^+ ion are calculated. That allows to reduce uncertainty in the frequency intervals between hyperfine sublevels of a given rovibrational state to about 10 ppm.…
We investigate interactions between the proton spin, the deuteron spin, and the orbital angular momentum in the electronic ground state of the HD molecule. These interactions lead to hyperfine splittings of molecular energy levels. Our…
We present a comprehensive analysis of all currently available high-accuracy frequency measurements of rotational and rovibrational transitions in the hydrogen molecular ion HD$^+$. Our analysis utilises the theoretically calculated…
The complete second-order hyperfine-interaction correction is calculated for centroid energy levels of H, D, and $^3$He atoms. For $^3$He, the corrections of $-2.075$~kHz and $-0.305$~kHz beyond the leading hyperfine-mixing contribution are…
We reconsider the calculation of rovibrational transition frequencies in hydrogen molecular ions. Some previously neglected contributions, such as the deuteron polarizability, are included into consideration in comparison with our previous…
Expectation values of the Breit operators and the $Q$ terms are calculated for HD$^+$ with the vibrational number $v=0-4$ and the total angular momentum $L=0-4$. Relativistic and radiative corrections to some ro-vibrational transition…
The effective Hamiltonian of $m\alpha^6$ and $m\alpha^6(m/M)$ order corrections for hydrogen molecular ions has been derived in [ Z.-X. Zhong, \emph{et al.}, Phys. Rev. A {\bf98}, 032502(2018).], in this work we express the energy…
The OH$^+$ ($X ^3\Sigma^-$) radical cation has been investigated by combining a 4 K 22-pole ion trap apparatus with high-resolution IR and THz radiation sources. Applying different types of action spectroscopic methods, the fundamental…
We revisit the $m \alpha^6 (m/M)$ order corrections to the hyperfine splitting in the H$_2^+$ ion, and find a hitherto unrecognized second-order relativistic contribution associated with the vibrational motion of the nuclei. Inclusion of…
The indirect nuclear spin-spin coupling tensor, $\mathbf J$, between mercury nuclei in Hg-containing systems can be of the order of few kHz and one of the largest measured. We conduct an analysis of the physics behind the electronic…
We present a nonrelativistic calculation of the rotation-vibration levels of the molecular ions H2+, D2+ and HD+, relying on the diagonalization of the exact three-body Hamiltonian. The J=2 levels are obtained with a very high accuracy of…
The static dipole polarizability for the hydrogen molecular ions H$_2^+$, HD$^+$, and D$_2^+$ are calculated. These new data for polarizability takes into account the leading order relativistic corrections to the wave function of the…