Fundamental transitions and ionization energies of the hydrogen molecular ions at the few ppt level

Abstract

We calculate ionization energies and fundamental vibrational transitions for H${}_2^{+}$, D${}_2^{+}$, and HD${}^{+}$ molecular ions. The NRQED expansion for the energy in terms of the fine structure constant $\alpha$ is used. Previous calculations of orders $m{\alpha }^6$ and $m{\alpha }^7$ are improved by including second-order contributions due to the vibrational motion of nuclei. Furthermore, we evaluate the largest corrections at the order $m{\alpha }^8$. That allows to reduce the fractional uncertainty to the level of $7\cdot 10^{-12}$ for fundamental transitions and to $4\cdot 10^{-12}$ for the ionization energies.

5 pages, 5 tables, submitted to PRL

References in corpus (10)

• CODATA Recommended Values of the Fundamental Physical Constants: 2014
• High-precision measurement of the atomic mass of the electron
• Complete two-loop correction to the bound-electron g factor
• Nonrelativistic QED approach to the Lamb shift
• Relativistic corrections of mα^6 order to the ro-vibrational spectrum of H_2^+ and HD^+ molecular ions
• Hydrogen molecular ions for improved determination of fundamental constants
• Test of the theoretical hyperfine structure of the molecular hydrogen ion at the 1-ppm level
• Relativistic corrections of order mα^6 to the two-center problem
• Precision spectroscopy of the hydrogen molecular ions HD${}^{+}$
• One-loop vacuum polarization at m$\alpha$7 and higher orders for three-body molecular systems

Cited by in corpus (35)

• Proton-Electron Mass Ratio from Laser Spectroscopy of HD${}^{+}$ at the Part-Per-Trillion Level
• Toward a determination of the proton-electron mass ratio from the Lamb-dip measurement of HD
• Benchmarking theory with an improved measurement of the ionization and dissociation energies of H${}_2$
• Proton-electron mass ratio by high-resolution optical spectroscopy of ion ensembles in the resolved-carrier regime
• Nonadiabatic QED correction to the dissociation energy of the hydrogen molecule
• Dissociation energy of the hydrogen molecule at 10${}^{-9}$ accuracy
• Rotational spectroscopy of cold, trapped molecular ions in the Lamb-Dicke regime
• Penning-trap mass measurements of the deuteron and the HD+ molecular ion
• Quantum control of molecules for fundamental physics
• Trapping, cooling, and photodissociation analysis of state-selected H$\_2^{+}$ ions produced by (3+1) multiphoton ionization
• Self-consistent extraction of spectroscopic bounds on light new physics
• NRQED approach to the fine and hyperfine structure corrections of order $m{\alpha }^6$ and $m{\alpha }^6(m/M)$ -- Application to the hydrogen atom
• Hyperfine structure in the H${}_2^{+}$ and HD${}^{+}$ molecular ions at $m{\alpha }^6$ order
• Ro-vibrational states of H${}_2^{+}$. Variational calculations
• Improved Ionization and Dissociation Energies of the Deuterium Molecule
• Towards highly accurate calculations of parity violation in chiral molecules: relativistic coupled-cluster theory including QED-effects
• Higher-order corrections to spin-spin scalar interactions in HD${}^{+}$ and H${}_2^{+}$
• Leading order relativistic corrections to the ro-vibrational spectrum of $\mbox{H}^+_2$ and $\mbox{HD}^+$ molecular ions
• Explicitly correlated Gaussian functions with shifted-center and projection techniques in pre-Born-Oppenheimer calculations
• H${}_3^{+}$ as a five-body problem described with explicitly correlated Gaussian basis sets
• Canceling spin-dependent contributions and systematic shifts in precision spectroscopy of the molecular hydrogen ions
• Proton-electron mass ratio from HD${}^{+}$ revisited
• High-precision solution of the Dirac Equation for the hydrogen molecular ion using a basis-set expansion
• Prospects for the determination of fundamental constants with beyond-state-of-the-art uncertainty using molecular hydrogen ion spectroscopy
• Stark quenching of rovibrational states of H2+ due to motion in a magnetic field
• Higher-order corrections to the spin-orbit and spin-spin tensor interactions in HD${}^{+}$
• High-precision solution of the Dirac Equation for the hydrogen molecular ion by an iterative method
• Precision spectroscopy of the hydrogen molecular ions: present status of theory and experiment
• Quantum control of a single ${\mathrm{H}}_2^{+}$ molecular ion
• Light one-electron quasi-molecular ions within the finite-basis-set method for the two-center Dirac equation
• Spin-orbit interaction in the HD${}^{+}$ ion
• High-precision minmax solution of the two-center Dirac equation
• Ro-vibrational spin-averaged transitions in the hydrogen molecular ions
• QED corrections of orders $m{\alpha }^6$ and $m{\alpha }^6(m/M)$ for HD${}^{+}$ rovibrational transitions beyond Born-Oppenheimer approximation
• State-Selective Ionization and Trapping of Single H${}_2^{+}$ Ions with (2+1) Multiphoton Ionization