Relativistic corrections of order mα^6 to the two-center problem

Abstract

Effective potentials of the relativistic mα^6 order correction for the ground state of the Coulomb two-center problem are calculated. They can be used to evaluate the relativistic contribution of that order to the energies of hydrogen molecular ions or metastable states of the antiprotonic helium atom, where precision spectroscopic data are available. In our studies we use the variational expansion based on randomly chosen exponents that permits to achieve high numerical accuracy.

arXiv comment12 pages, 3 tables 2 figures; submitted to the Journal of Physics B

References in corpus (1)

• Molecular Dynamics Simulation of Sympathetic Crystallization of Molecular Ions

Cited by in corpus (18)

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• Theoretical transition frequencies beyond 0.1 ppb accuracy in H${}_2^{+}$, HD${}^{+}$, and antiprotonic helium
• Calculation of the relativistic Bethe logarithm in the two-center problem
• Relativistic corrections of mα^6(m/M) order to the hyperfine structure of the H_2^+ molecular ion
• Self-consistent extraction of spectroscopic bounds on light new physics
• Ro-vibrational states of H${}_2^{+}$. Variational calculations
• Hyperfine structure in the H${}_2^{+}$ and HD${}^{+}$ molecular ions at $m{\alpha }^6$ order
• Precision Spectroscopy of Molecular Hydrogen Ions: Towards Frequency Metrology of Particle Masses
• Solution of the two-center Dirac equation with 20 digits precision using the finite-element technique
• High-precision solution of the Dirac Equation for the hydrogen molecular ion by an iterative method
• One-particle operator representation over two-particle basis sets for relativistic QED computations
• Static Dipole Polarizability for the $1S\sigma$ electronic state of the $H_2^{+}$ molecular ion
• Light one-electron quasi-molecular ions within the finite-basis-set method for the two-center Dirac equation
• One-loop vacuum polarization at $m{\alpha }^7$ order for the two center problem
• 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
• Double-pair Coulomb and Breit photon correction to the correlated relativistic energy