Hyperfine structure of the first rotational level in H${}_2$, D${}_2$ and HD molecules and the deuteron quadrupole moment

Abstract

We perform the four-body calculation of the hyperfine structure in the first rotational state $J=1$ of the H${}_2$, D${}_2$, and HD molecules and determine the accurate value for the deuteron electric quadrupole moment $Q_d=0.285699(15)(18)$ fm${}^2$ in significant disagreement with former spectroscopic determinations. Our results for the hyperfine parameters agree very well with the currently most accurate molecular-beam magnetic resonance measurement performed several decades ago by N.F. Ramsey and coworkers. They also indicate the significance of previously neglected nonadiabatic effects. Moreover, a very good agreement with the recent calculation of $Q_d$ based on the chiral effective field theory, although much less accurate, indicates the importance of the spin dependence of nucleon interactions in the accurate description of nuclei.

arXiv comment6 pages, 1 figure, improved numerics

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• Higher-order corrections to the spin-orbit and spin-spin tensor interactions in HD${}^{+}$
• Thermal radiative corrections to hyperfine structure of light hydrogen-like systems
• Hyperfine and Zeeman interactions in ultracold collisions of molecular hydrogen with atomic lithium
• Bound Deuteron-Antideuteron System (Deuteronium): Leading Radiative and Internal-Structure Corrections to Bound-State Energies
• Relativistic and Recoil Corrections to Light-Fermion Vacuum Polarization for Bound Systems of Spin-0, Spin-1/2, and Spin-1 Particles