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

TL;DR

This study performs detailed four-body calculations of hyperfine structures in H$_2$, D$_2$, and HD molecules, providing a precise deuteron quadrupole moment that challenges previous estimates and aligns well with historical measurements.

Contribution

It introduces an accurate four-body calculation method for hyperfine structures and determines a new value for the deuteron quadrupole moment, highlighting nonadiabatic effects and spin-dependent nuclear interactions.

Findings

Deuteron quadrupole moment determined as 0.285699(15)(18) fm$^2$

Results agree with historical molecular-beam magnetic resonance data

Highlights importance of nonadiabatic and spin effects in nuclear modeling

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 $Q_d = 0.285\,699(15)(18)$ 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.