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arXiv · 1510.05206

Test of the theoretical hyperfine structure of the molecular hydrogen ion at the 1-ppm level

Vladimir I. Korobov·Jeroen C. J. Koelemeij·Laurent Hilico·Jean-Philippe Karr
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Abstract

We revisit the $m α^6 (m/M)$ 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 this correction term produces theoretical predictions which are in excellent agreement with experimental data [K. B. Jefferts, Phys.\ Rev.\ Lett.\ \textbf{23}, 1476 (1969)], thereby concluding a nearly fifty years long theoretical quest to explain the experimental results within their 1-ppm error. The agreement between theory and experiment corroborates the proton structural properties as derived from the hyperfine structure of atomic hydrogen. Our work furthermore indicates that for future improvements, a full three-body evaluation of the $m α^6 (m/M)$ correction term will be mandatory.

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Vladimir I. Korobov, Jeroen C. J. Koelemeij, Laurent Hilico, Jean-Philippe Karr. 2015-10-18. Test of the theoretical hyperfine structure of the molecular hydrogen ion at the 1-ppm level. https://doi.org/10.1103/physrevlett.116.053003

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