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

Abstract

We revisit the $m{\alpha }^6(m/M)$ 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 $m{\alpha }^6(m/M)$ correction term will be mandatory.

4 pages, 1 figure, 2 tables

References in corpus (1)

• Relativistic corrections of mα^6(m/M) order to the hyperfine structure of the H_2^+ molecular ion

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