title: Theoretical Hyperfine Structure of the Molecular Hydrogen Ion at the 1 ppm Level.
abstract: We revisit the mα^{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. 23, 1476 (1969)], thereby concluding a nearly 50-year-long theoretical quest to explain the experimental results within their 1-ppm error. The agreement between the 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 mα^{6}(m/M) correction term will be mandatory.
authors.affiliation: Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia.
authors.forename: Vladimir I
authors.initials: VI
authors.lastname: Korobov
authors.affiliation: LaserLaB and Department of Physics and Astronomy, VU University, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands.
authors.forename: J C J
authors.initials: JC
authors.lastname: Koelemeij
authors.affiliation: Laboratoire Kastler Brossel, UPMC-Sorbonne Universités, CNRS, ENS-PSL Research University, Collège de France, 4 place Jussieu, F-75005 Paris, France and Université d'Evry-Val d'Essonne, Boulevard François Mitterrand, F-91000 Evry, France.
authors.forename: L
authors.initials: L
authors.lastname: Hilico
authors.affiliation: Laboratoire Kastler Brossel, UPMC-Sorbonne Universités, CNRS, ENS-PSL Research University, Collège de France, 4 place Jussieu, F-75005 Paris, France and Université d'Evry-Val d'Essonne, Boulevard François Mitterrand, F-91000 Evry, France.
authors.forename: J-Ph
authors.initials: JP
authors.lastname: Karr