Higher-order corrections to spin-orbit and spin-spin tensor interactions in hydrogen molecular ions: Theory and application to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">H</mml:mi></mml:mrow><mml:mn>2</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:math>

Abstract

We consider higher-order corrections to hyperfine coefficients related to the spin-orbit and spin-spin tensor interactions in hydrogen molecular ions. The $m{\ensuremath{\alpha}}^{7}ln(\ensuremath{\alpha})$-order radiative correction is derived in the NRQED framework. We present complete numerical calculations, including as well the $m{\ensuremath{\alpha}}^{6}$-order relativistic correction, for the case of ${\mathrm{H}}_{2}^{+}$. The theoretical uncertainty is reduced by more than one order of magnitude with respect to the Breit-Pauli level, down to a few ppm. We also compare our results with available rf spectroscopy data.

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