Hyperfine structure in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi mathvariant="normal">H</mml:mi><mml:mn>2</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>HD</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:math> molecular ions at order <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>m</mml:mi><mml:msup><mml:mi>α</mml:mi><mml:mn>6</mml:mn></mml:msup></mml:mrow></mml:math>
V. I. Korobov, Jean‐Philippe Karr, Mohammad Haidar, Zhen-Xiang Zhong
Abstract
A complete effective Hamiltonian for relativistic corrections at orders $m{\ensuremath{\alpha}}^{6}$ and $m{\ensuremath{\alpha}}^{6}(m/M)$ in a one-electron molecular system is derived from the nonrelativistic QED Lagrangian. It includes spin-independent corrections to the energy levels and spin-spin scalar interactions contributing to the hyperfine splitting, both of which had been studied previously. In addition, corrections to electron spin-orbit and spin-spin tensor interactions are obtained. This allows the improvement of the hyperfine structure theory in hydrogen molecular ions. Improved values of the spin-orbit hyperfine coefficient are calculated for a few transitions of current experimental interest.