Higher-order corrections to spin-orbit and spin-spin tensor interactions in hydrogen molecular ions: Theory and application to ${\mathrm{H}}_{2}^{+}$

Higher-order corrections to spin-orbit and spin-spin tensor interactions in hydrogen molecular ions: Theory and application to $H_{2}^{+}$

Mohammad Haidar, Vladimir I. Korobov, Laurent Hilico, and Jean-Philippe Karr

Phys. Rev. A 106, 022816 – Published 29 August 2022

Abstract

We consider higher-order corrections to hyperfine coefficients related to the spin-orbit and spin-spin tensor interactions in hydrogen molecular ions. The $m α^{7} ln (α)$ -order radiative correction is derived in the NRQED framework. We present complete numerical calculations, including as well the $m α^{6}$ -order relativistic correction, for the case of $H_{2}^{+}$ . 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.

Received 4 July 2022
Accepted 19 August 2022

DOI:https://doi.org/10.1103/PhysRevA.106.022816

Physics Subject Headings (PhySH)

Fine & hyperfine structure Relativistic & quantum electrodynamic effects in atoms, molecules,& ions

Atomic, Molecular & Optical

Authors & Affiliations

Mohammad Haidar ^1,*, Vladimir I. Korobov ², Laurent Hilico ^1,3, and Jean-Philippe Karr ^1,3

¹Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France, 4 place Jussieu, F-75005 Paris, France
²Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia
³Université d'Evry-Val d'Essonne, Université Paris-Saclay, Boulevard François Mitterrand, F-91000 Evry, France

^*Present address: Sorbonne Université, Laboratoire de Chimie Théorique (LCT), 4 place Jussieu, F-75005 Paris, France; Sorbonne Université, CNRS, Université Paris Cité, Laboratoire Jacques-Louis Lions (LJLL), 4 place Jussieu, F-75005 Paris, France; TotalEnergies, Tour Coupole, 2 Pl. Jean Millier, F-92078 Paris la Défense, France.

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Vol. 106, Iss. 2 — August 2022

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Physical Review A

covering atomic, molecular, and optical physics and quantum science

Higher-order corrections to spin-orbit and spin-spin tensor interactions in hydrogen molecular ions: Theory and application to $H_{2}^{+}$

Mohammad Haidar, Vladimir I. Korobov, Laurent Hilico, and Jean-Philippe Karr

Phys. Rev. A 106, 022816 – Published 29 August 2022

Abstract

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Physical Review A

covering atomic, molecular, and optical physics and quantum science

Higher-order corrections to spin-orbit and spin-spin tensor interactions in hydrogen molecular ions: Theory and application to H2+

Mohammad Haidar, Vladimir I. Korobov, Laurent Hilico, and Jean-Philippe Karr

Phys. Rev. A 106, 022816 – Published 29 August 2022

Abstract

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Higher-order corrections to spin-orbit and spin-spin tensor interactions in hydrogen molecular ions: Theory and application to $H_{2}^{+}$