Bound deuteron-antideuteron system (deuteronium): Leading radiative and internal-structure corrections to bound-state energies

We evaluate the energy levels of the deuteronium bound system, which consists of a deuteron and an antideuteron, with a special emphasis on states with nonvanishing orbital angular momenta. The excited atomic bound states of deuteronium constitute probes for the understanding of higher-order quantum electrodynamic corrections for spin-1 particles in a bound system where the typical field strength of the binding Coulomb field (at a distance of the generalized Bohr radius) exceeds Schwinger’s critical field strength. For states with nonvanishing angular momenta, effects due to the internal structure of the deuteron and virtual annihilation contributions are highly suppressed. Relevant transitions are found to be in a frequency range accessible by standard laser spectroscopic techniques. We evaluate the leading and next-to-leading energy corrections of orders <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msup> <a:mi>α</a:mi> <a:mn>3</a:mn> </a:msup> <a:msub> <a:mi>m</a:mi> <a:mi>d</a:mi> </a:msub> </a:mrow> </a:math> and <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:msup> <b:mi>α</b:mi> <b:mn>4</b:mn> </b:msup> <b:msub> <b:mi>m</b:mi> <b:mi>d</b:mi> </b:msub> </b:mrow> </b:math> , where <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mi>α</c:mi> </c:math> is the fine-structure constant and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:msub> <d:mi>m</d:mi> <d:mi>d</d:mi> </d:msub> </d:math> is the deuteron mass, and also investigate internal-structure corrections: hadronic vacuum polarization, finite-size effects, and strong-interaction corrections.