Bound Deuteron-Antideuteron System (Deuteronium): Leading Radiative and Internal-Structure Corrections to Bound-State Energies

Abstract

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 alpha^3 m_d and alpha^4 m_d , where alpha is the fine-structure constant and m_d is the deuteron mass, and also investigate internal-structure corrections: hadronic vacuum polarization, finite-size effects, and strong-interaction corrections.

Figures (3)

• Figure 1: Feynman diagrams contributing to the leading radiative corrections in deuteronium. Light fermions (virtual electrons and positrons) are denoted as "$e$", and the hadronic loop is denoted by the letter "$h$". Panel (a) represents the leading-order eVP correction, (b) is the loop-by-loop reducible contribution, (c) and (d) are the two independent contributions to the two-loop irreducible correction, (e) represents the second-order perturbation theory contribution of two one-loop potentials, and (f) represents the hadronic vacuum polarization contribution.
• Figure 2: The dipole-allowed $3D$--$3P$ transitions are displayed graphically. The transitions are resolved with respect to the (hyper)fine-structure of the levels [denoted as (H)FS]. When the upper sublevel undergoes only one dipole-permitted transition, we use thick lines. Others transitions are denoted by ordinary solid lines. The viewgraph illustrates the much more complex (hyper)fine-structure that is encountered in the bound system of two spin-1 particles, as compared to bound systems involving a light spin-1/2 particle orbiting a heavy nucleus.
• Figure 3: Same as the viewgraph Fig. \ref{['fig2']}, but for the dipole-allowed $4F$--$4D$ transitions.