Complete ${\alpha }^{6}m$ Corrections to the Ground State of ${\mathrm{H}}_2$

We perform the calculation of all relativistic and quantum electrodynamic corrections of the order of ${\alpha }^{6}m$ to the ground electronic state of a hydrogen molecule and present improved results for the dissociation and the fundamental transition energies. These results open the window for the high-precision spectroscopy of ${\mathrm{H}}_2$ and related low-energy tests of fundamental interactions.

Figure 1

Nonlogarithmic photon exchange contribution $E_Q^{\prime }+E_A^{\prime }+E_C+E_H^{\prime }$ as a function of the internuclear distance $R$. The horizontal line is located at $-1/8$, which is twice the atomic hydrogen value, and the dashed curve shows the $0.529947904/R^2-1/8$ asymptotics, which is obtained from the small $R$ expansion of the Casimir-Polder potential [22].