At the level of accuracy required (less than about 1 meV), the effects beyond
the Coulombic, nonrelativistic point-like description of the muonic
molecules are important. Because of the heavy mass of the muon, muonic
hydrogen atoms and molecules are sensitive to effects such as QED vacuum
polarization and the nuclear charge form factor as well as hyperfine
effects. However, it is the difference between the corrections to the
atomic and molecular energy levels which affects the binding energy
Hyperfine structure of the and further introduces corrections for F=0 of +35.2 meV (S=0), and for F=1 of -8.3 meV (S=0), -14.9 meV (S=1), and -8.5 meV (S=2), where F is the total spin of and S, that of .