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We derive a set of exact solutions of the Dirac equation for a single electron moving in a multimode quantized radiation field. All the modes in this field are propagating in the same direction. Our method entails the application of the Lie-algebra procedure. We discuss the physical meaning and possible applications of these solutions. \textcopyright{} 1996 The American Physical Society.

The theory of the spin-rotation interaction is discussed and its relation to the paramagnetic part of the magnetic shielding tensor derived with consistent treatment of the electric field in the molecule. The latter point yields agreement between theory and experiment for the first time in the case of isotopes of the hydrogen molecule. The paramagnetic part of the shielding constant for ${\mathrm{H}}_{2}$ ($J=1$) is found to be -5.66(6) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}6}$ in the gauge where the vector potential is zero at the nucleus.