  In an atom, the interaction of a bound electron with the vacuum fluctuations
of the electromagnetic field leads to complex shifts in the energy levels of
the electron, with the real part of the shift corresponding to a shift in the
energy level and the imaginary part to the width of the energy level. The most
celebrated radiative shift is the Lamb shift between the $2S_{1/2}$ and the
$2P_{1/2}$ levels of the hydrogen atom.~The measurement of this shift in 1947
by Willis Lamb Jr. proved that the prediction by Dirac theory that the energy
levels were degenerate was incorrect. Hans~Bethe's calculation of the shift
demonstrated the renormalization process required to deal with the divergences
plaguing the existing theories and led to the understanding that it was
essential for theory to include interactions with the zero-point quantum vacuum
field. This was the birth of modern quantum electrodynamics (QED). Other
calculations of the Lamb shift followed by Welton and Power in an effort to
clarify the physical mechanisms leading to the shift. We have done a
calculation of the shift using a group theoretical approach which gives the
shift as an integral over frequency of a function, which we call the spectral
density of the shift. The spectral density reveals how different frequencies
contribute to the total energy shift. We find, for example, that half the
radiative shift for the ground state 1S level in H comes from photon energies
below 9700 eV, and that the expressions by Power and Welton do not have the
correct low frequency behavior, although they do give approximately the correct
value for the total shift.
