  We investigate the gauge invariance of the leading logarithmic radiative
correction to the two-photon decay width in hydrogenlike atoms. It is shown
that an effective treatment of the correction using a Lamb-shift "potential"
leads to equivalent results in both the length as well as the velocity gauges
provided all relevant correction terms are taken into account. Specifically,
the relevant radiative corrections are related to the energies that enter into
the propagator denominators, to the Hamiltonian, to the wave functions, and to
the energy conservation condition that holds between the two photons; the form
of all of these effects is different in the two gauges, but the final result is
shown to be gauge invariant, as it should be. Although the actual calculation
only involves integrations over nonrelativistic hydrogenic Green functions, the
derivation of the leading logarithmic correction can be regarded as slightly
more complex than that of other typical logarithmic terms. The dominant
radiative correction to the 2S two-photon decay width is found to be -2.020536
(alpha/pi) (Zalpha)^2 ln[(Zalpha)^-2] in units of the leading nonrelativistic
expression. This result is in agreement with a length-gauge calculation [S. G.
Karshenboim and V. G. Ivanov, e-print physics/9702027], where the coefficient
was given as -2.025(1).
