  We report the first calculations of cross sections for the radiative capture
reactions t(alpha,gamma)^7Li and ^3He(alpha,gamma)^7Be below 2 MeV which use
wave functions derived from realistic nucleon-nucleon interactions by the
variational Monte Carlo technique. After examining several small corrections to
the dominant E1 operator, we find energy dependences for the low-energy
S-factors which agree reasonably with experimental measurements. There is no
contradiction with the previous theoretical understanding of these processes,
but the zero-energy derivative of the t(alpha,gamma)^7Li S-factor is smaller
than in most models. While this method can in principle predict cross section
normalizations, the normalizations of our results are mostly too low.
