  We report on the results of the \hethet\ experiment at the underground
accelerator facility LUNA (Gran Sasso). For the first time the lowest
projectile energies utilized for the cross section measurement correspond to
energies below the center of the solar Gamow peak ($E_{\rm 0}$=22 keV). The
data provide no evidence for the existence of a hypothetical resonance in the
energy range investigated. Although no extrapolation is needed anymore (except
for energies at the low-energy tail of the Gamow peak), the data must be
corrected for the effects of electron screening, clearly observed the first
time for the \hethet\ reaction. The effects are however larger than expected
and not understood, leading presently to the largest uncertainty on the quoted
$S_{\rm b}(E_{\rm 0})$ value for bare nuclides (=5.40 MeV b).
