  We suggest that Hamiltonian matrix elements between physical states in QCD
might be approximated, in Coulomb gauge, by "lattice-improved" tree diagrams;
i.e. tree diagram contributions with dressed ghost, transverse gluon, and
Coulomb propagators obtained from lattice simulations. Such matrix elements can
be applied to a truncated-basis treatment of hadronic states which include
constituent gluons. As an illustration, we apply this hybrid approach to the
heavy quark potential, for quark-antiquark separations up to 2.4 fm. The
Coulomb string tension in SU(3) gauge theory is about a factor of four times
greater than the asymptotic string tension. In our approach we show that a
single constituent gluon is in principle sufficient, up to 2.4 fm, to reduce
this overshoot by the factor required. The static potential remains linear,
although the precise value of the string tension depends on details of the
Couloumb gauge ghost and gluon propagators in the infrared regime. In this
connection we present new lattice results for the transverse gluon propagator
in position space.
