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We study a model Dyson-Schwinger equation for the quark propagator closedusing an {\it Ansatz} for the gluon propagator of the form \mbox{$D(q) \simq^2/[(q^2)^2 + b^4]$} and two {\it Ans\"{a}tze} for the quark-gluon vertex: theminimal Ball-Chiu and the modified form suggested by Curtis and Pennington.Using the quark condensate as an order parameter, we find that there is acritical value of $b=b_c$ such that the model does not support dynamical chiralsymmetry breaking for $b>b_c$. We discuss and apply a confinement test whichsuggests that, for all values of $b$, the quark propagator in the model {\bf isnot} confining. Together these results suggest that this Ansatz for the gluonpropagator is inadequate as a model since it does not yield the expectedbehaviour of QCD.Comment: 21 Pages including 4 PostScript figures uuencoded at the end of the  file. Replacement: slight changes of wording and emphasis. ADP-93-215/T133,  ANL-PHY-7599-TH-93, FSU-SCRI-93-108, REVTEX 3.

Dynamical chiral symmetry breaking and confinement with an infrared-vanishing gluon propagator?