  We probe the U(N) chiral Gross-Neveu model with a source-term
$J\l{\Psi}\Psi$. We find an expression for the renormalization scheme and scale
invariant source $\hat{J}$, as a function of the generated mass gap. The
expansion of this function is organized in such a way that all scheme and scale
dependence is reduced to one single parameter $d$. We obtain a non-perturbative
mass gap as the solution of $\hat{J}=0$. A physical choice for $d$ gives good
results for $N>2$. The self-consistent minimal sensitivity condition gives a
slight improvement.
