  We probe the U(N) Gross-Neveu model with a source-term $J\bar{\Psi}\Psi$. 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 get a non-perturbative mass gap as the
solution of $\hat{J}=0$. In one loop we find that any physical choice for d
gives good results for high values of N. In two loops we can determine d
self-consistently by the principle of minimal sensitivity and find remarkably
accurate results for N>2.
