Abstract
We present a new approximation scheme to solve the Non-Perturbative Renormalization Group equations and obtain the full momentum dependence of n-point functions. The core of the method consists in deriving approximate flow equations that are then solved exactly. The results thus obtained can next be improved through an iteration procedure. The approximations proposed in this paper lead to approximate equations that are accurate both in the perturbative and the scaling regimes. The scheme is tested with the calculation of the shift ΔTc in the transition temperature of the weakly repulsive Bose gas, a quantity which is very sensitive to all momentum scales. The leading-order result is in agreement with lattice calculations, albeit with a theoretical uncertainty of about 25%. The next-to-leading order differs by about 10% from the best accepted result.