0 20 40 60 80 0.0 0.2 0.4 0.6 0.8 =10 ( =0.2) N=16 14 12 10 8 6 N=4 G/G$_{0}$ J/ 0 20 40 60 80 0.0 0.2 0.4 0.6 0.8 Fig. 4 N=16 14 12 10 8 6 N=4 G/G$_{0}$ = 5 ( =0.4) ω $_{l}$= ε $_{d}$- ε F J/ FIG. 3: Conductance G in units of quantum conductance G 0 = e $^{2}$/h plotted versus contact interaction J at resonance α = ε$_{F}$ for ξ = 10 and ξ = 5 computed using extended molecules with N = 4   6   8   10   12   14   16 sites (values increase upwards). energies Σ$_{x}$ instead of Σ 0 $_{ x}$  by devising certain diagrammatic approximations. We shall not pursue this line here  because as noted in Sect. II  the validity of such approximations is usually not transparent physically. We present instead a simple renormalization scheme  which turns out to work surprisingly well for the IRLM. Inspired by the rather general framework of the Landau Fermi liquid theory [54]  we shall simply suppose that the aforementioned renormalization can be accounted for by means of a multiplicative ε -independent factor F   G $^{r}$( ε ) |$_{exact}$ ≃ F G $^{r}$( ε ). Then  the problem is to deduce this factor. For the IRLM at resonance  this can be done  because  as already noted in Sect. V A  the exact conductance is known  G |$_{α}$ = ε$_{F}$ = G 0 . This condition determines the needed factor at resonance for given values of N   ξ and J (remember that we keep β = 1)  but F could dependent on α . Because G = G ( α ) reaches its maximum at α = ε$_{F}$ one can admit that  at least not too far away from resonance  F only slightly depends on α and neglect this dependence altogether. We have computed and examined the curves of G = G ( α ) obtained within this renor- malization procedure. The results are very encouraging. The renormalized curves are much less size-dependent than the unrenormalized ones. The smaller the values of ξ and J   the weaker is the dependence on N . For illustration  we present in Fig. 4 for comparison the renormalized curves along with those unrenormalized in the rather unrealistic situation of very large values of J = 10 and ξ = 10  which corresponds to a very large ratio J/ Γ = 50. The fact that  with increasing N   the renormalized curves tend to become size-independent much faster than the unrenormalized curves is clearly visible even in this less favorable case. 16