shell correction value is better defined. The values resulted by the new procedure are free from most of the uncertainties of the generalized Strutinski smoothing procedure. E.g. they do not depend on the position of the interval where the linearity of the smoothed level density is required. The most important advantage of the new procedure is that it can be applied for light nuclei where, as we have discussed in Sec.IV. the generalized Strutinski procedure can not be applied. The results of the new method for light nuclei are shown in Table IV for neutrons and in Table V for protons. One can see that the agreement with the semi-classical values are as good it was for heavier nuclei. We received specially good agreement for oxygen isotopes even at the neutron drip line. In Fig.7 we show the neutron plateau curves for the new double magic nucleus $^{24}$O as functions of the renormalized smoothing range parameter Γ$_{p}$, for p = 6 , 8 , ..., 14. The semi- classical result is the dotted horizontal line. The minima of each curve are denoted by filled circles on the corresponding curves. One can see that the δE$_{n}$ (Γ$_{p}$ , p ) values denoted by circles are between -0.9 and -2.3 MeV and their Γ$_{p}$ values are quite similar at Γ$_{p}$ ∼ 8 MeV . The variation of the δE$_{n}$ (Γ$_{p}$ , p ) values are σ ∼ 0 . 5 MeV and their mean value coincide with the semi-classical value. This is certainly an accident but one can see that the Δ value is small for the other O isotopes too. Observe also that the positions of the minima of the different p curves in this figure scatter much less in Γ ( ∼ 15 %) than the locations of the minima in Fig.6 where the smoothing range γ was used ( ∼ 90 %) or in Fig.5 where the smoothing range γ was used ( ∼ 70 %). Therefore, we believe that the finite range smoothing allows us to approach the drip line closer than we can approach it by using the infinite range Gaussian weight function. The new method uses a finite range smoothing function which makes it possible to localize the effect of a single particle state with energy e$_{i}$ to a finite energy range: [ e$_{i}$ − γ, e$_{i}$ + γ ]. This localization makes possible to extend the region of applicability of the method to closer to the end regions of the spectrum. This helps in calculating shell corrections for slightly bound nuclei lying closer to drip lines and also for lighter nuclei, where the shell gap is large, VII. CONCLUSION 16