Since in Ref.[15] this variation was reasonably small for most of the nuclei, the mean in Eq.(23) was used to define the shell correction and the variation in Eq.(24) was considered as an uncertainty of the method. The procedure described above was called as a generalized Strutinski procedure . In order to illustrate the use of the modified plateau condition we present the smoothed level densities for the $^{146}$Gd nucleus in Fig. 2. The lower and upper ends of the energy interval in which the best linear fit of the ˜ g ( E ) is required are shown by filled triangles on the E -axis. Practically no p -dependence of the ˜ g ( E ) curves can be observed in the [ e$_{l}$, e$_{u}$ ] interval where ˜ g ( E ) is apparently behaves as a linear function of E . Some p -dependence can only observed at around E ≈ − 10 MeV being a bit above the ˜ λ value and at higher energy in the E = 0 MeV region which has no influence on the shell correction. The large bump of the smoothed level density around E = 0 MeV is the effect of the higher end of the spectrum. In the positive part of the spectrum only a few neutron resonance contribute to the level density and their effect is smoothed by the smoothing parameters which are the abscissas of the filled circles in Fig.1. These γ$_{p}$ values are between 10 − 15 MeV, therefore the end effect is spread well below the threshold. The effect of the lower end is less pronounced but can be seen at E < − 35 MeV. Here the derivative of ˜ g ( E ) with respect to E changes and at E < − 45 MeV ˜ g ( E ) goes below zero for a while. The main feature of the ˜ g ( E ) is that the linearity required in Eq.(1) holds only in a certain distance from the lower and upper ends of the spectrum. In Fig.1 the filled circles on the different p curves show the ( γ$_{p}$, δE$_{n}$ ( γ$_{p}$, p )) points where the γ$_{p}$ values are those where the function in Eq.(21) has its minimum. One can see from the circles that these shell correction values have much smaller variation ( σ ) than the shell correction values at the minima of the curves. Moreover the mean of the δE$_{n}$ ( γ$_{p}$, p ) values denoted by circles is in good agreement with the dotted line showing the semi-classical value. In the work [15] it was found that this situation is quite typical and the generalized Strutinski procedure gave similar values to the result of the semi-classical averaging based on the Wigner–Kirkwood expansion [21–27] in those cases in which the later could be applied. Moreover the generalized Strutinski procedure gave similar results to that of the standard one for all cases where the plateau condition is fulfilled. But it gave a well defined value for the smoothed energy even in cases like $^{146}$Gd where we can not really speak about plateau. It turned out only later, in the work [16] where the generalized Strutinski procedure was 9