used for deformed nuclei, that the function in Eq.(21) might have more than one minimum in γ . It was concluded in that the minimum at the smaller γ value should be selected. An uncertainty of the generalized Strutinski smoothing procedure is that the results are slightly depend on the position of the [ e$_{l}$, e$_{u}$ ] energy interval used. For medium and heavy nuclei the uncertainty of the generalized Strutinski procedure was always below 250 keV. To get this small variation, the energy interval [ e$_{l}$, e$_{u}$ ] was adjusted to the smoothed Fermi-level, and the upper end of the energy interval was e$_{u}$ = ˜ λ − ℏ Ω$_{0}$. If the interval was shifted up to have e$_{u}$ = ˜ λ and the length was kept the same as in Eq.(22) a variation of the shell correction by around 400 keV was observed. This uncertainty was still reasonably small and it was comparable to the typical deviation from the semi-classical result. The dependence on the position of the interval become stronger for light nuclei. If the mass number A is reduced, the distance of the shells estimated in Eq.(18) increases and the length of the interval in Eq.(22) also increases. We should use larger and larger γ values for smoothing the shell fluctuations. On the other hand the region in which ˜ g ( E ) is linear becomes shorter and shorter because the effect of the lower end shifts higher and that of the higher end shifts lower. Therefore for small A there is not enough space where the required linear region could develop. The linearity of ˜ g ( E ) function is spoiled by the end effects. This explains why the generalized Strutinski procedure breaks down for light nuclei. Therefore, in this work our goal is to find a new smoothing procedure which is less sensitive to the end effects, but it still keeps the advantages of the generalized Strutinski procedure i.e. the shell correction is practically independent of the p values ( σ is small). An additional requirement is that ˜ E resulted by the new procedure should not be too different from the result of the semi-classical procedure (Wigner–Kirkwood method) if the later approach can be applied. A disadvantage of the smoothing procedures used so far is that the Gaussian weight function w ( x ) used has an infinite range, therefore, the effect of an energy e$_{i}$ is smeared to the whole energy axis from −∞ to ∞ . Therefore, the effect of the lower and upper ends of the spectrum influences the whole region of the smoothed level density and also the shell correction δE . In this work we try to reduce the end effects in these quantities by using V. NEW SMOOTHING PROCEDURE 10