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continuum beside the discrete single particle levels. The treatment of the single particle level density due to the continuum was a long standing problem [12, 13] but an elegant solution was finally reached [14, 15]. 

A large part of the uncertainty due to the proper choice of the technical parameters of the smoothing method has been removed by introduction of the generalized Strutinski procedure[15, 16], which made it possible to calculate reliable shell correction values for medium and heavy nuclei, where the smoothed level density has a long region with linear energy dependence. As it will be discussed in Sec. IV., for lighter nuclei the length of the linear region is reduced due to the reduction of the number of the occupied shells and the increase of the shell gap. For light nuclei the lower and upper ends of the spectrum distort linearity, therefore the method is not appropriate for light nuclei. 

The main goal of this work is to develop a new method which is free from this limitation and is applicable for the whole nuclear chart, even in the vicinity of the two drip lines. We are solving this problem by introducing a finite range smoothing instead of the infinite range Gaussian smoothing used in the Strutinski method. 

The paper is organized as follows. In Sec. II. we recapitulate the formalism of the calculation of the shell correction. In Sec. III. we describe the standard Strutinski method with the plateau condition. In Sec. IV. we do the same with the generalized Strutinski procedure, what we want to replace in this work. In Sec. V. we describe the new method with finite range smoothing in details. In Sec. VI we apply the new method for several nuclei and calculate shell corrections for neutrons and protons. Finally in Sec. VII. we end with the main conclusions of the paper. 

## II. CALCULATION OF THE BINDING ENERGY BY USING THE SHELL COR- RECTION. 

The binding energy of an atomic nucleus composed of A = N + Z nucleons ( N neutrons and Z protons) B ( N,Z ) can be calculated in the microscopic-macroscopic model (MM) as 

<img src='content_image/364883.jpg'>

where E$_{macr}$ ( N,Z ) is the binding energy calculated in the macroscopic model (e.g. liquid drop or droplet model) and δE ( N,Z ) is the shell correction. While E$_{macr}$ ( N,Z ) is a smooth 

