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is the approximate p -independence of the δE ( γ$_{p}$, p ) values, which is satisfied if the variation of the δE ( γ$_{p}$, p ) values are small. 

It was shown in Ref.[15] that sometimes even the local plateau condition might not be fulfilled and the smoothing procedure of the standard Strutinski method might not able to furnish us with well defined smoothed energy. A typical nucleus for which the local plateau condition fails if the continuum part of the spectrum is taken into account is the $^{146}$Gd , as one can see in Fig. 1. Although one can find minima for each plateau curves, the shell correction values at these minima vary too much (even an approximate p -independence is not hold). Therefore it is not surprising that the δE ( γ$_{p}$, p ) values deviate considerably from the semi-classical value. 

In order to cure this difficulty in the work [15] a modified plateau condition was suggested. In the modified plateau condition the plateau condition in Eq.(19) is replaced by the require- ment that in a certain energy region the smoothed level density should be fitted well by a straight line. 

The shell correction δE ( γ$_{p}$, p ) for a given p should be calculated with those γ$_{p}$ value for which the smoothed level density can be fitted best by a linear function: y ( E ) = aE + b in a certain energy range: [ e$_{l}$, e$_{u}$ ]. So we should find the minimum of the function in the variable γ for each p value n u 

Here q$_{i}$ for i = 1 , .., n$_{u}$ is a mesh of the energy interval [ e$_{l}$, e$_{u}$ ] used, and γ$_{p}$ is the value where the function χ 2 has its minimum at a given p -value. To get rid of the shell fluctuations the length of the interval has to be larger than the estimated shell gap 

<img src='content_image/356547.jpg'>

<img src='content_image/356548.jpg'>

Having selected the proper γ$_{p}$ value for a set of p values between p$_{min}$ = 6 and p$_{max}$ = 14, the mean value and the variation of the corresponding δE ( γ$_{p}$, p ) values have to be calculated as follow: 

<img src='content_image/356549.jpg'>

<img src='content_image/356550.jpg'>

