deletions | additions       diff --git a/Figure_ref_fig_log_stopping_power_shows__.tex b/Figure_ref_fig_log_stopping_power_shows__.tex  index 2f02c59..cc4c244 100644  --- a/Figure_ref_fig_log_stopping_power_shows__.tex  +++ b/Figure_ref_fig_log_stopping_power_shows__.tex 
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Figure \ref{fig:log_stopping_power} shows the log scale of the findings of  Figure \ref{fig:stopping_power}. At projectile velocities, $v < 0.1 ~\mathrm{a.u.}$ there is a slight  deviation from the  linearity of the $S_\text{e}$ for the channeling case. We attribute this observation to the crystalline structure of copper. $Cu$.  The error bars (channeling case) are rather  smaller than thecalculated value (of  point size); size calculated value;  for example at $v = 0.08 ~\mathrm{a.u.}$ the value of $S_\text{e}$ is $0.00995124~E_\text{h}/a_0$ but our fitting procedure produces the error limit of $\pm 1.105 \times 10^{-6} ~E_\mathrm{h}/a_0$ and therefore the error bars are practically invisible when plotted in figure Figure  \ref{fig:log_stopping_power}. Throught the studied velocity regime the limit of the error bar lies between $10^{-7}$ to $10^{-4}$ for the channeling case. At higher velocities our the present  $S_\text{e}$ (channeling case) results underestimates the experimental findings owing to lack of core electron effects which are not included in our calculations. The importance of core electrons has been discussed earlier by Earlier  Scheife {\emph et al} \cite{Schleife_2015}. \cite{Schleife_2015} have discussed the importance of core electrons.  However, at higher velocities  the off-channeling case gives a much reasonable results as  compared with experiment at higher velocities.% to experiment.%  %