deletions | additions       diff --git a/For_the_off_channeling_trajectory__.tex b/For_the_off_channeling_trajectory__.tex  index 8edacf7..b119700 100644  --- a/For_the_off_channeling_trajectory__.tex  +++ b/For_the_off_channeling_trajectory__.tex 
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For the off-channeling trajectory, the procedure for computing the electronic stopping is depicted in Figure \ref{fig:fit_off_channel}.   The sharp peak at distance ($\sim 16~a_0$) peaks  shows that when  the proton is in the vicinity of a host $\mathrm{Cu}$ atom, while the smaller peaks and flatter regions  indicates that the proton is not very close to any host atom. To obtain the electronic stopping we compute the slopes of the curves by a linear fit of the form $y = a + bx$ (black lines) using our data from $x = 5~a_0$ (to eliminate the transient region) to a given maximum position of $x$.   The slope ($b$) gives the electronic stopping for this off-channeling case.  %We have displayed the procedure used in obtaining the electronic stopping for the off-channeling trajectory case in Figure \ref{fig:fit_off_channel}.