deletions | additions       diff --git a/The_simulations_of_the_collisions__.tex b/The_simulations_of_the_collisions__.tex  index 71cfe9c..63f21df 100644  --- a/The_simulations_of_the_collisions__.tex  +++ b/The_simulations_of_the_collisions__.tex 
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The total electronic energy ($E$) of the system changes as a function of the projectile position ($x$) since the projectile   (forced to maintain its velocity) deposits energy into the electronic system as it moves through the host atoms.   The increase of $E$ as a function of projectile displacement $x$ enables us to extract the electronic stopping power. power as an average quantity.  \begin{equation}  S_\text{e}(x) S_\text{e}  = \frac{\mathrm{d}E(x)}{\mathrm{d}x} \overbar{\mathrm{d}E(x)/\mathrm{d}x}  \label{eq:stopping}   \end{equation}  $S_\text{e}(x)$ $S_\text{e}$  has the dimension of a force (e.g. $E_\text{h}/a_0$) and it is the drag force acting on the projectile.