deletions | additions       diff --git a/The_simulations_of_the_collisions__.tex b/The_simulations_of_the_collisions__.tex  index 0fbabb8..9e1dcda 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 as an a time  average quantity. \begin{equation}  S_\text{e} = \overline{\mathrm{d}E(x)/\mathrm{d}x}