deletions | additions       diff --git a/A_snapshot_of_the_distribution__.tex b/A_snapshot_of_the_distribution__.tex  index c38579c..fbc2285 100644  --- a/A_snapshot_of_the_distribution__.tex  +++ b/A_snapshot_of_the_distribution__.tex 
...
A snapshot of the distribution of the charge density as a function of time for the simulationusing VisIt~\cite{HPV:VisIt}  is shown in Fig.~\ref{fig:snapshot_copper}. At $t = 0~\text{attoseconds}$ (see Fig.~\ref{fig:snapshot_copper}a) the $\mathrm{H^+}$ interacts with the neighboring $\mathrm{Cu}$ atoms charge density where some electron density is acquired. Elongated wake tails are characteristic of projectiles traveling at or above the Fermi velocity\cite{Tehada_1980}.  As $\mathrm{H^+}$ moves further through the $\mathrm{Cu}$ atoms it acquires substantial electron densities from the adjacent $\mathrm{Cu}$ atoms as shown in Fig.~\ref{fig:snapshot_copper}b for $t = 91.65~\text{attoseconds}$.   %As $\mathrm{H^+}$ travels through the $\mathrm{Cu}$ crystal more electron density is acquired from the neighboring atoms as seen at $t = 91.65~\text{attoseconds}$.