deletions | additions       diff --git a/figures/energy_dis7/caption.tex b/figures/energy_dis7/caption.tex  index d99bf18..7a89ec2 100644  --- a/figures/energy_dis7/caption.tex  +++ b/figures/energy_dis7/caption.tex 
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\label{fig:fit_graph} (color online). The increase of $E$ as a function of proton position atvelocities  $v = 0.06 ~\mathrm{a.u.}$ (green dashed line) along $\langle 100\rangle$ channeling trajectory and the adiabatic energy (magenta dot-dashed line). The adiabatic curve would correspond to a proton moving infinitely slowly $v=0$), slowly,  where there is no transfer of energy, just oscillations of the total energy with a an overall  zero slope. %The initial (ground state energy) is subtracted.   The oscillations in the curves reflect the periodicity of the $\mathrm{Cu}$ lattice.   The red solid line shows the energy difference (subtraction of adiabatic energy from the $v = 0.06 ~\mathrm{a.u.}$ curves).  
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%%should be added a constant value of $-16856.62389 ~\mathrm{a.u.}$.%  A linear fit , $y = a + bx$ (blue line) yields a slope of $6.989 \times 10^{-3}~E_\text{h}/a_0$ with an error of $\pm 6.936 \times 10^{-5}~E_\text{h}/a_0$.   We then proceed for a linear fit in addition to an oscillatory function $y = a + bx + A\cos(k x + \phi)$ (black dotted line) to capture any remnant oscillation.   This oscillatory fit generates a slope of $7.435 \times 10^{-3}~E_\text{h}/a_0$ with an error of $\pm 8.52 \times 10^{-7}~E_\text{h}/a_0$, that is a minimal fitting error in is  obtained in the \emph{channeling} trajectory.