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\label{fig:fit_graph} (color online). The increase of $E$ as a function of proton position at velocities $v = 0.06 ~\mathrm{a.u.}$ (green dashed line) along [100] $\langle 100\rangle$  channeling trajectory and the adiabatic energy (magenta dot-dashed line). The adiabatic curve  would correspond to a proton moving infinitely slowly $v=0$), where there is no transfer of energy, just oscillations of the total energy with a 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).