We present results of classical trajectory (CT) calculations on the sticking of protons to the basal plane (0001) face of crystalline ice, for normal incidence at a surface temperature (Ts) of 80 K. The calculations were performed for moderately low incidence energies (Ei) ranging from 0.05 to 4.0 eV. Surprisingly, significant reflection is predicted at low values of Ei (< or = 0.2 eV) due to repulsive electrostatic interactions between the incident proton and the surface water molecules with one of their H-atoms pointing upward toward the gas phase. The sticking probability increases with Ei and converges to unity for Ei > or = 0.8 eV. In the case of sticking, the proton is trapped in the ice forming a Zundel complex (H5O2+), with an average binding energy of 9.9 eV with a standard deviation of 0.5 eV, independent of the value of Ei. In nearly all sticking trajectories, the proton is implanted into the ice surface, with a penetration depth that increases with Ei. The strong interaction with the neighboring water molecules leads to a local rupture of the hydrogen bonding network, resulting in collision induced desorption of water (puffing), a process that occurs with significant probability even at the lowest Ei considered. The probability of water desorption increases with Ei. In nearly all trajectories in which water desorption occurs, a single three-coordinated water molecule is desorbed from the topmost monolayer.