Dependences of the image potential U_im calculated from the extended two-fluid model (dotted curve), repulsive potential U_r (dashed curve), and the resulting total potential U_t (solid curve) on proton position y from the center of a straight nanotube in the cases of (a) (6,4) SWNT, (b) (8,6) SWNT, (c) (11,9) SWNT, and (d) (15,10) SWNT. Also shown are the results for the total potential U_t1f calculated with U_im from the one-fluid model with zero damping (dash-dotted curve). The proton velocity is v = 3 a.u. Vertical solid bars represent the positions of nanotube walls. The values of nanotube radius R are 0.346, 0.483, 0.689, and 0.865 nm for the (6,4), (8,6), (11,9), and (15,10) SWNTs, respectively. Vertical dotted bars refer to the value R − a_sc for each nanotube, where a_sc is the nanotube atom screening radius.