The interaction between an atom and a neutral helicoidal cavity is calculated for varying parameters—helix pitch and radius, matter density on the helix, number of helices schematizing the cavity,... . General conditions for the applicability of the continuum approximation, for the occurrence of geometrical confinement leading to atom supermobility in the helicoidal system, and for the influence of confinement on the adsorption energy are given when the interactions are described by a Lennard-Jones potential. It is shown that the atom remains confined along the symmetry axis of the cavity when the helix/atom radius ratio is smaller than or approximately equal to 1.2. In that case, the potential is analytic, linear with respect to the helix number, and flat for sufficiently large matter densities on the helices.