Absolute dissociation cross sections are reported for Hn+ clusters of varied mass (n = 3, 5, ..., 35) following collisions with He atoms at 60 keV / amu. Initial results have been published in a previous brief report for a smaller range of cluster sizes [Ouaskit et al., Phys. Rev. A 49, 1484 (1994)]. The present extended study includes further experimental results, reducing the statistical errors associated with the absolute cross sections. The previously suggested quasi-linear dependence of the Hn+ dissociation cross sections upon n is developed with reference to expected series of geometrical shells of H2 molecules surrounding an H3+ core. Recent calculations identify n = 9 as corresponding to the first closed H2 shell [e.g. Stich et al., J. Chem. Phys. 107, 9482 (1997)]. Recurrence of the distinct characteristics observed in the dissociation cross section dependence upon cluster size around n = 9 provides the basis for the presently proposed subsequent closed shells at n = 15, 21, 27, and 33, in agreement with the calculations of Nagashima et al. [J. Phys. Chem. 96, 4294 (1992)].