Absolute cross sections for the dissociation of hydrogen cluster ions in high-energy collisions with helium atoms

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Absolute dissociation cross sections are reported for $\mathrm{H}_{n}{}^{+}$ clusters of varied mass $(n=3,5,\dots{},35)$ following collisions with He atoms at $60\phantom{\rule{0.3em}{0ex}}\mathrm{keV}∕\mathrm{amu}$. Initial results have been published previously 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 quasilinear dependence of the $\mathrm{H}_{n}{}^{+}$ dissociation cross sections upon $n$ is developed with reference to expected series of geometrical shells of ${\mathrm{H}}_{2}$ molecules surrounding a $\mathrm{H}_{3}{}^{+}$ core. Recent calculations identify $n=9$ as corresponding to the first closed ${\mathrm{H}}_{2}$ shell [e.g., \ifmmode \check{S}\else \v{S}\fi{}tich 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)].