  We report on a combined experimental and theoretical study of Li$^+$ ions
solvated by up to 50 He atoms. The experiments show clear enhanced abundances
associated with He$_n$Li$^+$ clusters where $n=2$, 6, 8, and 14. We find that
classical methods, e.g.\ Basin-Hopping (BH), give results that qualitatively
agree with quantum mechanical methods such as path integral Monte Carlo,
diffusion Monte Carlo and quantum free energy, regarding both energies and the
solvation structures that are formed. The theory identifies particularly stable
structures for $n=4$, 6 and 8 which line up with some of the most abundant
features in the experiments.
